Proceedings of the Royal Irish Academy (2024)

From The Art and Popular Culture Encyclopedia

{{Template}}Proceedings of the Royal Irish Academy (1841)

7576PROCEEDINGSOFBIBL160" LecQUE- CHANTILLYTHE ROYAL IRISH ACADEMY.S.ALOYSDOM KFRS

PROCEEDINGSOF THEROYAL IRISH ACADEMY.OFVOL. II.ROYALHEWEWILLSEALIRISHUNDEAVOUREMYACADENDUBLIN:PRINTED BY M. H. GILL,PRINTER TO THE ACADEMY.MDCCCXLIV.

CONTENTS.VOL. II.1840-1844.AN ACCOUNT of a large reflecting Telescope, lately erected by LordOxmantown. By the Rev. T. R. Robinson, D.D.On the production of audible Sounds. By Dr. Kane.On the Course of the Diurnal Fluctuations of the Barometer. ByJames P. Espy, A.M. of Philadelphia. Communicated by Dr. Apjohn..22 13192121On the Sturgeon of the Dublin Markets. By Robert Ball, Esq.On an unpublished Irish Coin of Edward IV. By A. Smith, M.D.On the Improvement of the Voltaic Pile. By George J. Knox, Esq. 25On the Composition of Pyrope. By Dr. Apjohn.•On a Seal, supposed to have belonged to a Monastery at Ballindown,County Sligo. By J. Huband Smith, Esq.·On • the Leyden Jar. By Edward Clibborn, Esq.On the Deposits of Gravel in the Neighbourhood of Dublin. By Rev. Thomas H. Porter, D.D.Account of the Discovery of a Human Skeleton, &c. , near Larne.By J. Huband Smith, Esq.·On the Constant of Refraction, determined by Observations withthe Mural Circle of the Armagh Observatory. By the Rev. T. R. Robinson, D.D. •73032343741• 46, 5746 On the Heat developed during the Combination of Acids and Bases.By Dr. Andrews. .On two large Medallion Busts, with Greek Inscriptions, in the Library of Trinity College. By Rev. Dr. Todd, D.D. and V.P.On certain general Properties of Cones of the second Degree.By Rev. Charles Graves.4954On some ancient Weapons found at Kilmainham. By J. Huband Smith.On the Leafing of Plants. By His Grace the Archbishop of Dublin.6836263biv CONTENTS.On an ancient stone carved in Bas-relief. By Charles T. Webber,Esq.Collection of Notes in the early History of Science in Ireland. By James Orchard Halliwell, Esq.Report of Council for last year, ( 1840—1841 ) .PAGE.65•BELL8 6673Extract from a Patent Roll of James II. By Sir William Betham. 77On the Origin of the Emblem of the Shamrock. By Mr. Blacker. 77On the Human Eye. By J. M. Ferrall, Esq. .Audit of Treasurer's Account for Year ending March 16th,1841 . ·. 7881 .•On the Classification of ancient Military Weapons found in Ireland.By Samuel Ferguson, Esq.Abstract of Treasurer's Account to 31st March, 1840.On the Norse Geography of Ancient Ireland. By George Downes,Esq.85• 86On the Authorship of the Lines on the Burial of Sir John Moore.By Rev. Dr. Luby, D.D.88887On the mutual Action of permanent Magnets in an Observatory.(See Transactions, Vol. XIX. p. 159) . Bythe Rev. H. Lloyd, D.Ď.On some new Properties of Surfaces of the Second Order. By John F. Jellett, Esq.8992225692An Account of some ancient Irish Inscriptions found in the Islandof Arran. By G. Petrie, Esq.Some Remarks on the Theory of Types. By Dr. Kane.ཙཚཚ94· 94On the physical Properties, and Electro- Chemical, and other relations of the Alloys of Copper and Tin with Tin and Zinc. By Robert Mallet, Esq.On the Dynamical Theory of Crystalline Reflexion and Refraction.By Professor Mac Cullagh.3859596Particulars concerning an ancient Ink Stand. By J. H. Monck Mason, LL.D. 103On the Force of aqueous Vapour within the Range of Atmospheric Temperature. By J. Apjohn, M.D. 104On the Coins of Henry VII. By Dr. A. Smith. . 115A Note on the Mode of observing the vibrating Magnet so as to eliminate the Effect of the Vibration . By the Rev. H. Lloyd, V.P.On the Storm of May 26th and 27th. By the Rev. George S. Smith.On the Utility of the Irish Language in Classical Studies. By Francis Crawford, Esq. .•On a new Method of raising Ships of War out of the Water, forthe Purpose of Repair. By Robert Mallet, Esq. •ib.118• 120• 121· • 124127On the Egyptian Stele or Tablet. By the Rev. Dr. Hincks.On the Application of Analysis to Spherical Geometry. By the Rev. Charles Graves.CONTENTS. VAnew Demonstration of Fourier's Theorem. By Sir W. R. Hamil- ton , LL.D..Part I. of a Memoir on the Dyalitic Method of Elimination . ByJ. J. Sylvester, Esq.On a mechanical Theory which has been proposed for the Explana- tion of the Phenomena of circular Polarization in Quartz, orRock Crystal; with Remarks on the Corresponding Theory of Rectilinear Polarization. By Professor Mac Cullagh.On the recent Discovery of a Cairn in the County of Antrim. By J. Huband Smith, Esq. .PAGE.129130139163On the Composition of Forces. By Sir W. R. Hamilton, LL.D. 166On the compound Nature of Nitrogen. By George J. Knox, Esq. 171A simple geometrical Rule, which gives the Solution of the Problemof total Reflexion for ordinary Media, and for uniaxal Crystals.By Professor Mac Cullagh.•Address of the Academy to Earl De Grey, Lord Lieutenant of Ireland. •173176Answer of Earl De Grey to Address. 177Letter from the Right. Hon. Sir John Newport, Bart. , presenting to the Academy a MS. containing an Account of the Loans of Money to King Charles I. . 179On the Rectification of Lemniscates and other Curves. ByWilliam Roberts, Esq. · 180On Roman Coins found in Ireland. By Professor Mac Cullagh.On Roman Coins found in Ireland. By the Rev. W. H. Drum- mond, D.D.. .An Account of some Characters found on Stones on the Top ofKnockmany Hill, County Tyrone. By the Rev. G. Sidney Smith, D.D.. 184185190On the Loligo. By Robert Ball, Esq. .192On a Class of spherical Curves. By William Roberts, Esq.Letter from Andrew Durham, Esq. , on the Examination of Drum- boe Tower.• 194195On Metallic Alloy, in an unusual State of Aggregation. By Robert Mallett, Esq.· 197On the Motion of a Point upon the Surface of a Sphere. By the Rev. Charles Graves. > 207·On a New Magnetical Instrument for the Measurement of the In- clination and its Changes. By the Rev. H. Lloyd, D.D.Supplement to the same.· 210226OnMr. Stewart's Attempt to explain certain Processes of the Human Understanding. By the Rev. James Wills. 217On the peculiar System of Generation and Habits observed in cer- tain Acephalocysts, parasitical Animals inhabiting the human Body, and belonging to the Class of Hydatid Entozoa. ByEvory Kennedy, M.D. 221vi CONTENTS.PAGE.Onthe colouring Matter of Persian Berries. By Robert Kane, M.D. 222Supplementary Remarks to the Account of Researches respecting Fluctuating Functions. By Sir William R. Hamilton, President. 232Report of Council for the Year ending March 16th, 1842.Treasurer's Report, March 16th, 1842.239• • 243• 244 On the ancient Church of Kilmelcheder. By the Rev. A. B. Rowan.On an ancient Boat found near Drogheda. By W. J. Hughes, Esq. 246Researches in certain parts of Asia Minor. By the Rev. James Kennedy Baillie, D.D. •An Account of the Casting of the great Speculum by the Earl ofRosse. By the Rev. Thomas Romney Robinson, D.D.A Paper on the true Date of the Rosetta Stone. By the Rev. Ed- ward Hincks, D.D. ·On the day of the Vernal Equinox, at the Time of the Council ofNice. By Sir William R. Hamilton, President.Application ofthe Daguerreotype Process to Astronomicalpurposes.Bythe Rev. Thomas Knox.Letter from Thomas Hunter, M.D.· 248, 253248• 249249251• 257259· 262Onthe Phenomena of thin Plates in polarized Light. By the Rev. Humphrey Lloyd, D.D. 266269272Description of cinerary Urns discovered in the Hill of Rath, near Drogheda. By J. Huband Smith, .On the Coefficient of labouring Force in over-shot Water Wheels.By Robert Mallet, Esq.Observations on the above. By Professor Mac Cullagh.•An Account of a Visit he had paid to the Tomb ofthe Volumnii at Perugia. By H. J. Monck Mason, LL.D.On the Brain of the Chimpanzee. By James Macartney, M.D. 272Collection of Antiquities of the late Dean of St. Patrick's, pre- sented to the Academy in the Name of the Subscribers.On the Solution of Algebraic Equations of the fifth Degree. By SirW. R. Hamilton, President.• • 274275, 355On the Compensations of polarized Light, with a description of Polarimeter for measuring Degrees of Polarization. By Sir David Brewster.•On the Tanin of Catechu, and the chemical Substances derived fromit. By Robert Kane, M.D.Statement ofthe Proceedings of the Committee for the Purchase of the late Dean of St. Patrick's Collection of Antiquities.Rev. J. H. Todd, D.D.279282Bythe 283On the Heat developed during the Formation of metallic Compoundsof Chlorine, Bromine, and Iodine. By Dr. Andrews.On the Chronology of the Eighteenth Dynasty of Manetho. By the Rev. Edward Hincks, D.D.• 292293CONTENTS. viiOn Improvements effected in the Art of Glass-making for Optical purposes. By Robert Mallet, Esq.PAGE.293294 On Mr. Faraday's experiments onthe Manufacture of Glass for Op- tical purposes. By the Rev. T. R. Robinson, D.D.On the Determination of the Intensity of the Earth's magneticForce in absolute Measure. By the Rev. Humphrey Lloyd, D.D. 295, 346A Letter from Captain Boileau, Superintendent of the MagneticObservatory at Simila, in India.On the Catalogue of Egyptian Kings, which is usually known by the name of the Laterculum of Eratosthenes. By Professor Mac Cul- lagh..• 300· 305On an ancient Gravestone at Clonmacnoise. By George Petrie, Esq. 311On a Collection of Antiquities, presented by the Shannon Commissioners to the Museum of the Academy. ByRichard Griffith, Esq. 312On the muscular System of certain fresh Water ascidian Zoophytes.By G. J. Allman, M. B. · · 319On the Meteors observed at Armagh, 10th August, 1842. By theRev. T. Romney Robinson, D.D. 332On the Action of certain Salts as Manures. By the Rev. Thomas Knox. 333Account of an ancient Irish Manuscript, in the Bodleian Library,Oxford. Bythe Rev. James H. Todd, D.D. 336On Tiles found in the ancient Churches of Ireland. By T. Oldham,Esq. •353Report of Council for the Year ending March 16th, 1843.Abstract ofthe Treasurer's Account and Report for March 16th,1843.• · · 356365On an ancient Irish Deed · . By the Rev. James H. Todd, D.D. 368The Cathach, deposited in the Museum. By Sir Richard O'Don- nell. •370, 403A Letter from the Rev. Dr. Robinson, accompanying a box containing an original Pyrometer, presented to the Academy by MissMaria Edgeworth, H. M. R. Ì. A.On the Antiquities of certain Languages. By Sir W. Betham.On the Laws of metallic Reflexion, and on the Mode of making Ex- periments upon elliptic Polarization. By Professor Mac Cullagh.On anew Genus of Hydraform Zoophytes. By James Allman, M.B.Onthe Deprivation of the Faculty of Speech. By Jonathan Osborne,M.D.• 370· 372375395· 395On Rev. Dr. Robinson's Table of mean Refractions. By Sir W. R. Hamilton, President. • 400On Heat developed during the Formation of certain chemical Compounds. By Dr. Andrews. 404On a new Species of Linaria. By James Allman, M.B. 404viii CONTENTS.PAGE.On certain Greek Inscriptions copied on the Sites of ancient Teos and Aphrodisias in Asia Minor. By Dr. Kennedy Baillie. 406, 407On an Ogham Inscription. Bythe Rev. James Henthorn Todd,D.D.. · 410On a Dislocation in the Calp, near Killester. By G. W. Hemans, Esq. 411Address of the President, in presenting Dr. Kane with the Cun- ningham Medal.411On the Calculus of Probabilities. By Sir W. R. Hamilton, LL.D.President. 420On the Anatomy of Anthocephalus, a Genus of Entozoal Worms.By G. James Allman, M.B. 423On a new Species of Imaginary Quantities, connected with theTheory of Quaternions. By Sir W. R. Hamilton, President.Remarks on the Catalogue of Irish MSS. in the Academy, made by Eugene Curry, Esq. By Rev. Dr. Todd.424434On the chemical Composition of the Plants of Flax and Hemp. By Robert Kane, M.D. 437On the Surfaces of the Second Order. By Professor Mac Cullagh. 446On the Comparison of Arcs of Curves, particularly of plane andspherical Conics. By Professor Mac Cullagh.On the Means used by the Ancients for attaching Handles to theStone and Metal Implements called Celts. By Robert Ball, Esq.On some Stones with Ogham Characters. By Thomas Oldham,Esq. .

On Cyanogen, as a Food for Plants. By Rev. Thomas Knox.On the Rotation of a Solid Body. By Professor Mac Cullagh.On the chemical Composition of the different Kinds of Fuel in Ireland. By Robert Kane, M.D.507511513• · 517• 520• 526On the Irish Names of Animals. By Robert Ball, Esq.Further Remarks on the Rotation of a solid Body. By ProfessorMacCullagh..541542On the Existence of the pointed Arch in the early Buildings ofIreland . By G. Wilkinson, Esq. · 545On Fredericella Sultana. By G. James Allman, M. B. 545On the Defacement of divine and royal Names on Egyptian Monu- ments. By the Rev. Edward Hincks. 546A Notice respecting the Hyscos, or Shepherd Kings. By E. Clibborn, Esq.· 548Report of Council, for the Year ending 16th March, 1844.Report of Treasurer for the Year ending 1st March, 1844.On the Purification and Ventilation of Vessels. By the Rev. Thomas Knox.· • . 549559560On the hygrometric Correction in barometric Formula for theMeasurements of Heights. By James Apjohn, M.D. 561CONTENTS. ixOn an Ancient Stone Image presented to the Academy by CharlesHalpin, M.D. By E. Clibborn, Esq. .On the Algebraic Geometry of Curves traced upon given Surfaces.By the Rev. Charles Graves. ·PAGE.565576Report of Council in favour of certain arrangements for Museumand new Board Room in Academy House.. 580On the Pharos of Corunna. By W. R. Wilde, Esq.583List of Antiquities found in the River Shannon, presented to the Academy. • 594On approximating to the Calculation of Eclipses. By Sir W. R. Hamilton, President. 598• 598• 602607608On the Constitution of Jade; and also of two Ores of Manganese,from the South of Cork. By James Apjohn, M.D. .On the Genera of Fern Trichomanes and Hymenophylum. By William Andrews, Esq.A Notice of Motion for certain Returns. By Sir W. Betham.Withdrawal of Motion. By Sir W. Betham.On the Theodolite Magnometer. Bythe Rev. Humphrey Lloyd, D.D. 608A Notice of the Opening of some Tumuli, by Mr. Nugent. By W. R. Wilde, Esq. .· • 614On a Porcelain Clay, discovered at Howth. By Robert Mallet, Esq. 614 367 558OBJECTS EXHIBITED, —pp. 33, 62, 173, 346, 272, 528, 597.RESOLUTIONS, pp. 1 , 23, 64, 139 , 192, 207, 242, 271 , 283, 291 , 348, 370,372, 404, 420, 437, 548, 580, 583, 607.ELECTION OF COUNCIL, -pp. 82, 176, 242, 249, 283, 366, 541 , 558.ELECTION OF MEMBERS, pp. 2, 37, 73, 85, 92, 139, 191 , 192 , 217, 239,244, 249, 259, 295, 333, 368, 375, 395.APPOINTMENT OF VICE- PRESIDENTS, pp. 2, 82, 243, 367, 558.DONATIONS, pp. 12, 23, 61 , 83, 85, 94, 113, 121 , 130, 138 , 168, 177,179, 204 , 221, 238 , 252, 256, 257, 272, 274, 276, 282, 283, 291 , 316,333, 345, 355, 372, 401 , 406, 420, 422, 434, 509, 511 , 576, 581 , 594,605,616.APPENDIX.List of Subscribers to the Fund for the Purchase of the DawsonCollection of Irish Antiquities (see page 274).Account of the Royal Irish Academy from 1st April, 1841 , to 31st March, 1842.No. I.• No. II.Account of the Royal Irish Academy from 1st April, 1842, to 31st March, 1843. No. III.Account of the Royal Irish Academy from 1st April, 1843, to 31st March, 1844. No. IV.Meteorological Journal, commencing 1st January, 1843, ending31st December, 1844. By George Yeates, Esq. No. V.INDEXOF CONTRIBUTORS' NAMES TO PROCEEDINGS,VOLS. I. AND II.Allman, vol. II. 319, 395, 404, 423 , 545. -Andrews, T., I. 157, 465; II.46, 292, 404, 602. —Apjohn, I. 44, 51 , 162, 206, 259, 287, 407, 433, 469;II. 30, 104, 300, 561 , 598.Bache, I. 71.- Bald, I. 245, 263. -Ball, J. , I. 451. -Ball, R. , I. 17, 253,362; II. 21 , 192, 511 , 541.-Baillie, II. 248, 253, 406, 407. - Bergin,I. 258. Betham, I. 8, 20, 34, 63 , 127, 151 , 194 , 196 , 200, 211; II.77, 372.-Bigger, I. 81.-Blacker, II. 77.- Booth, I. 53.-Bruce, I. 241.-Brewster, II. 279.Clarke, I. 86, 166, 373. - Clibborn, II. 34, 548, 565. -Crawford, II. 120.Davy, I. 88. - Dawson, Very Rev. Dean, I. 143. -Dickinson, I. 358.- Donop, I. 47. -Downes, I. 202, 234, 260; II. 87. -Drummond, II.185. -Dublin, Archbishop of, I. 414; II. 63. —Durham, II, 195.Espy, II. 19.Ferguson, I. 130, 133 , 180; II. 85.-Ferrall, II. 78.Graves, II. 54 , 127 , 207, 394, 576. - Gregory, I. 33, 49. - Grimshaw, I. 405.-Griffith , II. 312.Halliwell, I. 366, 415 , 417; II. 66. - Hamilton, I. 76, 107, 212, 245, 249,267, 276, 341 , 350, 475; II. 129, 166, 232, 249, 275, 355, 400, 411 ,420, 424, 598.-Hemans, II. 411. -Hincks, I. 160, 169; II. 124, 249,293, 546.-Hughes, II. 246.Jellett, II. 92.Kane, I. 1 , 12, 42 , 58, 83, 89, 154, 171 , 182, 193 , 223, 254, 330; II.-13, 94, 222, 282, 437 , 526. -Kennedy, II. 221. -Knox, Rev. G. J. , I. 270,448, 299, 335, 473; II. 25, 171. -Knox, Rev. T. , I. 90 , 146; II. 251 ,333, 517, 560. —Knox, G. J. and Rev. T. , I. 54, 369, 371 , 393, 455.Lentaigne, I. 309. —Lloyd, I. 10, 25, 38, 136 , 138 , 145 , 148, 163, 254,264, 272, 379, 459; II. 92, 115, 210, 226 , 266, 295, 346, 608. —Luby,II. 89.Macartney, II. 272.-MacCullagh, I. 2 , 27, 66, 158, 229, 326, 374, 385;II. 96, 139, 173 , 184, 269, 305, 375, 446, 507, 520, 542. —Mallet , I. 56 ,178, 300, 329; II. 95, 121 , 197 , 262, 293 , 614.- Marsh, I. 317. - Mason,II. 103, 272. -Moore, I. 73.Newenham, I. 247.Oldham, IL. 353, 513. -Osborne, I. 427; II. 395. -Otway, I. 210. - O'Brien,I. 322.Paterson, I. 237, 357. -Petrie, I. 37, 68 , 71 , 75, 140, 174, 274, 382, 477;II. 94, 311.— Portlock, I. 30, 52. -Porter, II. 37.Robinson, I. 238, 338, 454; II. 2, 46, 57, 248, 294, 332. -Roberts, II. 180,194.-Rowan, II. 244.Singer, I. 121. -Smith, A. , I. 367; II. 21 , 115.-Smith, Rev. G. S., II. 118,190.-Smith, J. H., I. 380, 390; IL. 32, 41 , 62 , 163, 259, 597. - Sylvester,II. 130.Thompson and Paterson, II. 147.-Thompson, I. 177.- Todd, I. 22, 40, 135,430, 449, 458; II. 49 , 283, 336, 368, 410, 434.Walsh, I. 296. - Wall, I. 97. - Webber, II. 65. -West, I. 144.- Wilde, I. 293, 312, 420; II. 583, 614. -Wills, II. 217.Yeates, II. Appendix V.LIST OF MEMBERS AND HONORARY MEMBERS OF THE ROYALIRISH ACADEMY FOR MARCH 16TH, 1843.PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1840. No. 25.November 9.SIR WM. R. HAMILTON, LL.D., President, in the Chair.The President read a letter from the Secretary of Statefor the Home Department, informing him that her Majestyhad been pleased to receive very graciously the address ofthe President, Council, and Members of the Royal IrishAcademy, congratulating her Majesty on the recent providential deliverance of herself and her illustrious Consort.The decease of the Very Rev. the Dean of St. Patrick's,V.P., having been announced to the Academy, it was resolvedThat we have heard with deep regret of the death ofour valued Vice- President, the Dean of St. Patrick's; andthat while we sympathize with all classes of our fellowcitizens, in lamenting the removal of one so universally beloved and esteemed, we would desire to record our sense ofthe peculiar loss sustained by the Academy, in being deprived of the assistance of one who could estimate the valueof our Institution, and give to it his most cordial cooperation; one who found leisure from the multifarious duties ofVOL. II. B2his station, to cultivate successfully the researches connectedwith the antiquities of Ireland, and had earned for himself ahigh place among those who labour to illustrate her ancientrecords, or to save from destruction the perishing relics ofher former civilization.Samuel Ferguson, Esq. , was elected to the vacant placein the Council; and the Rev. J. H. Todd, D.D., was appointed by the President, under his hand and seal, to sucIceed the Dean of St. Patrick's in the office of Vice- President.The Rev. T. R. Robinson, D.D. , M.R.I.A. , gave the Academy an account of a large reflecting telescope, lately constructed by Lord Oxmantown, and of the processes employed in forming its specula.After explaining the relative importance of magnifyingand illuminating power, Dr. R. proceeded to give a briefsketch of the history of the reflecting telescope, whichseemed to have been forgotten for many years after its invention, till it was revived by Hadley. The labours ofShort soon gave it celebrity; yet even this artist limitedhimself in almost every instance to sizes which were notmore powerful than the achromatics of his day, and hislarge instruments appear to have been failures. * It wasnot till a full century after the publication of Newton'spaper, that Sir William Herschel gave this telescope thegigantic development which has crowned him with imperishable fame; and by the construction of telescopes of nineteen

• A Newtonian of six feet focus, and 9-4 inches aperture, is said by Maskelyne

to have shewn the first satellite of Jupiter 13" longer than a triple achromatic of3.6 inches aperture. The telescope of twelve feet focus, and eighteen inches aperture, now at Oxford, shewed inultiple rings of Saturn.3and forty-eight inches aperture, placed regions almost beyondthe scope of measurement within the reach of human intellect. But as Short, in a spirit unworthy of his talents, tookcare that his knowledge should die with himself, and Herschel published nothing ofthe means to which his successwas owing, the construction of a large reflector is still asmuch as ever a perilous adventure, in which each individualmust grope his way. Accordingly, the London opticiansthemselves do not like to attempt a mirror even of nineinches diameter, and demand a price for it which shews theuncertainty and difficulty of its execution. In Ireland weare more fortunate, for a member of our Academy, Mr.Grubb, finds no difficulty in making them of admirablequality up to this size, or even fifteen inches; but with allhis distinguished mechanical talent, he is believed to bedoubtful of the possibility of more than doubling this lastmagnitude in perfect speculum metal.Under these circ*mstances, too much praise cannot begiven to Lord Oxmantown, who, in the midst of other pursuits, has found leisure for such researches; and by a rarecombination of optical science, chemical knowlege, and practical mechanics, has given us the power of overcoming thedifficulties which arrested our predecessors , and of carryingto an extent which even Herschel himself did not venture tocontemplate, the illuminating power of this telescope, alongwith a sharpness of definition scarcely inferior to that oftheachromatic.The chief difficulties which are to be overcome in theconstruction of reflectors, arise from the excessive brittlenessof the composition of which specula are made, and from thenecessity of giving them figures which shall be free fromaberration. The great mirror in the Newtonian form is(if the eyepiece and plane mirror be correct) the conicalparaboloid.B 24It is necessary that speculum metal should possess, inthe highest attainable degree, the qualities of whiteness,brilliancy, and resistance to tarnish. Lord Oxmantown hasfound that these conditions are best satisfied in the definitecombinations of four equivalents of copper to one of tin; orby weight, 32 and 14-7 nearly. Metals differing from thisby a slight excess of either component, are, when firstpolished, scarcely less brilliant, but are dimmed so rapidlythat the lapse of a few days produces a sensible difference .On the other hand, some large specula of the atomic compound have been lying uncovered for years, without material injury to their polish.But this compound is brittle almost beyond belief; aslight blow, or even the application of partial warmth, willshiver a large mass of it; though harder than steel, its surface is broken up with the utmost facility, and it has amost energetic tendency to crystallize. The common process ofthe founder fails with it, except for masses ofverylimited magnitude, as the cast cracks in the mould, and thesubsequent difficulties ofthe annealing are such, that it hasbeen a very general practice to use an alloy lower ( containing more copper) than the atomic standard. Even SirWilliam Herschel was obliged to yield to this necessity. Itappears from a letter of Smeaton, (Rees' Cyclopædia, Art. Telescope,) that for his 20 feet mirror of 19 inches aperture, thecomposition was 32 copper to 12.4 tin; and that for the 40feet it was even lower. Yet two out of three attempts to castthis huge speculum failed.Lord Oxmantown at first endeavoured to evade the difficulty, by constructing a speculum in pieces, soldering platesoffine metal to a back of a peculiar brass, ascertained tohave the same expansion; and has completed one of thirtysix inches aperture and twenty-seven feet focal length,which performs very well on stars below the fifth magnitude,5but above that exhibits a cross formed by the diffraction atthe joints; and in unsteady states of the air exhibits the sixteen divisions of the great mirror on the star's disk. By diminishing the number and size of the joints it is found, thatthese inconveniences can be diminished, so as to be scarcelyperceptible; and in all probability this is the process bywhich the remotest limits of telescopic vision will ultimatelybe attained. It is, however, not necessary for instrumentsof even greater dimensions than this, since Lord Oxmantownhas succeeded, by a contrivance as simple as ingenious, incasting at the first attempt a solid mirror of the same size;and there is no reason to suppose that it will be less effective on a much larger scale.But however difficult it may be to obtain the rough speculum of large dimensions, it is still more so to give it aproper figure, combined with that brilliant polish which istechnically called black, because it reflects no light out ofthe plane of incidence . In such mirrors as can be wroughtby hand, they are worked by short cross strokes on thepolisher, and at the same time have a slow rotation relativeto it. This might be expected to produce merely a sphericalfigure; but by varying the length of the stroke, by circularmovement, elliptic figure of the polisher, or removing portions of its pitch covering, a parabolic figure is obtained.For sizes above nine inches diameter, the work must be performed by machinery; but in all which Dr. R. has seen,(the most remarkable of which are those of Sir WilliamHerschel and Mr. Grubb, ) the cross stroke is given by alever moved by hand; and it is supposed that perfect resultscannot be obtained but by the feeling of the polisher'saction. Sir John Herschel is believed to have made important

• Dr. R. had the good fortune to see this at Slough, in 1830, while at work

on a twenty-feet mirror.6additions to his father's apparatus; and it is t › be hoped hewill soon redeem his promise (Mem. R. Ast. Soc. vol . vi . )of publishing his improvements.Lord Oxmantown has in many respects deviated fromthe usual process . His polisher, of the mirror's diameter,intersected by transverse and circular grooves, into portions not exceeding half an inch of surface, is coated, first,with a thin layer of the common optical pitch, and then witha much harder compound. It is worked on the mirror, andcounterpoised so that but little of its weight bears; but thewant of pressure is compensated by a long and rapid stroke.The mirror revolves slowly in a cistern of water, maintainedat a uniform temperature, to prevent the extrication of heatby friction. The polisher moves slowly in the same direction, while it is also impelled with two rectangular movements. The machine is driven by steam, and requires nosuperintendence, except to supply occasionally a little waterto the polisher, and to watch when the polish is complete.By an induction from experiments on mirrors from six tothirty-six inches aperture it was found, that if the magnitudes of the transverse movements be and 18 of the aperture, and their times be to its period of rotation as I and1.8 to 37, the figure will be parabolic: but to combine withthis the highest degree of lustre, it is found necessary toapply, towards the close, a solution of soap in liquid ammonia,which seems to exert a specific action.The certainty of the process is such, that the solidmirror ofthirty-six inches aperture, after being scratched allall over its surface with coarse putty, was, in Dr. R.'s presence, perfectly polished in about six hours, and was placedin its tube for examination, without any previous trial as toquality.Lord Oxmantown has preferred the Newtonian to theHerschelian form, and, in Dr. R.'s opinion, with good7reason . In the latter, the inclination of the great mirror tothe incident rays must deform the image, * and it is nowknown, that even with faint objects sharp definition is ofhigh importance. It should, in fact, be a segment of aparaboloid, exterior to the axis; and though a theorem ofSir William Hamilton (Trans. R. Irish Acad. , vol. xv. p.97,) might seem to indicate mechanical means of approximating to the figure, yet Dr. R. fears there would be greaterdifficulty in applying them than in enlarging the aperture ofthe Newtonian, so as to make up for the loss of light.Another serious objection is, that in the Herschelian theobserver's position at the mouth of the tube, must causecurrents of heated air, which will materially interfere withsharpness of definition.As to the loss of light by the second reflexion, Dr. R.thinks it has been much overrated , and expresses a wish thata careful set of experiments were made on reflexion by planespecula at various incidences, on prisms of total reflexion,and the achromatic prism, proposed as a substitute by SirDavid Brewster.As to the rest of the instrument, it may suffice to say,that it bears a general resemblance to that of Ramage, butthat the tube, gallery, and vertical axis of the stand arecounterpoised, so that one man can easily work it, notwithstanding its enormous bulk. The specula, when not in use,are preserved from moisture or acid vapours, by connectingtheir boxes with chambers containing quicklime, which isoccasionally renewed. This arrangement, (which also occurred to Dr. R., and has been for several years applied byAny one who has a Newtonian telescope can verify this, by inclining a littlethe great mirror, so however as not to pass the edge of the plane mirror bythepencil. In Lord O.'s instrument, an inclination of 11′ sensibly injures it; were itHerschelian, the inclination must be 3º 11 '.8him to the Armagh reflector, ) appears to be very effective inpreserving the polish.In trying the performance of the telescope, Dr. R. hadthe advantage of the assistance of one ofthe most celebratedof British astronomers, Sir James South; but they were unfortunate in respect to weather, as the air was unsteady inalmost every instance; the moonlight was also powerful onmost ofthe nights when they were using it. After midnight, too, (when large reflectors act best, ) the sky, ingeneral, became overcast. The time was from October 29thto November 8th.Both specula, the divided and the solid, seem exactlyparabolic, there being no sensible difference in the focaladjustment of the eyepiece with the whole aperture ofthirty-six inches, or one of twelve; in the former case thereis more flutter, but apparently no difference in definition,and the eyepiece comes to its place of adjustment verysharply.The solid speculum showed a Lyræ round and well defined, with powers up to 1000 inclusive, and at momentseven with 1600; but the air was not fit for so high a poweron any telescope. Rigel, two hours from the meridian, with600, was round, the field quite dark, the companion separatedby more than a diameter of the star from its light, and sobrilliant that it would certainly be visible long before sunset.Orionis, well defined , with all the powers from 200 to1000, with the latter a wide black separation between thestars; 32 Orionis and 31 Canis minoris were also well separated.It is scarcely possible to preserve the necessary sobrietyof language, in speaking of the moon's appearance with thisinstrument, which discovers a multitude ofnew objects atevery point of its surface. Among these may be named amountainous tract near Ptolemy, every ridge of which is9dotted with extremely minute craters, and two black parallelstripes in the bottom of Aristarchus.The Georgian was the only planet visible; its disc didnot show any trace of a ring. As to its satellites, it is difficult to pronounce whether the luminous points seen near itare satellites or stars, without micrometer measures. OnOctober 29, three such points were seen within a fewseconds ofthe planet, which were not visible on November5; but then two others were to be traced, one ofwhich couldnot have been overlooked in the first instance, had it beenin the same position . If these were satellites, as is not improbable, there would be no great difficulty in taking goodmeasurement both of their distance and position.There could be little doubt of the high illuminatingpower of such a telescope, yet an example or two may bedesirable. Between ¹and & Lyræ, there are two faintstars, which Sir J. Herschel ( Phil. Trans. 1824) calls " debilissima," and which seem to have been, at that time, theonly set visible in the twenty-feet reflector. These, at thealtitude of 18° were visible without an eye-glass, and alsowhen the aperture was contracted to twelve inches . Withan aperture of eighteen inches, power 600, they and twoother stars (seen in Mr. Cooper's achromatic of 13.2 aperture, and the Armagh reflector of 15) are easily seen.With the whole aperture, a fifth is visible, which Dr. R.had not before noticed. Nov. 5th, strong moonlight.In the nebula of Orion, the fifth star of the trapeziumis easily seen with either speculum, even when the apertureis contracted to eighteen inches. The divided speculumwill not shew the sixth with the whole aperture, on accountof that sort of disintegration of large stars already noticed,but does, in favourable moments, when contracted toeighteen inches . With the solid mirror and whole aperture,it stands out conspicuously under all the powers up to 1000,10and even with eighteen inches is not likely to be overlooked.Comparatively little attention was paid to nebulæ andclusters, from the moonlight, and the superior importance ofascertaining the telescope's defining power. Of the fewexamined were 13 Messier, in which the central mass ofstars was more distinctly separated, and the stars themselveslarger than had been anticipated; the great nebula of Orionand that of Andromeda shewed no appearance of resolution,but the small nebula near the latter is clearly resolvable.This is also the case with the ring nebula of Lyra; indeed,Dr. R. thought it was resolved at its minor axis; the fainternebulous matter which fills it is irregularly distributed,having several stripes or wisps in it, and there are four starsnear it, besides the one figured by Sir John Herschel, in hiscatalogue of nebulæ. It is also worthy of notice, that thisnebula, instead of that regular outline which he has theregiven it, is fringed with appendages, branching out into thesurrounding space, like those of 13 Messier, and in particular, having prolongations brighter than the others in thedirection of the major axis, longer than the ring's breadth.A still greater difference is found in 1 Messier, described bySir John Herschel, as " a barely resolvable cluster," anddrawn, fig. 81 , with a fair elliptic boundary. This telescope,however, shews the stars, as in his figure 89, and some moreplainly, while the general outline, besides being irregularand fringed with appendages, has a deep bifurcation to thesouth.From these and some other discrepancies, Dr. R. thinksit of great importance that the globular nebulæ and clustersshould be all carefully reviewed, as it is chiefly from theirsupposed regularity that the hypothesis of the condensationof nebulous matter into suns and planets has arisen, anhypothesis which he thinks has, in some instances, been carried to an unwarrantable extent.11On the whole, he is of opinion that this is the mostpowerful telescope that has ever been constructed . Solittle has been published respecting the performance of SirW. Herschel's forty-foot telescope, that it is not easy toinstitute a comparison with that, the only one that can fairlybe made to compete with it. But there are two facts onrecord which lead to the inference that it was deficient indefining power; one, the low power used, which Dr. R.thinks was not above 370; the other, the circ*mstance thatneither the fifth nor sixth stars of the trapezium of thenebula of Orion were shewn by it. As to light, there is noreason to believe that the composition of the forty- footmirror was as reflective as that of the twenty-foot; and ifDr. R. be correct in the opinion, that the latter* did notshew the fifth star easily, or the sixth at all, and that it onlyexhibited the " debilissima" and one star near the ring-nebula, then it has decidedly less illuminating power thaneighteen, perhaps not more than fourteen inches aperture ofLord Oxmantown's mirror, notwithstanding the loss oflight in that by the reflexion at the second speculum.However, any question about this optical pre-eminenceis likely soon to be decided, for Lord Oxmantown is aboutto construct a telescope of unequalled dimensions. He intends it to be six feet aperture, and fifty feet focus, mountedin the meridian, but with a range of about half an hour oneach side ofit. Ifhe succeeds in giving it the same degreeof perfection as that which he has attained in the presentinstance, which is exceedingly probable, it will be, indeed, aproud achievement; his character is an assurance that itwill be devoted , in the most unreserved manner, to the service of astronomy, while the energy that could accomplish

• In its original state, not as improved by the more perfect means latterly

employed by Sir John Herschel.12such a triumph, and the liberality that has placed his discoveries in this difficult art within reach of all, may justly bereckoned among the highest distinctions of Ireland.DONATIONS.Eleven Quern Stones ofdifferent Kinds.Eight Methers of different Sizes and Patterns.Around wooden Goblet.An ancient Horn Vessel. Presented by Captain Portlock,M.R.I.A.An ancient Spur found in the Grave-yard at Ferns. Presented by Stephen Radcliffe, Esq. , per Haliday Bruce,Esq. , M.R.I.A.APapal Bulla, found near the Foundation ofthe Cathedral of Cloyne, ( Clemens PP. IIII.) Presented by R. J.Graves, M.D.Fisica di Corpi ponderabili. 2 vols. 8vo. By the Chevalier Amadeo Avogadro. Presented by the Author.Third Annual Report of the Proceedings ofthe BotanicalSociety ofEdinburgh. Presented by the Society.Sixth Report of the Poor Law Commissioners in Ireland.Presented by George Nicholls, Esq.Ancient Laws and Institutes of England. Presented bythe Commissioners of the Public Records of the Kingdom.A Geological Map of England and Wales. By G. B.Greenough, Esq. Presented by the Geological Society.Transactions ofthe Geological Society ofLondon. Vol. V.(1840.) Presented by the Society.Quarterly Journal of the Statistical Society of London.July, 1840. Presented by the Society.Address ofthe General Secretaries of the British Association. Presented by the Authors.Journal of the Franklin Institute. Vol. XXV. (1840.)Presented by the Institute.- 13Transactions of the Royal Society of Gottingen, from1828 to 1831. Vol. VII. Presented by the Society.Proceedings of the American Philosophical Society, toJuly, 1840. (No. 12.) Presented by the Society.Directions for using Philosophical Apparatus. By E.M. Clarke, Esq. Presented by the Author.Manuscript Notices relating to the Cathedral of St.Patrick, Armagh. By John Davidson, Esq. , M.R.I.A.Presented by the Author.Ordnance Survey ofthe King's County. In 49 Sheets,including Title and Index. Also,Ordnance Survey of Carlow. In 28 Sheets, includingTitle and Index. Presented by His Excellency the LordLieutenant.November 30, (Stated Meeting. )SIR WM. R. HAMILTON, LL.D., President, in the Chair.Dr. Kane read a Paper " On the Production of AudibleSounds," of which the following is an abstract.The sensation of sound is produced upon the ear by thetympanum being thrown into vibratory motion, isochronous with the vibrations transmitted from the soundingbody.Any body which vibrates as a single mass gives origin atthe same moment to two waves, whose motions are in oppositedirections, and of which one is rarefied and the other condensed.If these two arrive at the tympanum at the same moment and with equal power, perfect neutralization shouldresult, and no sound be heard: hence, where a vibratorybody produces upon the ear the sensation of sound, it arises14from one wave ofthe two being either totally interceptedor, at least, diminished in force, and the loudness of thesound is proportional to the difference of the intensity ofthetwo waves when they affect the ear.All instruments for increasing sound, and producing resonance, act upon this principle.The following facts will illustrate these principles in detail. A tuning fork is a centre of fourwaves, two + and two but unless it be+-- ,very close to the ear, no sound is heard fromit; because the centre of all the four wavesbeing very close, all act on the ear withequal force, and the difference is 0, (approximatively. )+Now, if an open tube, of the same length as a one- phasewave from the fork, be approached to one centre, as A, inthe adjoining figure, the air in it commences to vibrate inunison with the fork, from being set in motion by the first+сwave which passes into it:the vibration of the tube is,however, a phase behindthat of the fork, and hence,when a--wave passes fromthe centre A, it meets a + wave from the end ofthe tube E,and both are destroyed. The centre, c, destroys also a+ centre, as D, and there remain only the centres of +waves, B from the fork, and F from the tube, and these actingin concert on the tympanum produce the sound that wehear.If the tube be closed, and of only one-half the length,the wave, which emanates from the centre A, passes in,and being reflected from the bottom, issues again at themoment when the next -wave from A is about to enter; Eand a then destroy each other, and c and d also interfering,there results only the + wave B, which acts unimpeded on15∞+the ear. The sound of an opentube is, therefore, ceteris paribus,- E A- C much stronger than that of aclosed tube, as there are twowaves in place of one.That the office of closed tubes, when resonant, is to destroy a portion of the sound of the original vibrating body,and ofthe open tubes to afford , in addition to that, a newcentre of a wave of the same phase as that which remains,may be exhibited in many ways. Thus, Mr. Adams shewedlong since, that when two closed tubes are placed at rightangles to each other, they interfere when made to speak toa tuning fork, and for this effect no explanation has hithertobeen given. But it is evident that the tubes being at rightangles to each other, the waves destroyed are in oppositephases, and those which remain are in opposite phases also,so that the effect is the same as if no tubes were present atall. The same effect may be producedABCby a single tube, bent so that its apertures may be at right angles to each other;the and waves, D and c, meeting inthe tube, produce neutralization , and thewaves A and B, also + and which re--19main, interfere also, and hence no soundresults. In an open tube bent into a circle,as in the figure, the two waves destroyed (A c) are of theE+B+to+Fsame phase, and also those whichremain, (B D,) and hence, such atubesoundswith nearly double thepower of an ordinary open tube.That it is the sound of the waveswhich do not go into the tube,and not that of the waves in thetube, we hear, may be shewn by applying two closed tubes, asin the next figure. When the two waves are absorbed16E1- ++1+the preceding figure.by the circular open tube, eachclosed tube absorbes a + wave,and hence, notwithstanding thatthere is so much vibrating material, no sound is heard. But ifthe tubes Aand Bwere open, thenthe vibrating centres shouldhave been simply transferred totheir farther extremities, and thetubes would emit sound as thefork had done without them inIfthe open tube be double the length of a phase, thentheneutralization oc144 +8B+A-00-0curs as in the figure,the residual waves C+Dbeing в and F, in opposite phases; butas their centres areseparated so far, they interfere only in hyperboloidal planes,which are not detected unless when carefully sought for, buthave been noticed to exist by Savart, although he did notsuspect their cause.All these principles have received very full verificationfrom an instrument constructed for the purpose, and termeda Chorizophone. It consists of a square glass plate, whichis placed above a set of closed tubes of such size, that whenthe plate vibrates in four pieces, with diagonal nodal lines ,the length of each tube is half the length of the phase of thewave produced, and their form is triangular, ofthe magnitudeof one ofthe four vibrating portions of the plate; when oneof these tubes is presented to the plate, and this brought tovibrate by a violin bow applied to the centre of one of thesides, the tube resounds, and more loudly in proportion as theplate is brought nearer to its orifice. Nowhere the entire17wave from the plate is caught by the tube, and the more perfectly its escape into the air is prevented , the louder is thesound produced, the sound must arise therefore from thewaves which do not pass into the tube. Any one or morewaves may thus be absorbed by the closed tubes, and a rangeofloudness of sound produced from the same plate with oneor more of the four tubes, according as they are disposed asfollows:The vibrating plate gives eight waves, four above andfour below, 4 being + and 4 minus.With one tube, one wave is absorbed, and 3+ and 3 -destroying each other, a wave remains opposite in phase tothat which is absorbed, and produces an audible sound.With two tubes, the waves absorbed may be either ofopposite or of the same phases. If opposite, then, the remaining waves are 3 + and 3 and no sound is produced; butif the waves absorbed be of the same phase as +, then thereremains 4 and 2+, and hence the ear is doubly affectedby 2 The two tubes may be either both above or bothbelow, or one above and one below the plate.1.--With three tubes, the absorbed waves may be either allofthe same phase, or two of one and one ofthe other. In thefirst instance, 3+ being absorbed, there remains 4 and1 -, and the ear receives the impulse of 3. In the othercase 2+ and 1- being absorbed, there remains 2+ and 3-and the impulse on the ear is only 1-. The position ofthetubes may vary in this as in the former case.With four tubes, the absorption may be either all of thesame phase, or 2+ and 2. In the former case, the remaining waves will be either 4+ or 4-, in which case thegreatest sound the plate can produce is heard, or else thereremain 2+ and 2-, in which case the plate gives no sound.These results prove fully that it is the residual sound that isheard , and not that which passes into the tube.VOL. II. C18A vibrating plate gives some sound always, even withoutthe tubes, for since there are at least eight waves, some onewill always be more favourably disposed for acting on the earthan another, this difference will increase with the numberof waves; and hence, the independent sound of a plate increases in proportion as the vibrating portions into which itdivides, become more numerous.A string vibrating in free space, produces little or nosound; but if it be strung over, or in connexion with, anelastic board or box, a great resonance is produced . Thisarises from two sources; first, the string when by itself is thecentre of two waves excessively close, and the action ofwhichis therefore interfering. But if the string AB, vibrate near aplane surface c, the wave - 1 , which passestowards it is reflected back, and meetingthe wave +2, which follows, it neutralizesit partly, and enables the wave - 2, toreach the ear without diminution. It isprobable, however, that the great portionA睡Bof the sound arises from the board or plateitself vibrating in parts, or as a whole. Ifin parts, these parts are variously situated, as regards theear, and hence produce an effect upon it. Or if, as a whole,the plate c is so broad, or bounded, if a box, that one waveis lost by internal reflexion, and only the wave emanating fromthe outer surface can arrive at the ear.When a tuning fork is placed on a table, one wave is lostby internal transmission and reflexions, whilst that directedfrom the outer surface reaches to the ear.In the case of reed instruments, the reed produces twowaves, which, if it vibrated freely, should neutralize eachother on the ear; but in practice whilst an open passage is allowed to one by the mouth-piece, the other wave is lostwithin the cavities ofthe lips and mouth. In mouth-pieceinstruments, as bugles and trumpets , the cavity of the mouth•19serves also for the absorption of the one wave, leaving theother free to act.The following note, " On the Course ofthe diurnal Fluctuations of the Barometer," by James P. Espy. A.M., of Philadelphia, was communicated by Dr. Apjohn." It is a law of inertia, that if a body is forced upwards,it will react and press on its support, more than its naturalgravity; and if it is permitted to descend , it will press on itssupport less than its natural gravity, and the increase anddiminution of pressure will be proportional to its velocity." Moreover, if a body is permitted to descend with a certain velocity, and then retarded, it will, when retarded, pressmore on its support than its natural gravity, and that in proportion to the rapidity of its retardation." This principle will explain the four fluctuations of thebarometer which occur every day." Just before sunrise, when the atmosphere is neitherbecoming hotter nor colder, the barometer will indicate thenatural weight ofthe air, which we may call a mean; as thesun rises the air will begin to expand by heat, and the wholeatmosphere will be lifted up by this expansion, and by itsreaction will cause the barometer to rise; and this will bethe greatest, at the time when the air is receiving the mostrapid accessions of heat, which must take place before thehottest time of the day, when the air is becoming neitherhotter nor colder. On this principle, then, the maximumday fluctuation will take place between daylight in the morning and the hottest time of the day, and this corresponds withthe fact; for this maximum, which amounts to more thanthe tenth of an inch, takes place about nine or ten o'clock,A. M."At the hottest part of the day, when the air is neitherexpanding nor contracting, it is manifest that the barometerwill stand again at a mean. Soon after this, however, the air20will begin to contract from diminishing temperature, and atthe moment of the most rapid acceleration of contraction, thebarometer will stand at its day minimum, which will probablybe late in the afternoon; and it is found in fact to be fromfour to five o'clock. Fromthis time the rapidity of the downward motion of the air from contraction begins to diminish ,and the barometer of course begins to rise; and at the moment when it is most rapidly retarded in its contraction, thebarometer will be at its maximum night fluctuation, and willagain be above the mean, but not so much as the day max." This max. is found to occur about ten or eleven o'clock,P. M. The air will now go on contracting more and moreslowly, until about daylight, when it will be at rest, and the barometer will again be at a mean." This theory was given by me to the Journal of theFranklin Institute, and published ten or twelve years ago." I ventured in that paper to predict, notwithstandingsome alleged observations at St. Bernard's Hospital to thecontrary, that it would be found by more careful observationsthat the morning max. fluctuation would be greater in loftysituations on the sides ofmountains, provided they were notvery lofty, than on the plain below." For it is manifest, that there will be not only a reactionat these lofty situations, (a little less, it is true, than below,)but some ofthe air will be lifted up, by the expansion of theair below, above the upper place of observation; which wouldin all probability more than compensate the diminished reaction at moderate elevations." This prediction has been entirely verified by Lieutenant- Colonel Sykes's observations in India, and this verification may be considered as a strong proof of the correctnessof the theory. It is quite probable, that max. day fluctuation occurs later at considerable elevations than on the plainbelow." The theory would lead us also to suppose, that at very21great elevations, where the reaction is very minute, only twofluctuations would be found in the day: the maximum atabout two o'clock, P. M. , when most air would be above thebarometer; and the minimum at daylight in the morning,when least air would be above it; but I know of no observations to confirm or refute these deductions. "Mr. Ball brought under the notice of the Academy thefact, that the ordinary sturgeon of the Dublin markets is anundescribed species. He stated that Mr. Thompson of Belfast, and Professor Agassiz, concurred with him in this opinion, and he proposed to call it Accipenser Thompsoni, purposing, ifpermitted , to give figures and full descriptions in afuture number ofthe Proceedings.A notice of an unpublished Irish coin of Edward IV. wasread by A. Smith, M.D., M.R.I.A." Within the last month some workmen were employedin cleaning one of the city drains in the Cross Poddle, and afew coins were found. Among them was one of no intrinsicvalue, and apparently of no interest whatever. It is made ofbrass, and was originally plated with silver, traces of whichstill remain. On one side it has a crown within a circle ofpellets, outside which, in place of a legend, are crosses androses alternately; on the other side it has the common type—a cross, with three pellets in each quarter; the legend is defaced. It weighs nearly five grains, and is now in the cabinetofLieutenant- Colonel Weld Hartstonge."This little coin bears no evidence in itself which wouldenable us to say to what king's reign it should be appropriated,or even to what country. But on referring to an Act passedin the second year of Edward IV. , at a parliament held inDublin, we find it enacted, that a coyne of copper mixedwith silver, be made within the Castle of Dublin, having onone side the print of a cross, and on the other part a crown, ofwhich four shall be taken for a penny; and that the saidC22coyne shall havegraven within the circumference of the saidcross, the name of the place where it was made; and on theother part suns and roses in the circumference of the saidcrowne.""It is to be regretted , that this little coin, the only one ofthe kind which has been found, is not in better preservation;but such as it is , it corresponds in every particular with thedescription in the Act; and, therefore, we do not hesitate toassert that it is one of the farthings of mixed metal orderedto be made in 1462."It may be objected, that this coin has crosses instead ofsuns round the crown, and it would be difficult indeed to givea more accurate symbol of the sun, in so many places, withinso limited a space; but we should recollect, that similarcrosses occur on some of the silver groats of Edward IV. ,coined in Dublin, in the beginning of his reign. On thesegroats, immediately over the crown, on the obverse, are placedthree small crosses, which have usually been considered asprivy marks.+"Nowtaking for granted, that these crosses on the groatswere intended to represent suns , as they evidently were onthe farthing, we suspect we can account for them, not onlyas privy marks, indicating that the coins on which they arefound belong to Edward IV. , but also assign a probable reason why three only should appear."" The sun was first introduced by Edward IV. upon thecoins, in commemoration ofan extraordinary appearance inthe heavens, immediately before the battle of Mortimer'sCross, in Herefordshire, (in 1461 , ) where three suns were seenwhich shone for a time, and then were suddenly conjoinedin one.'1" It matters little whether the extraordinary phenomenon

• Simon's Essay on Irish Coins, Appendix, No. VII.

+ Simon, pl. 4, fig. 71.Ruding's Annals of the Coinage, vol. ii . p. 359, 2nd Edition , 8vo.23just alluded to be explained or not; it is sufficient for ourpurpose to know, that it gave rise to the introduction of thesun as a privy mark on the coins of Edward; and we may bepermitted to hazard the conjecture, that the three crosses onhis Irish groats, coined shortly after the battle of Mortimer'sCross, were intended to represent the three suns."We could refer to many instances in which dates andother matters were determined with certainty, by studyingwith attention minute particulars in the type of coins, concerningwhich the records were unsatisfactory, or altogetherwanting; and there are still in existence authentic records ofmore than one Irish coinage, specimens of which have notyet been discovered; and within the last fewyears numerouscoins, whose existence had not been suspected , have come tolight, for the preservation of many of which we are indebtedto the indefatigable zeal and research of a highly esteemedand deeply lamented individual, whose memory will long beregarded with respect and admiration, and the recollectionof whose labours in preserving the proud memorials of ourcountry, will, we trust, be perpetuated by depositing withinthese walls his collection of Irish antiquities, in accordancewith his well known intention , and thus constituting a monument worthy ofthe late Dean of St. Patrick's."The Archbishop of Dublin made some observations on aremarkable meteor, lately seen in different parts of Britain.Resolved-That the Committee of Antiquities be requested to take immediate steps towards opening a subscription for the purchase of the collection of Irish antiquitieswhich belonged to the late Dean of St. Patrick's.DONATIONS.Memoires de l'Academie Imperiale des Sciences de St.Petersbourg. Tome I.-XI.124Sciences Mathematiques, &c . Tome IV. 3rd and 4thLivraisons, and Tome IV. Sciences Politiques, Histoire, &c.4th and 5th Livraisons.Novi Commentarii Academiæ Scientiarum Imperialis Petropolitana. Tom. I.-XX.Nova Acta Academia Scientiarum Imperialis Petropolitana. Tom. VI. VII. VIII, and XV.Recueil des Actes de l'Académie Impériale des Sciences deSt. Petersbourg. An. 1838 and 1839. Nos. 13 and 14.Presented bythe Academy.The Polytechnic Journal. Vol. III. Part 5. Presentedby W. Farran, Esq.Quarterly Journal of Statistical Society. Vol. III . Part 3.Oct. 1840. Presented by the Society.An Inquiry into the Causes of popular Discontents inIreland. By an Irish Gentleman . 1804. Presented byJoseph Hone, Esq.Descriptive Catalogue of the Museum of the Royal College of Surgeons in Ireland. Vol. II. By John Houston,M.D., M. R. I. A. , &c. Presented by the College of Surgeons.On the Diminution of Temperature with Height oftheAtmosphere.Researches on Heat. Fourth Series.Additional Experiments on1837. By James D. Forbes, Esq.terrestrial Magnetism inPresented by the Author.Memorie della Reale Academia delle Scienze di Torino.Second Series. Vol. II. Presented by the Academy.Transactions ofthe American Philosophical Society. NewSeries. Vol. VII. Part 1. Presented by the Society.PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1840.December 14, 1840 .No. 26.REV. J. H. TODD, D.D. , Vice-President, in the Chair.Dr. Apjohn read the following notice, by George J.Knox, Esq. , of " some Improvements in the Voltaic Pile."" The chief imperfection in the voltaic pile, its want of aconstant uniform powerof long duration, bywhich it is renderedalmost useless as an instrument of research, having beenovercome by the ability of Professor Daniell, the only thingthat remained to render it efficient seemed to be, to increaseits power; a desideratum accomplished byMr. Grove, by substituting for copper and sulphate of copper, platinum and nitric acid. To give to Grove's battery a constancy of actionequal to that ofProfessor Daniell's, would require an increasein the quantity of acids, (particularly the sulphuric, ) intowhich the metals are immersed; but inasmuch as in galvanicbatteries ofthe ordinary construction an increase of acid solution would require an increased distance of the metalsfrom each other, producing a diminution ofintensity, I endeavoured to obviate these disadvantages by the following contrivance. Porous vessels are fixed half an inch apart in lateralwooden supports, in which grooves are cut, to retain the zincplates from touching; the porous vessels are filled with nitric acid, from a long glass tube, sealed at one end, and bentVOL II. D26•at the other at right angles. Along the side of the tube alsoholes are bored at distances corresponding to the distancesofthe porous vessels from each other; so that, upon pouring nitric acid into the tube, the vessels are all filled at thesame moment; when filled , the entire apparatus is placed ina vessel containing sulphuric acid. The advantages of thisarrangement were, that I had only two solutions to pour in,whatever number of alternations were employed; a sufficientsupply of acid solutions to keep up a constant action for alength of time; and a distance between the plates scarcelyexceeding the thickness ofthe porous vessel employed."The following experiments were undertaken with theintention of estimating the relative values of the different constructions of Grove's battery, recommended by Mr. Knightof Foster Lane, as far as respects the arrangement of thezinc and platina plates, when, to my surprise, I found thesame quantity of electricity to be evolved when the zinc isbent so as to expose an opposing surface to each surface ofa platinum plate, as when a platinum plate, of the size ofthe former zinc, is similarly placed with respect to a plate ofzinc of the same size as the former platinum, affording aneconomical method of arranging a Wollaston's battery, thezincs being bent round the coppers, in place of the coppersround the zincs.66 Experiments with Grove's Battery."The acid solutions were those recommended by Mr.Grove, i. e. pure nitric acid, in contact with the platina; sulphuric acid 4-5 water by measure, in contact with thezinc. The surfaces of zincs immersed were 3 by 2.5 inches;those ofthe platina, bent round the porous vessel holdingthe zincs, were 6 by 2.5 inches. The glasses containing theacid, &c. , were 3.2 inches long, 1.5 broad, 3-5 deep. Thelength ofthe porous vessel of pipeclay was 2.5 inches, the27breadth 0.3, the depth 3.5. The number of alternations wasfive.Time, 2 minutes,Cubic Inches.8.0The battery being at rest for 10 minutes, · 8.099 99 25 99 3.099 "" 1 hour,1.099 99 19 hours,none" The porous vessel was found filled with sulphate of zinc ,which stopped the action of the battery."Second Experiment."The zinc plates being of the same size as the former platina, and the platina of the same size as the former zincs,the zincs bent round the platina, all other things being asbefore.Time, 2 minutes,After 10 minutes,"" 25·Cubic Inches.• 8.8.8." Third Experiment."Another battery, the diameter ofthe cells of which was2 inches, gave a diminution of only one- half ofthe quantityofgas after the lapse offorty-eight hours, shewing the advantage ofhaving a large supply of sulphuric acid.*66 Experiments with Smee's Battery ofPlatinized Silver."The acid solution was of the same strength as before,and the sizes of the zincs and platinized silver the same as

• "The porous vessels were of pipeclay. The same expertments repeated with

unglazed porcelain gave 10 cubic inches in two minutes; with very porous pipe.clay, they gave as much as 15.cubic inches in two minutes, shewing the importance of attending to the nature of the porous vessel employed. "D 228ofthe zincs and platina formerly employed. The zincs werebent round the platina.*Time, 2 minutes, •After 5 minutes, •"Second Experiment.Cubic Inches.3.2.6"The zincs being raised out ofthe acid, cut in two, andre-immersed.Time, 2 minutes,After 5 minutes,Cubic Inches.• 1.61.6"Third Experiment."The zincs and platinized silver being removed, the acidremaining untouched; the platinized silver plates were bentround the zincs.Cubic Inches.Time, 2 minutes,After 5 minutes,"Fourth Experiment."The platinized silver cut in two.• 2.62.4Time, 2 minutes,After 5 minutes,·Cubic Inches.• 1.41.4"Supposing from these experiments the same quantity ofelectricity to be developed, whichever of the opposedsurfaces ofthe two metals be the greater, I placed in separate glasses five zinc cylinders, one-inch diameter, immergedThe most advantageous method of arranging a Smee's battery is, packingthe zincs and platinized silvers in the manner recommended by Dr. Faraday inhis 10th series, (also by Mr. Young, Phil. Mag. vol. x. p. 241 , ) placing thepackage on supports so as to allow the sulphate of zinc to fall to the bottom ofthe vessel, while the fresh acid rises to the surface."29eight-tenths of an inch in the acid; platina foil, connected bybinding screws with the zincs, was rolled into cylinders twotenths of an inch in diameter, and then immersed in pipeclaytubes one inch deep.Cubic Inches.Time, 2 minutes,After 10 minutes,· 1.0• 1.0"Second Experiment."Platina foil of the same size as the zincs, and zinc rodsof the same diameter as the platina cylinders being employed,the effects were precisely the same.Time, 2 minutes,Cubic Inches.· 1.0After 10 minutes,1.0"Third Experiment." The zinc cylinders being made twice the diameter of theformer; the quantity of gas generated in two minutes wasthe same as before; the increased number of lines of electrical force compensating the increased resistance offered bythe acid solution."Fourth Experiment."With cylinders twice the diameter of these, a very feeble current passed, the obstacle being too great to be overcome; by increasing the diameter of the porous vessels,and thereby of the nitric acid solution, which is a good conductor, the impediment is diminished , as shewn in experiment fifth . Thus Mr. Binks (Phil. Mag. vol. xi. p. 68)finds, that in dilute sulphuric acid, the size of the coppercompared to a given surface of zinc, to produce a maximumeffect, should be 16, that ofthe zinc to a given surface ofcopper being7; while in a galvanic arrangement, in which thezinc is immersed in dilute sulphuric acid, inclosed in a mem-30branous bag, and the copper in a surrounding solution of sulphate of copper, the proportion of zinc to copper was as oneto eight, the impediment to the passage ofthe current beingdouble in the latter case what it was in the former.66 Fifth Experiment." Five cylinders of zinc, 10 inches high, diameter, wereplaced in glass vessels, containing sulphuric acid, as before.Into these were placed cylindrical earthenware vessels , 11inches diameter, containing pure nitric acid; slips of platinafoil were rolled into cylinders as before.Time, 2 minutes,After 1099•309999•Cubic Inches.· 2.0· 2.53.0*" From these data may be calculated the heights of thezinc pipes, and the weight of platina foil required to obtainany given decomposition, to be employed, as shewn byJacobi, either as a motive power, or applied to light-houses,to the polariscope, or to the fusion of refractory substances.For the latter purposes, I had fixed to a strong, shallowwoolfbottle, two tubes with glass co*cks, and to them tubescontaining chloride of calcium, applied to a Daniell's jet,playing upon a cylinder of lime, rotated by clock work.A third tube was inserted in the bottle, intended as a regulation of the pressure, or a safety valve, in case of explosion. "Dr. Apjohn then made a brief verbal communication onthe subject of the Composition of Pyrope. This mineral, long

• "The dilute acid in the voltameter began to boil; the cause of the increase

of decomposition, compared to what took place in the small cylinder, was the smallstratum of sulphuric acid between the porous vessel and the zinc . For a continuous action the zinc pipes, sealed at one end and amalgamated, should be connectedby pipes at top and bottom, with an earthenware vessel, containing the sulphuricacid."31confounded with garnet, is known to be distinguished fromit by containing chrome, and by exhibiting, not the dodecahedral, but the hexahedral form. The best analyses of it,however, which are by Kobel and Wachtmiester, are obviously imperfect, of which no better proofcan be given thanthat Gustavus Rose, in his Crystallography, does not attemptto give the formula of the mineral, but contents himself withenumerating the different oxides of which it is composed.Under these circ*mstances, Dr. Apjohn conceived that are-examination ofthe constitution of pyrope would not bewithout interest. He, therefore, undertook its analysis; andthe result has been that he has detected in it yttria, one ofthe rarest ofthe earths; one, in fact, which had previouslybeen known to exist only in a few minerals of exceedingscarcity. The yttria was insulated in the following manner.The mineral being fused with carbonate of potash, andthe silex separated in the usual way, the peroxide of iron ,alumina, and yttria were precipitated together by a mixedsolution of ammonia and sal-ammoniac. The alumina wastaken up by caustic potash; and to the iron and yttria, dissolved in a minimum of muriatic acid, such a quantity oftartaric acid was added, that upon subsequently pouring inammonia in excess there was no precipitate produced . Theiron was now removed by sulphuretted hydrogen; and thesolution evaporated to dryness, and ignited in a large platinum crucible, so as to volatilize the ammoniacal salts , andburn away the carbon of the tartaric acid, left the yttriaslightly coloured by oxide of chrome. From this latter substance it is separated, but not perfectly, by the action of adilute acid, and by the addition of ammonia, or caustic potash ,to the solution the yttria is again recovered. That the substance thus obtained is yttria seems proved by the followingconsiderations.It is separated , though not completely, from acids by32ammonia largely diluted with sal-ammoniac, and hence cannotbe one of the alkaline earths.It is insoluble in potash, and is, therefore, not alumina orglucina. After ignition it dissolves readily in dilute acids, andis hence not zirconia or thorina. From zirconia it is furtherdistinguished by its saline solutions, being precipitated byferrocyanide of potassium.It is not oxide of cerium, for it does not redden in theexterior flame of the blow-pipe, and because its salts are notprecipitated by the sulphate of potash. The quantity oftheyttria amounts to at least 3 per cent.Dr. A. is still engaged in investigating the compositionof pyrope; and expressed his intention of bringing his results on a future occasion in a more detailed form under thenotice ofthe Academy, when he hoped also to be able toassign the true formula ofthe mineral.Mr. J. Huband Smith exhibited to the Academy an ancient monastic seal, from an impression ofwhich the annexedwood engraving is taken.This seal has been for some time supposed to have beenthat of the Dean and Chapter ofLismore, and it was recentlyfound among the effects ofthe late Rev. Sir George Bisshopp,formerly Dean of Lismore; but the legend around the sealshews this supposition to be totally groundless.Itreads thus: " SIGILLVM: CAPITVLI: PRIORIS: ET: CONVENTVS: DE: BVLLYNGIONA. " It surrounds the figures ofthe Virgin and Child. She appears seated, and wearing a highlyornamented crown; her robe, which falls in gracefully arranged folds, displays no inconsiderable degree of skill andtastefulness of design. In her right hand is a star of fiverays, intended possibly to represent the star of Bethlehem,to which the infant Saviour points. It is observable thathis head displays the ecclesiastical tonsure. The seal is of33a pointed oval form, and measures two inches and seveneighths in length, and one inch and three-quarters in itsgreatest breadth.Wet sul to DE: BVLLUNGIOUTGILLVM:ИЗЛИОДIt has been surmised, with considerable appearance ofprobability, that this seal (which, if an inference were drawnsolely from the style of the characters, might be pretty confidently referred to the close of the fourteenth, or thebeginning of the fifteenth century) belonged to a monasticestablishment dedicated to the Virgin, as Archdall states ,[Monast. Hibern. 626, ] at Ballindown, on Lough Garagh, inthe county of Sligo, of which but inconsiderable remainsnow exist. It is said to have been founded by M'Donogh,lord of Corran and Tirreril, A.D. 1427, for nuns ofthe orderof Saint Dominick, about the very period to which the characters ofthe legend may be attributed.Like other names of places in Ireland, that of Ballindownis variously written. In a tract entitled, "Valor beneficiorumecclesiasticorum in Hiberniâ, " we find " V. de Ballendowne34in the " Dioecesis Tuamensis," of which the " Extenta ettaxatio facta fuit, 28mo. Eliz. " So that it seems highly probable that " Bullyngiona" may have been but an arbitraryLatinization of the same name by the artificer by whom theseal was made, possibly a monk of the religious house towhich it belonged.Mr. Clibborn made the following communication on thesubject of the Leyden Jar." In Brand's Manual of Chemistry, vol. i . , 3rd Edition,p. 76, I find it stated, that, if one Leyden jar be insulated , with its internal surface connected with the positiveconductor, another jar may be charged from its exteriorcoating; and if this second jar be insulated, a third may becharged from its exterior coating, and so on for any numberofjars, provided always that the exterior coating of the lastjar be connected with the ground.'"As myelectrifying machine was but small, it occurred tome that I might economise both time and labour by constructing a battery of jars so arranged that I should be ableto take advantage of this principle, and make one jar chargeanother, instead of my being obliged to charge the wholeseries; for, though they are all connected together, andcharged by the same operation in the common electric battery, yet the time and labour consumed in charging thebattery is exactly the same as if each jar were charged separately and then added to the series. A great saving of labourand time would have been effected had the arrangement ofjars answered, for it was exactly the same as that describedby Brand, so far as the charging part ofthe apparatus wasconcerned; but when the jars were loaded , or rather shouldhave been loaded, they were made to turn through a quadrant, and form a new arrangement, by which all their outside coatings were connected together by a common conductor. A similar arrangement connected all their inside35coatings, which made all the conditions necessary to theperfection of the common battery; and I found it capable ofbeing charged by the electrifying machine in this form, butit could not be charged to any extent in the other. It appeared, that but few sparks would pass from the conductorto the first jar. If the last one was removed, and its chainfastened to the next, the first jar would take a few moresparks, and so on; for it was found that whenever the lastjar in the series at any time was removed, the same resultsfollowed; and this was the case when the last but one wasremoved, clearly proving, that the capacity or aptitude ofthe first jar to take a charge was influenced and diminishedby the second, more so by the third, fourth, &c. Its aptitude was greatest when it was by itself, and not connected,as described, with the others."This result disappointed my expectations, so far as myintended improvement on the electric battery was concerned;and it also appeared to point out the existence of a principleinfluencing the charge of the electric jar, which was notrecognized in the popular treatises on electricity. I procureda number of glass plates with fixed and moveable coatings.These plates were insulated and arranged with and withoutcoatings in every way that Brand's rule required, but thegeneral result was the same as that given above."From numerous experiments made with these plates, Icame to the following general conclusions:" 1. That the actual quantity of the positive and negativeelectricities which we can accumulate in the opposite surfaces ofan electric or non-conductor, as a plate of glass ordry ice, depends upon the distance of these surfaces."2. Every case of charge of one jar or plate may be assimilated to that of any number ofjars or plates in a series, suchas Brand's, by supposing the one jar or plate to be dividedinto the greater number, its thickness being the sum ofthethicknesses of all the segments or plates . The inside of the36"first jar or surface of first plate, in contact with conductor,and outside of last jar or plate in contact with the ground,being considered as the proper opposite surfaces of the proper plate, and those on which the electricities evolved by thefriction ofthe cylinder and rubber ofthe electrifying machineare accumulated or heaped."Ifwe make a pile of the plates coated or not, and chargethe outside surfaces by coating them, and connecting onewith the cylinder and the other with the rubber of the machine, we find all the conditions ofthe experiment compliedwith. There is nonecessity for any connexion with the ground,which in Brand's can act merely as the conductor to conveythe negative charge of the rubber to the extreme surface."Let us nowunpack the pile, and we find that the chargeof the intermediate plates diminishes, as we approximatetowards the centre of the pile, being greatest near the extremes. At equal distances the charges are equal; for thecharges ofthe first plate but one, and the last but one, willas perfectly neutralize each other as the charges of the surfaces ofthe first and last. The same is found to be the casewith the surfaces ofthe third plates from each extreme, andso on ofthe others; but it is not the case with a second anda third, a first and a fourth plate, and so on, no two unequalsas to place exactly neutralizing each other. Hence wemay conclude, that the charge of the intermediate jarsin a series, such as described by Brand, though it really depends on inductive agency, is altogether different from thatkind he alludes to, which may be inferred from his erroneousrepresentation of the actual fact; and the charge of theextreme surfaces is immediately the result of that actiononly, which several electricians have called conduction,arising from the connexion of these surfaces with the sourcesofthe free electric forces ."The fact here described appears capable of throwingmuch light on the corpuscular arrangement of the atoms of37bodies, which retain an electric charge on their surfaces, orwhich, by a change of form from mechanical pressure or difference oftemperature, exhibit differences of electric state.In speaking of a charged electric, we may consider it a pileof an infinite number of plates, each of which, except theextreme surfaces, is composed of a surface of atoms, whichare acted on by two sets of induced electric forces, whosedifferences, arising from their distances from the extremes,we discover when we split the plate, or if it be a pile, whenwe separate the plates from each other."January 11 , 1841.His Grace the ARCHBISHOP OF DUBLIN, V. P.,in the Chair.Rev. Henry Barry Knox, Rev. John West, ThomasFortescue, Esq. , M. P. , Chichester Bolton, Esq. , and HenryCoulson Beauchamp, M. D., were elected Members of theAcademy.The Rev. Thomas H. Porter, D.D. , read a paper " On theDeposits of Gravel in the Neighbourhood of Dublin. ”After detailing the facts commonly known as to the stratified beds and ridges of limestone gravel, lying over thegreat central limestone region of Ireland, and the continuance of deposits containing a large proportion of roundedpebbles and stones ofthe same material, over the graniteand other primitive rocks to the eastward of the limestonecountry; it was argued that there were clear indications ofa great diluvial action from west to east, by which the surface of the limestone was reduced to its present level, andthe remains of its upper portions spread over the limestone38region itself, and carried eastward to the sea. The occurrence of similar calcareous deposits in the seaward glensand valleys of the Dublin and Wicklow mountains for somemiles south, and on their sides to a considerable height,was ascribed to the current of the same deluge, sweepingthe transported substances over the lower parts of the mountain range, and then turning southwards along the sea coast,after passing the north flank of the mountains. Similarfacts, but in an inverted order, from south to north, havebeen observed towards the southern flank, in the CountyWexford.It was urged, that the subsiding waters of this inundation, rushing down the valleys, and meeting below with themain current on the plains, would throw up those ridgesalong the sides of the hills, and on the flats beneath; ofwhich a remarkable example is presented in the glen ofBallynascorney, (through which the Dodder descends fromthe Dublin mountains, ) and in the gravel hills in front ofthat, from Tallaght to Crumlin.The direction assumed in this paper for the diluvial current agrees remarkably with that assigned by ProfessorPhillips, as the cause of the distribution of the Shapfellboulders over the north-east of England. A conjecturewas proposed as to the possible occasion of such a movement of water over the country. The limestone tract wasevidently formed under the sea. Its elevation may havebeen connected with the last great convulsion, which determined nearly the present form of the surface. Greatdisturbances are seen at Killiney, the Scalp, &c. , to haveattended the appearance of the granite, and even to havefollowed that period, affecting the granite itself. Manyparts of the Irish coasts present such abrupt terminationstowards the sea, as to indicate either a violent raising of theisland from a continuous tract at the bottom, or a suddensinking of an extent of dry land around the present surface.39Either of these events would create immense commotions inthe waters.Reference was made, in the course of this argument, tothe theory of Professor Agassiz , respecting the supposedevidence, that glaciers once existed in the mountains of thisisland, and produced, as moraines, some of the accumulations of mountain debris commonly attributed to the agencyof water. This theory having been pushed so far by someeminent British geologists as to have almost every ridge ofgravel and stones unhesitatingly called a moraine, it wasurged, that their principle could not be applied here at least,since the limestone abounding in the deposits of the glenscould never have been brought down by ice from mountainsin which no limestone rocks exist. It is but justice to Professor Agassiz to state, that he did not ascribe the limestonegravel ridges at Ballynascorney to a glacier; but professedto find the traces of one higher up the course of the stream.Against the glacier theory, in general, it was maintained,that evidences of a glacier having existed in any localitymust be derived from the existing form of the ground; andthat, therefore, no considerable change of the surface couldbe admitted, since the time when the moraines wereimagined to have been thrown up. More especially, nodeluge could have taken place since their formation; for inthat case, the moraines must have been swept away. Hencethey must be supposed to have existed between Noah's floodand the commencement ofthe historical periods. This interval, it was contended , would not allow time for their formation and disappearance.A gradual change of the temperature of the whole northern hemisphere would be at variance with the fact established by geologists , that the heat ofthe earth's surface hadbeen formerly much greater than now.Had the degree of cold necessary for the formation ofglaciers, been owing to a greaterelevation of this entire coun-40try, its sinking to its present level must have been attendedwith convulsions and floods, which could scarcely have failedto obliterate all vestiges of moraines.An objection, brought from the known change of temperature in Greenland within modern times, was met by observing, that Greenland in its best days was always a land ofglaciers; in the extent of which it is easy to suppose an occasional increase or diminution.Mr. J. Huband Smith gave an account of the discovery,in the month ofNovember last, of a human skeleton, accompanied with weapons, ornaments, &c. , interred on the seashore, in the vicinity of Larne, in the county of Antrim.He suggested, that a timely effort to preserve a record ofsuch interesting discoveries, can hardly fail to rescue fromdestruction some valuable " scattered leaves belonging to thelost books of history. "The locality in which these remains were found is one ofconsiderable historical interest; it was within less than a mileof Olderflete Castle, where it will be remembered that Edward Bruce landed with a considerable force for the invasionofthis country, in the beginning ofthe fourteenth century.Averycursoryinspection, however, suffices to shew that theseweapons and ornaments could not have belonged to one of hisfollowers, but must be referred to a period considerably moreremote. They consist ofa sword of very characteristic form,double edged, and rounded at the point; measuring two feeteight inches and nearly a quarter in its extreme length; asmall portion, said to have been about six inches in length,was broken offand lost at the time of its discovery; the bladevaries from two inches to two inches and a quarter inbreadth; the head of a lance (both this and the sword are ofiron or steel, much corroded);-a small and very elegantlyformed bronze pin, which measures five inches and a half in41length, thickly encrusted with verd antique, and of the shapeusually supposed to have been used in fastening the cloak ormantle; and lastly, four fragments ofbone; three ofthem beeneding portions of a comb, theback ofwhich (attached tothe serrated part by rivets)is slightly but not untastefully carved on both sides;and the fourth is so minuteand indistinct, as to renderits original use and formuncertain.The manner in whichthe skeleton was discoveredwas thus some lime quarries havingbeenlately opened along the shore , at a distance from the jetty, orwooden pier, at which smallcoastingvessels, trading between Larne and the opposite ports of Scotland,usually take in their cargoes, it became necessary,forthe greater convenienceof transporting limestonefrom the newly openedquarries, to construct arail or tramway. In leveling the line marked outfor the purposes of such construction, in the afternoon ofthe 7th of last November, the workmen discovered these remains at a spot three quarters ofa mile distant from the townVOL. II. E42ofLarne, about seventy yards fromthe sea shore, and aboutfive feet above the level of high water mark. The skeleton ,when uncovered, lay obliquely, the head pointing towards theN. W. The soil about it, consisting of sand , without almostany admixture of clay, may have, in the lapse of time, shiftedits depth; but there scarcely appeared to have been morethan from eighteen inches to two feet of sand or soil abovethese remains.There was no appearance of stone kist, or hollow spaceformed by flags set edgeways, which appear to belong exclusively to the more ancient interments preceded by cremation; fragments of the skeleton alone being found in such,with indications of the action of fire, and usually accompaniedby one or more cinerary urns. Yet although there was inthe present instance no trace of coffin, either of stone orwood, there appeared no reason to doubt that the interment was effected in a regular and orderly manner. Acrossthe breast was found the sword, its handle disposed towardsthe right hand. On the same side, but beneath the sword ,was the lance head. The position of the remaining articleswas not noticed at the time by the workmen, and thereforecannot now be ascertained.Mr. Smith placed beside these weapons a sword and lancefrom his collection , selected from some found in the remarkable heap of bones in the townland of Lagore, near Dunshaughlin, in the County of Meath; a paper descriptive ofwhich was read before the Academy by Doctor Wilde, on the27th ofApril last. The straight shape and uniform breadthof the blade ofthis last mentioned sword, and the form ofthelance head, appeared remarkably similar, though on a reducedscale, to those of the weapons found near Larne. The comband bronze pin are nearly identical with several of those discovered at Dunshaughlin, where, it is observable, no brazenweapon of any description occurred.43From a consideration of all these circ*mstances , Mr. Smithventured to express an opinion that the remains found at Larne,as well as those at Dunshaughlin, are to be referred to that remote period when the use of brass or bronze was supersededby iron and steel in the manufacture ofoffensive weapons, whileit was yet retained in the lighter works of ornament. Fromthe invariable shortness of the Dunshaughlin swords, he wasdisposed to infer, that the remains there discovered were of aperiod not far removed from the age ofthe bronze swords ofsimilar length , still not unfrequently found in Ireland; whilehe suggested, that the articles to which the present paper referred might be considered as furnishing a closely following,though later link in the chain.The sword bears no slight resemblance to one which hasbeen engraved in Walker's Essay on the Costume and Armsof the Ancient Irish, and which , attributing it to the KnightsTemplars, he states to have been found about forty yearsbefore, near the site of the old priory of Kilmainham. Itwas accordingly objected, that the weapons found at Larnebelonged to some one of that Order, and were therefore of amuch later date than that assigned to them as above mentioned. In reply to this, Mr. Smith urged the remarkablecirc*mstance of the bronze pin, of unquestionable antiquity,having been found in connexion with the sword, a fact ofwhich he was able to give the most decisive assurance, uponthe testimony of the overseer of the works, a person of strictest integrity, and who, not having any antiquarian predilections, could not be aware of the force or nature of the evidence he was furnishing. It was also to be recollected , thatlong antecedent to the establishment ofthe priory ofKnightsTemplars by Richard Earl Strongbow, in 1174, a monasticinstitution had been founded there by St. Magnen, fromwhom Kilmainham (which in many ancient documents is written Kilmayman) took its name so early as the sixth or seventh century of our era; and that the adjoining burial44ground was used by the Irish, we learn from the Munsterbook of battles, attributed to Mac Liag, a poet who died inthe year 1015, where it is recorded , that several ofthe chiefswho fell at the battle of Clontarf were interred at Kilmainham.In the hall of the Commander of the Forces is suspendeda sword ofthe same shape and character found in the oldburial ground, vulgarly known by the name of" Bully's Acre, "about forty years ago. In some adjacent fields, between theimmediate grounds ofthe Royal Hospital and the brink ofthe river Liffey, about four years ago, some labourers, employed in raising gravel, discovered a skeleton, around whichwere disposed a variety of weapons and ornaments; they arenow in the possession of the Commander of the Forces, andMr. Smith had the advantage of inspecting them. They consist ofa sword, lance head, and brass or bronze pin, all of precisely the same form and character as that now exhibited tothe Academy. The total length of the sword is 3 feet 2inches, the blade being 2 feet 8, and the handle 6 inchesin length; the pin measures about 6 inches . There wasalso found along with these a hatchet head, and some fragments of iron, so much shattered and corroded as to occasion some difficulty in coming to the conclusion, which however may be just, that they once formed an iron skull cap .Commonrumour asserts, that the labourer, by whom these remains were discovered , had also the good fortune to find withthem some ornaments of gold of considerable value; whichfact, for prudential reasons, he kept profoundly secret; butit* effects became speedily apparent, in a well- stocked shop,which he soon afterwards opened in a village not ten milesdistant from Dublin.In the Memoirs of the French National Institute, * a memoir is given, furnished by M. Mongez, concerning a Gaulishsword, as he denominates one found in the bed of the river

• Literature et Beaux Arts, tom. V.

45Somme, near Abbeville. A comparison of his description ,as well as of the engraving appended, shews this sword tohave been nearly identical in form and size with those foundin Ireland. This description , which applies in a remarkablemanner to the sword exhibited to the Academy, is as follows:• • ·"Sa lame et sa poignée ne font qu'un tout solidement affermi; elle a deux tranchans, et, loin d'être terminée enpointe, elle est obtuse et arrondie a son extremité. . . . Iln'y manque que l'osier tressé, ou la corde, ou le bois , ou enfinla substance qui entouroit la soie pour former une poignéesolide. La lame prolongée forme la soie sur laquelleest fixée la traverse de la poignée par le moyen de deuxclous rivés; et la masse imparfaitement arrondie qui la termine est traversée et maintenue par cette même soie.Longueur totale, 33 pouces 10 lignes; lame seule, 28 pouces10 lignes; poignée, 5 pouces; largeur de la lame a la poignée, 2 pouces 3 lignes."·Ifit be kept in recollection, that the French inch is somewhat greater than the English, these measurements will beseento correspond surprisingly with those ofthe sword foundat Larne. M. Mongez's paper exhibits great research andlearning. He quotes passages at length, from Polybius, Plutarch's Life of Camillus, Dion Cassius, and Strabo , whichdescribe with considerable minuteness the swords which theGauls used in their engagements with the Romans; and herests his argument not only onthe identity he alleges of thesedescriptions with that ofthe sword found near Abbeville, butalso on the fact of bronze and brazen ornaments having beenfound with skeletons having similar iron or steel weaponsabout them, discovered in 1788 at Velu, near Bapaume, inArtois. He adds, " Je puis donc assurer que l'épée qui estsous les yeux de la classe est l'épée gauloise décrite par lesauteurs anciens. J'ajouterai que c'est la seule à ma connaissance qui soit conservée. On jugera d'apres cela combien elle est précieuse pour l'etude des costumes anciens ."46Mr. Smith, in conclusion , drew the attention of the Academy to the circ*mstance that those and many other venerable and most interesting remains of remote antiquity, whichare but rarely, and at distant intervals of time, discovered inGreat Britain, and on the Continent, literally abound in Ireland; and hence inferred, the incalculable advantage whichwill be attained, in the study ofthe ancient history not only ofthis country but of the world, by the formation of a greatNational Museum of Irish Antiquities, such as is at presentprojected to be formed under the auspices ofthe Academy." Without claiming any undue importance for the pursuitof antiquarian research, it nevertheless has its office , andthat by no means an ignoble one, as the handmaid of history-' Principatum non habet; ancillari debet. ' It furnishes thecritical student not only with curious information and themost valuable commentary on minute points, but summonsup for him a host ofmost important witnesses, whom, thoughsilent, he can subject to the most scrutinizing examinationagain and again; on whose testimony, carefully weighed as toits true value, history ever rests as on its securest basis."The reading of a paper by the Rev. T. R. Robinson,D. D. , " On the Constant of Refraction, determined by Observations with the Mural Circle of the Armagh Observatory," was commenced.A paper by Dr. Andrews of Belfast, " on the Heat developed during the Combination ofAcids and Bases, " was read.The general conclusions at which the author arrives arecontained in the two following Laws.Law 1. " The heat developed during the union of acidsand bases is determined by the base, and not by the acid;the same base producing, when combined with an equivalentofdifferent acids, nearly the same quantity of heat, but different bases a different quantity.".47Law 2. " When a neutral is converted into an acid salt,no change of temperature occurs. "In the commencement ofthe paper a preliminary experiment is described, the object ofwhich is , to determine the exact quantity of heat evolved during the combination of nitricacid and potash. The solutions, both acid and alkaline, weretaken so weak in this and all the other experiments detailedin the communication, that subsequent dilution with water didnot produce any change of temperature. On neutralizing thesolution ofcaustic potash, containing 0.353 grammes of purealcali, with nitric acid, the temperature of the resulting solution of nitrate of potash, whose weight amounted to 30 gr. ,was found (after all corrections had been made) to rise 6.75°, F.To illustrate law first, the author adduces tables whichshew, at a glance, the heat produced when an equivalent ofeach base is neutralized by different acids. Thus, when thesame proportion of pure potash is combined under similarcirc*mstances with the arsenic, phosphoric, nitric, boracic,hydrochloric, hydriodic , and oxalic acids, the elevations oftemperature, indicated by the thermometer, vary onlyfrom 6.8 to 66°. Sulphuric acid produces rather ahigher temperature than any other acid (7.3°) , and theacetic, formic, tartaric, citric, and succinic acids, give rather less heat than those before mentioned (from 6· 4° to 6· 1º)In like manner, ammonia produces an increase of temperature varying from 5· 7° to 5.5° , when neutralized by the nitric,hydrochloric, hydriodic, arsenic, oxalic, and acetic acids;the greatest divergence from these numbers occurring, on theone hand, with the sulphuric acid (6.3°), and on the other,with the citric, tartaric, and succinic acids ( 5.1 °) . Analogousresults are described as having been obtained with otherbases, such as soda, barytes, magnesia, lime, and the oxidesof zinc and lead. On the contrary, the heat developed byeach base is peculiar to itself; and, consequently, the sameacid gives different elevations of temperature, with equiva-48lents of different bases. To take, as an example, the nitricacid, which also produces very nearly the mean quantityof heat given by all the acids, the following numbers express the increments of temperature obtained on combiningthe same quantity of it with each base: magnesia, 8· 1 °; lime,7.2°; barytes, 6· 9°; potash, 6· 8°; soda, 6· 5°; ammonia, 5· 6°;oxide of zinc, 4· 8 °; oxide of lead , 4· 2°; oxide of silver, 3.2°.The numbers for barytes, potash, soda, and ammonia, arestrictly comparable with one another (except a slight correction for differences in the specific heats ofthe solutions; ) butin the case ofthe other bases, an absorption ofheat, unknownin amount, takes place in consequence of their conversionfrom the solid to the fluid state. Hence the numbers forthese bases are all below the truth .Two singular anomalies are described as occurring in thecombinations of the peroxide of mercury with the hydracids,and in those of the hydrocyanic acid with the bases.In confirmation of the second law the author adduces aseries of experiments, which prove, that during the conversion ofa neutral into a supersalt no heat is produced. Thuswhile the normal development of heat occurs when a solutionofcaustic potash is neutralized by oxalic acid, the subsequentadditions, first of one, and afterwards of two more atoms ofthe same acid, so as to convert the neutral oxalate into thebinoxalate, and the latter again into the quadroxalate ofpotash, is not accompanied by any change of temperature inthe solutions. In testing the accuracy of this law, it is necessary to select examples where all the compounds are solublein water, otherwise the heat arising from the formation ofprecipitates would interfere with and complicate the result.The second law does not extend to the case ofthe conversion ofneutral into basic compounds,-a part of the subjectwhich the author has carefully investigated.PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1841. No. 27.January 25, 1841 .SIR WM. R. HAMILTON, LL.D., President, in the Chair.The Rev. Dr. Todd, V.P., made some remarks on twolarge medallion busts, with Greek inscriptions, which arepreserved in the Manuscript Room of the Library of TrinityCollege. These busts have been in the possession oftheCollege for upwards of a century, but there is no record inthe archives of the University stating how or from whomthey were obtained . In the Appendix to the Preface ofGudius's Inscriptiones Antiquæ, * the editors of that workhave given a list of inscriptions, which they state to havebeen furnished by Herman Van der Hoorst, Chaplain tothe Dutch in Smyrna; and, in this list, the very busts nowin Dublin are thus described, (No. XIII. ):"No. XIII. Smyrna in domo cujusdam Græci ZachariæThe full title of this work is as follows:-" Antiquæ Inscriptiones olim aMarquardo Gudio collectæ, nuper a Ioanne Koolio digestæ, hortatu consilioqueJoannis Georgii Grævii; nunc a Francisco Hesselio editæ, cum annotationibus eorum." Leovard. 1731. Fol.VOL. II. F50nomine, duæ muliebres imagines sculptæ adfabre, et incorruptæ; altera cum hac inscriptione,ΚΑΣ . ΛΥΣΙΜΑΧΗΝ ΤΗΝ ΦΙΛΑΝΔΡΟΝΟ ΘΡΕΨΑΣ ΘΗΛΥΜΙΤΡΗΣaltera cum hac inscriptioneΤΗΝ ΝΕΑΝ ΜΥΗΣΙΩΝ ΠΟΛΙΝΤΙΑΣ ΑΤΤΙΚΟΣ.”Dr. Todd stated that he had met with a letter in theBodleian Library, in which these busts are mentioned, and theinterpretation of the inscriptions discussed. It is preservedin the valuable correspondence of Dr. Thomas Smith, whowas Fellow of Magdalen College at the Revolution, andwhose lot it was to have been twice deprived of his Fellowship by the opposite parties of that period; first, by KingJames II. , when the attempt was made by that monarch toalter the constitution of the College; and secondly, by KingWilliam III. , when Dr. Smith resigned his preferment ratherthan take the oath to the new dynasty. The letter is addressedby Dr. Smith to Dr. Narcissus Marsh, then Lord Primate ofIreland, who had been Principal of St. Alban Hall , Oxford,and subsequently Provost of Trinity College, Dublin. Theportion ofthe letter which relates to the busts is as follows: -"The two busts sent to Dublin from Legorne, I supposecame from Smyrna, or the country thereabout, where oldmonuments are continually discovered."The first erected to the honour (for so I will favourablyinterpretit) ofClodia Lysimache (whois styled there píλavdpos,i. e. viri sive mariti amans; tho' oftentimes píλavdpos yuvǹ istaken in an ill sense for a lascivious and incontinent woman)by one who bred her up and maintained her, viz. , Thelymitres, if that be his proper name, which is not unlikely, tho'the appellative Onλúшurpos is used of an effeminate manabandoned to the excessive love of the other sex, and there-51fore explained by Suidas by the word róovoç. But bee thatas it will, hee was desirous to preserve the memory of hisOρεTTǹ or Alumna by this representation , as some of theΘρεπτῆρες οι οἱ Θρέψαντες used to do frequently enough, asis evident from undoubted inscriptions." "Tis pity, that the other inscription is imperfect anderased. Stephanus Byzantinus, in his booke Tɛpì wódɛwv,mentions Müns a city of Ionia, its viкòv or Gentilitiumnomen Munσlos, wch is the name in the inscription; butwhether Myes bee here meant by via róλis then newlyerected into a city, or some other city built by the inhabitants ofthe former, forced to remove to a more convenientand healthier place, the defect in the beginning, owing to theinjury of time after so many ages, will not suffer us to knownow who it was that did honour to this new city by settingup this monument, who I suppose was a Greeke of Attica,and the word preceding it may be the name of the tribe orSãμos to which hee belonged. If it be the same with Myûs,Muovç, as is very likely, then it is certaine that it was a maritime city of Ionia, not farre from the river Mæander, wch Ipassed over in my travells to take a view of the once famouschurches of Asia, on a rotten wooden bridge going thence,leaving Caria on the other side into Ionia, of we wee haveseveral accounts given by Strabo, Pausanias, and Pliny, notto mention other authors both Greek and Latine. Pliny nowlying upon my table I think fit to transcribe his words, Nat.Histor. lib. v. cap. 29 - Myús, quod primo condidisse Ionesnarrantur, Athenis profecti. But I do not pretend to write acommentary on these marbles, but leave that to be done bythose learned men, who are in possession of them. ”In a P. S. he adds:" Reviewing those hasty notes upon the two Greek inscriptions, I began soone to doubt of my conjecture aboutAtticus, as ifit had beene a patronymic, and the name ofthetribe or dãμos of Attica prefixed: but now I am prone to be1F 252lieve that this Atticus reckoned among the most famousorators of Greece, who flourished in the times of Hadrianand Antoninus Pius, and who had been sent upon several embassyes πρɛσßɛĩaɩ to Smyrna, and other free cityes of thelesser Asia, where hee presided with great honour, as appearsfrom Philostratus in the life of Scopelianus, and was thefather of Herodes Atticus, as hee is commonly called by theRoman writers, as if it were the name ofthe familye: whereasit should bee more properly Herodes Attici, viz., filius, as inthe inscription on his monument at Athens preserved byPhilostratus in his life.᾿Αττικοῦ Ἡρώδης, Μαραθώνιος, οὗ τάδε πάνταΚεῖται τῷδε τάφῳ, πάντοθεν εὐδόκιμος.This Herodes succeeded his father in the same honours athome, and in the like governments abroad, and was magnificent in his buildings and public works, in Greece and Italy,having been preceptor to Marcus Aurelius in the studyes oforatory (of which he was universally esteemed a most celebrated Master) as Julius Capitolinus has observed in the lifeof that Emperour, and Consul A.U.C. 896. A. Ch. 143. ButI thinke to the father, rather than the son, the Atticus inthe inscription is to bee ascribed, and if so, how hee comesto bee called Hippitias or Hippotias if that bee his prenomen, and the right reading , or whether Hippatias, orwhatever it should bee, bee the proper name of the person,who put up the monument, and Atticus of his country, Ihave not time nor leisure to enquire; and in the whole amno way fond of my conjecture, wch I look upon as altogetheruncertaine.""4 Nov. 1707. "*

• Collect. Smith, vol. 58 , p. 257.

53The following are exact representations of the inscriptions reduced to one-fifth of the original size: ΚΛ'ΛΥΣΙΜΑΧΗ -ΝΤΙΝΦΙΛ ΑΝΔΡΟΝ ΟΘΡΕΥΑΙ ΘΗΛΥΜΙΤ PHC ΑΝΜΥΗΣΙΝ ΠΟΛΙΝ ΤΙΑΣ ΑΤΤΙΚΟΣDr. Todd stated that one of the busts appears to havesuffered some injury since they were described by the editors54of Gudius, and by Dr. Smith. The second inscription haslost some letters; instead of THN NEAN, the words withwhich its first line then commenced, the last two letters ofthese words only are now discernible. He also exhibited tothe Academy fac-similes of the inscriptions, and made someremarks on the differences observable in the characters inwhich they are written.The Rev. Charles Graves, F.T.C.D. , read a paper Oncertain general Properties of the Cones ofthe Second Degree.Let a sphere be described whose centre is at the vertexof a cone of the second degree, and through the vertex lettwo planes be drawn parallel to the planes of the circularsections of the cone; the curve formed by the intersectionof the cone and sphere is called a spherical conic, and thetwo planes meet the surface of the sphere in two great circleswhich are called the cyclic arcs of the conic. These arcs,as M. Chasles has observed, possess properties relative tothe conic exactly analogous to those of the asymptotes ofa hyperbola. Moreover, many of their properties dependon the most elementary ones of the circle; but, as all theproperties of cones, and therefore of spherical conics, aredouble, each theorem relative to the cyclic arcs furnishes acorresponding one relative to the foci of the supplementaryconic, formed by the intersection of the sphere with a conewhose generatrices are perpendicular to the tangent planesof the cone on which the proposed conic is traced . Andfurther, the theorems relating to spherical conics becomeapplicable in general to the plane conic sections, by supposing the radius of the sphere to become infinite.These considerations, for which we are indebted to M.Chasles, are calculated to direct the attention of geometersto the cyclic arcs of the spherical conics. In following thistrack, Mr. Graves has been led to many new and general55properties ofthe cones of the second degree, amongst whichthe following deserve to be noticed:1. If two fixed tangent arcs be drawn to a sphericalconic, and any third tangent arc be drawn meeting them intwo points, the arcs passing through these two points andthrough the pole of a cyclic arc will intercept on that cyclicarc a portion of a constant length.2. If from two fixed points in a spherical conic, arcs bedrawn to any third point on the curve, and produced to meetone of the director arcs, they will intercept between them onthat director arc a portion which will subtend a constantangle at the corresponding focus.3. A spherical conic and one of its cyclic arcs beinggiven, if, round the pole of this cyclic arc, as vertex, a spherical angle of variable magnitude be made to turn, whose sidesintercept between them on the cyclic arc a portion of a constant length, the arc joining the points in which the sides ofthe moveable angle meet the given conic will envelope asecond spherical conic: the given cyclic arc will be a cyclicarc of the new conic, and this arc will have the same polewith relation to the two curves.4. A spherical conic and one of its foci being given, ifround that focus, as vertex, a constant spherical angle bemade to turn, and from the points in which its sides meet thedirector arc corresponding to the given focus, two arcs bedrawn touching the given conic, their point of concourse willgenerate a second spherical conic: the given focus will be afocus of the new conic, and the corresponding director arcwill be the same in the two curves.5. Ifa variable spherical angle turn round a fixed pointon the surface of a sphere so as to intercept between its sidesa constant segment on a fixed arc, the arc joining the pointsin which its sides meet two other fixed arcs will envelope aspherical conic touching these two fixed arcs.6. If a constant spherical angle turn round a fixed point56on the surface of a sphere, the arcs joining the points inwhich its sides meet a fixed arc with two other fixed pointswill intersect in a point, the locus of which will be a spherical conic passing through these two last mentioned fixedpoints.If two tangents to a parabola intersect at a constantangle, the radii vectores drawn from the focus to the twopoints of contact will also contain between them a constantangle. But, as is well known, in any conic section, thepoint ofconcourse of the tangents at the extremities of twofocal radii vectores, which contain between them a constantangle, will generate a conic section. Hence we deduce thefollowing very general properties of spherical conics.7. If two tangent arcs to a spherical conic intercept between them a segment of a constant length on a fixed tangent arc to the curve, their point of concourse will generatea second spherical conic.8. If aconstant spherical angle turn round a fixed pointon a spherical conic, the arc joining the points, in whichits sides meet the curve, will envelope a second sphericalconic.9. In theorem 7, if the segment intercepted on the fixedtangent arc be a quadrant, the point of concourse of thetangent arcs will move along an arc of a great circle.10. In theorem 8, if the constant angle be right, the arcwhich it subtends in the spherical conic will pass through afixed point.The two following theorems may be obtained by the aidof the equation of a spherical conic, expressed in sphericalcoordinates:11. From two fixed points on the surface of a sphere,the distance between which is 90°, let arcs p, p' , be drawnperpendicular to a moveable arc, and let a, ß, be arcs of asin 2p sin 2p'given length; if + 1 , the moveable arc will cos 2a cos 2B57envelope a spherical conic whose principal diametral arcsare 2a, and 2ẞ; they will pass through the fixed points, andthe centre of the conic will be the pole of the great circlepassing through the two fixed points.12. The base of a spherical triangle being a quadrant, ifcot 2aits base angles a, b, be such that +cot 23tan 26 = 1 , where tan 2aa and B are given arcs, the locus of the vertex will be aspherical conic, whose principal diametral arcs are 2a, and23; they will pass through the extremities of the given quadrant, and the centre of the conic will be the pole of thequadrant.Some of the preceding theorems lead to new and verygeneral properties of the conic sections: and one (No. 6)gives rise to a new and remarkably simple organic description of them. It should be observed that the arcs herespoken of are all arcs of great circles.His Grace the Archbishop of Dublin having taken theChair, the President continued the reading of Dr. Robinson's Paper " On the Determination of the Constant ofRefraction by Observations with the Mural Circle of theArmagh Observatory."The author remarks, that the problem of astronomicalrefraction is embarrassed by two causes of error. The differential of the refraction is obtained by supposing the atmosphere to consist of spherical shells concentric with theearth; and the integral of this, by assuming some mathematical relation between the height above the earth and thecorresponding density of the air. He shews that the firstof these cannot be rigorously true; and that the relationbetween density and height, besides being unknown in general, may be expected to vary with the latitude. Hetherefore considers all existing refraction tables as approxi-58mations which require correction for each individual observatory.For about 74° from the zenith, the refraction is independent of the law of density, and requires only an exactknowledge of the air's refractive power; this, however, hasnot been yet obtained with sufficient accuracy by directexperiment, and, therefore, must be deduced from astronomical observations. At greater zenith distances some constitution of the atmosphere must be assumed, and if itsexpression contain a sufficient number of arbitrary constants,the resulting refraction can always be made to representwith sufficient exactness what is actually observed . As,however, neither the formula of Bessel, nor that of Ivory,very readily admits such modifications, Dr. R. used themethod given by the late Bishop of Cloyne, in the twelfthvolume of the Royal Irish Academy's Transactions, which,however, he has extended to 85° zenith distance.If the atmosphere be supposed of uniform temperaturethe refraction has been computed by Kramp; it is foundgreater than the truth. If the density be supposed to decrease uniformly as the height above the surface increases,the refraction is given by Simson; it is nearly as much indefect as the other in excess, and it is found that their meanis very near the truth. If then the differential equation ofrefraction be developed in terms of the tangent of the apparent zenith distance, it is found, on integrating, that the firstterm belongs to an atmosphere bounded by parallel planes;the second depends on the equilibrium of the strata,and the others alone are affected by the assumed hypotheses. Their geometrical means are found to satisfy theArmagh observations as far as 85° zenith distance, belowwhich the series ceases to converge, and the mean changesits relation to the true refraction according to the temperature and pressure. The expression thus obtained for re-59fraction admits of being tabulated with the corrections forthe thermometer and barometer in a couple of pages; andhe thinks this form of tables more convenient than any otherwith which he is acquainted .To compute them are required the expansion of air byheat; the ratio of the height of the hom*ogeneous atmosphere to the radius of curvature of the meridian at the placeofobservation, and the refractive power of air at a giventemperature and pressure. For the first he has used thevalue given by Rudberg, namely, that 1 of air at 32° becomes 1.365 at 212° . This differs from Gay Lussac, but isidentical with that deduced by Bessel from astronomical observations. The second is derived from the researches ofArago and Biot, corrected for the change of gravity fromParis to Armagh.Of the refractive power of air there are different valuesof high authority. Denoting by the symbol u the quantitysin I Sig sin Rsin R Xsin 1 for 50° Fahrenheit and 29-60 inches pressure, the experiments of Arago and Biot give it 57-82. Theobservations of Delambre with a repeating circle give 57.72,which is also adopted by Brinkley. But the barometer usedby this great astronomer is shewn by Dr. R. to require thecorrection +0.078, which would change the constant to57.567; and as he also used the internal thermometer, perhaps a further diminution might be necessary. That ofBessel is 57.524, and that deduced by Dr. R. from his ownobservations is 57.546; but they cannot be exactly comparedwithout a knowledge of the length of the pendulum at eachstation, as the measure of density given by the barometerdepends on local gravity.It was determined as follows by circumpolar stars. Therefraction is obtained by subtracting from the subpolar distance 270° plus the declination observed above the pole. Ifthe constant of refraction require a correction, it affects this60declination both at the star and at the polar point, and thelatter also affects the subpolar observation; hence, callingthe tabular refraction μv, and the difference between it andthe observed dr, we have for each observation the equationof conditiondr = du { v - v' — 2P } = dµ × K;combining which by minimum squares, the value of du for thatstar is obtained. If the values of it at different zenith distances are equal, or differ only by what may reasonably beconsidered error of observation, then it may be also inferred ,that the formula correctly assigns the refraction throughthe range of zenith distance included by the observations.Dr. R. then gives details respecting the mural circlewhich he used, the permanence of its microscopes as to run,and the mode of obtaining its index correction, and the correction of its divisions. When the stars are spectra, hebisects the yellow near the green, and remarks that the fluctuations of irregular refraction are often of considerableduration. The hygrometric state of the air does not seem toproduce any effect, and he shews that the external thermometer is to be used at his observatory. The details of observation are then given for seventeen stars, from 77° 10' to84° 56′ zen. dist. , of which there are 317 subpolar observations.If a southern star be determined at a place when itpasses near the zenith, so that its place may be assumedas free from error of refraction, the value of du is multipliedby a much larger factor. This advantage, however, is morethan balanced by the uncertainty caused by the difference ofinstruments and local circ*mstances at the two observatories;but Dr. R. has given the result of such a trial. He usedthe declinations of Mr.Johnson, ( St. Helena Catalogue, ) and,in many instances, those of Mr. Henderson at the Cape, andby 241 observations from 77° 53′ to 84° 40′ he found for μ57.586; but conceives the result obtained from the northern61stars decidedly preferable, and has used it alone in computingthe tables which are given at the end of the paper.DONATIONS.Proceedingsofthe Royal AcademyofBerlin. July, 1838—January, 1840, with Index from 1836-39. Presented by theAcademy.Observations of the Magnetic Intensity in Europe. ByA. D. Bache, LL.D., &c. Presented by the Author.The Seventh Annual Report of the Royal Cornwall Polytechnic Society for 1839. Presented by the Society.Natural History as a Branch of General Education. Presented by the Natural History Society of Belfast.Proceedings ofthe Numismatic Society of London. 1838,1839. Presented by the Society.Proceedings ofthe American Philosophical Society. No.13. Presented by the Society.Flora Batava. By Jan Kops. Nos. 120 and 121. Presented by the Author.Memoirs of the Royal Astronomical Society. Vol. XI.Presented by the Society.Edinburgh Astronomical Observations. Vol. III . 1837.Presented by the Royal Astronomical Society.On Paralytic, Neuralgic, and other Nervous Diseases ofthe Eye. By Arthur Jacob, M.D. Presented by theAuthor.Quarterly Journal of the Statistical Society ofLondon.Vol. III. Part 4. Presented by the Society.An ancient Silver Ringfoundnear Drogheda. Presentedby Lieut. W. Persse Newenham, R.N.Model of Thumb Screws lately found in the Priory ofSt.James, Drogheda. Presented by the same.Alarge Collection of Miscellaneous Antiquities, consistingof Stone, Flint, Bronze, and Iron Instruments, Coins, &c. &c.Presented by Captain Portlock, M.R.I.A.62The special thanks of the Academy were voted to Captain Portlock for his large donation of Irish Antiquities.February 8, 1841 .SIR WM. R. HAMILTON, LL.D., President, in the Chair.Mr. J. Huband Smith submitted to the inspection of theAcademy the sword and other iron weapons, brass mantle-pin,&c. , with which he had been favoured bythe Commander oftheForces, and which were discovered , with a human skeleton,at Kilmainham some years since. He further produced astill more perfect iron sword, which was also most obliginglylent to him by Captain Hort of the Royal Hospital. This,too, had been found about eight years ago in the same vicinity, and under similar circ*mstances with the weaponsabove mentioned.The remarkable similarity of these, and all the incidentsof the interments which they appear to have accompanied,with the remains found in the county of Antrim, describedin the paper which Mr. Smith read before the Academy, onthe 25th of January, as well as with the engraving and description of the Gaulish (Celtic) weapons, the account ofwhich by M. Mongez, Keeper of the Museum of St.Genevieve at Paris, he had also on that occasion alluded to,together with the invariable discovery of bronze, or brassornaments, unquestionably Celtic, in connexion with them,induced Mr. Smith to adhere to his opinion, that allthese various remains were to be referred to people of Celticrace.If this conclusion be just, the inference would seem tofollow, that in the skeletons accompanying these weapons,&c. , an opportunity is offered to the student of ethnography63and the natural history of the human family, of investigatingthe characteristics of the pure Celtic type of a considerablebranch of the Caucasian variety of man.His Grace the Archbishop of Dublin communicated someobservations " On the Leafing of Plants."e.It is well known that there is a diversity in the times ofleafing and shedding in individual trees of the same species;.g. hawthorn, sycamore, horse-chesnut, beech, &c. , sometimes as much as a fortnight; and the earliest in leafare alsothe earliest shed, the same individuals keeping their time everyyear. Hence the question, whether this diversity arises fromthe " separable accidents" of soil, situation, &c. , or whetherfrom " inseparable accidents" which constitute what physiologists call varieties?An experiment was tried by grafting an early hawthorn ona late, and vice versa. The scions kept their times (about afortnight's difference) as if on their own stocks; thus provingthat it was a case of " seedling variety. "Many other such varieties are known, not only of apples,peaches, &c. , but of wild trees also, differing in shape of leaf,form ofgrowth, colour and size of fruit, &c. , and also time ofripening. It was, therefore, to be expected that there shouldbe the like, in respect of times of leafing.This may throw some light on the question respecting"acclimating." It may be, that species may be brought tobear climates originally ill- suited , -- not by any especial virtuein the seeds ripened in anyparticular climate, but by multiplying seedlings, a few of which, out of multitudes, may havequalities suited to this or that country, e. g. some to cold,some to drought, some to wet, &c.In some cases, a plant's beginning to vegetate later maysecure it from spring frosts, which would destroy a precocious variety; in others, earlier flowering may enable a tree toripen fruit in a climate in which a later would be useless, &c.64Further, the experiment shews that the common opinionrespecting the commencement of spring vegetation, —the riseofthe sap from the roots, through the trunk and branchesto the twigs, is groundless; since a scion of an early variety,on a late stock, will be in leaf while the stock is torpid.RESOLVED, ( on the recommendation of Council, ) " thatthe sum of £200 be placed at the disposal ofthe Committeeof Antiquities, to employ such portion ofit as they may deemnecessary in increasing the present collection of Irish Antiquities in the possession ofthe Academy."PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1841. No. 28.February 22, 1841.REV. H. LLOYD, D. D. , Vice-President, in the Chair.Mr. Charles T. Webber presented to the Academy anancient stone, on which is carved a rude bass-relief, supposedto be the representation of a dog killing a wolf. Mr. Webberaccompanied the present with a communication to the effect,that the stone was taken from the Castle of Ardnaglass, inthe barony of Tireragh and county of Sligo, and wassaid to commemorate the destruction of the last wolf inIreland. The current tradition in the place from whenceit came was, that some years after it was supposed thatthe race of wolves was extinct, the flocks in the countyof Leitrim were attacked by a wild animal which turnedout to be a wolf; that thereupon the chieftains of Leitrim applied to O'Dowd, the chieftain of Tireragh, ( whopossessed a celebrated dog of the breed of the ancientIrish wolf dog) , to come and hunt the wolf; which application being complied with by O'Dowd, there ensued achase, which forms the subject of an ancient Irish legend,detailing the various districts through which it was pursued,until at length the wolf was overtaken and killed in asmall wood of pine trees, at the foot of one ofthe mountainsin Tireragh. The quarter of land on which the wolf waskilled , is to this day called Carrow na Madhoo, which meansG66the dogs' quarter. In commemoration of the event, O'Dowdhad the annexed represention of it carved on the stone,placed in the wall of his baronial residence.andThe Secretary read the following " Collection ofNotes onthe early History of Science in Ireland." By James OrchardHalliwell, Esq., F. R. S. , F. S. A. , F. R. A. S. , &c." The following scraps on a subject which has never yetbeen treated of by any writer with whose works I am acquainted, although unfolding no views of any great importance, will, it is believed, form a subject of discussion interesting to all natives of Ireland , who would think favourablyof the intellectual character and resources of their countrymen." The earliest remnant of Irish science that I have metwith, is contained in MS. Arundel, 333, in the BritishMuseum, which contains several medical and astrologicaltracts in the Irish language of the thirteenth century,together with similar tracts of the fourteenth and fifteenthcenturies. These tracts are of a similar nature with contemporary manuscripts written in England and on the continent.67For instance, at fol . 27 , is an extract translated from thetreatise ofthe venerable Bede, " De Divisionibus Temporis;"at fol. 35, is a short tract on the months of the year andtheir several durations; at fol . 76, is a scrap on the fourseasons ofthe year, and on the planets which govern them." The whole volume contains astrology, mixed with thesciences of medicine and astronomy. Medical manuscriptsin Irish of this early period are more numerous than others;and the Egerton collection in the British Museum contains several; one dated in the year 1303, and written on thecontinent. *" Some writers say, that Johannes de Sacro Bosco, thecontemporary of Roger Bacon, and who shines so conspicuously in the history of the mathematical sciences of thethirteenth century, was a native of Ireland; but, whateverobscurity may hang over the actual place of his birth, it iscertain that he resided nearly the whole of his life in England and France, and there is nothing to show that hiswritings were ever circulated in that country." Be this as it may, yet it appears from MS. Egerton,No. 90, that the Arabic numerals usually, though erroneously,† ascribed to Roger Bacon, were well known andunderstood in Ireland at the commencement of the fourteenth century. The document contained in this volume isvery valuable evidence, in the absence of any other as early.The MS. referred to contains an astronomical and ecclesiastical calendar, together with a table of ecclesiasticalcomputation, all in the Irish character, and the numerals arewritten in identically the same form as they appear in foreigndocuments ofthe same period:-2 Z 3 & 4 6 1 8 9 0" The introduction of the zero is a proof, that the Arabic

• MS. Egerton, No. 89. + See my Rara Mathematica, p. 114.

G 268notation was fully understood by the writer of the manuscript. It may be added, that there follows, immediately afterthe documents just mentioned, a table of the twelve signs ofthe zodiac, with their different astrological influences, viz.:Aries good; Taurus = evil; Gemini evil; Leo = evil;Virgo = evil; Libra = good; Sagittarius = good; Capricornus = evil; Aquarius = good. The others are said to neutralize their influences." In the Philosophical Transactions of the Royal Society ofLondon, * Dr. Ward has given an account of a date in Arabicnumerals found on a stone in Ireland, which he consideredto belong to the twelfth century. Professor Peaco*ck, however, in his History of Arithmetic, has ably confuted thisconjecture.'" The Liber Niger of Christ Church, Dublin, is said tocontain a curious treatise on arithmetic, exhibiting thestate of that science before the introduction of Arabic numerals.'t I much question the accuracy of this statement,and should be rather inclined to think, that it is merely anaccount ofthe numbers ofalgorism, so common in manuscriptsof this class. The same volume also contains, a transcriptofthe French poetical treatise entitled ' Imago Mundi,' oneof the most curious unpublished scientific tracts of the middleages. This latter treatise is now in the progress of publication, by the Historical Society of Science."But by far the most curious document that I have metwith relating to the early science of Ireland, is a manuscriptin the possession of C. Wright, Esq. , of Cambridge, whohas kindly allowed me to make use of it, and has also furnished me with a translation of the greater part, which hasbeen of great assistance to me. This MS. consists of sixfolio leaves on vellum, slightly injured by damp, apparently

• Forthe year1745 , p. 283.

+ Report on the Public Records of Ireland, p. 307.69belonging to the early part of the fifteenth century, andcontaining the following articles:if" 1. A brief treatise on arithmetic." This unfortunately commences imperfectly in the account of the rule of duplation; ' In duplation only one orderoffigures is necessary: in the three preceding kinds, we commenced from the right and from a smaller figure; but in thisthis, and the following kinds, we commence from the left andfrom a larger figure. For if you wish to double from thefirst figure, it happens that you must double it twice. Andyou can in any other manner commence from the righthand, the operation and construction will be much more difficult. If, therefore, you wish to double any number, thatnumber must be written by its differences, and the lastnumber must be doubled. From that duplation , therefore ,either results a digit, an article, or a composite. If a digit,it must be written in the place of the other blotted out. Ifan article , a 0 must be written in the place of the otherblotted out, and the article must be removed towards theleft hand. If a composite number, the digit which is a partofthat composite must be written in the place of the otherblotted out, and the article be removed to the left hand.This being done, the last figure must be doubled, and whatever thence arises must be dealt with as before; but if acipher turns up, it must be left untouched. We prove duplation by means of mediation . '" This extract will be sufficient to give an idea of the wholetract. After this rule, follow those of multiplication , division ,and progression in their proper order. For the comprehension of the uninitiated in the old arithmetic, it may be necessary to state, that a digit is any number below ten, an articleis ten, or any multiple of ten , and that all other numbers arecomposites, or composed of an article and some digit . Myfriend Mr. Wright, gives it as his opinion, that this tract isa translation from the Latin or French.70"2. Tractatus de Geometria. '" This is an Irish tract with a Latin title, and consists ofonly one page, containing the simplest rules of geometricalmeasurement, applied to one example of finding the heightof a tower. No mention occurs of any ofthe old geometers." 3. A treatise on the signs of the zodiac."An astrological tract with very curious drawings of thevarious signs . Messabalah, the famous Arabic astronomer,is mentioned at the commencement, and this tract is veryprobably translated from one of that author's works." 4. A treatise on the length of the days, in the year." 5. Afragment (one half page)." This terminates the contents of this manuscript, and iswritten in Latin. It appears to relate to abacal arithmetic,but as I confess myself unable to understand its meaning, Igive it here entire, in the hopes that some other may bemore fortunate in attempting to decipher its meaning." Intervalla autem in quibus distribuuntur. dicimus sedeshorum numerorum. qui in abaci regula secundum geometricam habitudinem sic proportionaliter ordinati continentur .ut juxta numerum novem caracterum nonis termis alternatidistinctis terminis. secundum propor."I have pointed this exactly as in the original manuscript,but the fragment appears to be altogether unconnected ." In addition to the above, I may mention, that in thelibrary of Trinity College, Cambridge, under the press markR. xiv. 48, is preserved a short poem in the Irish language onastronomy, of the early part of the thirteenth century. *And in the the Bodleian Library, MS. Rawlinson, B. 490, isa translation of the Secreta Secretorum,' of Aristotle, byJames Yonge, on vellum, of the early part of the fifteenth6

• This I learn from Mr. Wright. In the printed catalogue, it is said to be in

Saxon characters.71century. This work of Young is not mentioned by SirJames Ware, nor does it appear to be at all known to Irishwriters. It is almost unnecessary to observe, that this latterwork has no relation with science, but its rarity is a sufficient excuse for mentioning it here.6" It will now be necessary to pass over nearly two centuries before we meet with any traces of scientific progress.Some time about the year 1600, William Farmer, Chirurgian and Practitioner in the Mathematicall Artes,' dwelt atDublin; and among the manuscripts of Archbishop Tenison,at Lambeth Palace, No. 816, is an autograph MS. by him,entitled, ‘ A Prognosticall Almanack for this Bissextile yere,1612, composed with a three fould Kallender generally calculated for this Kingdom of Ireland, and will also serve verywell for alle the Northe and Northweste partes of England.'William Bourne also, who flourished at the same time, andgreatly distinguished himself by his mechanical inventions,was a native of Ireland . To these two we may add , NathanielCarpenter, an Englishman by birth, but who resided inDublin early in the seventeenth century, and left behind himtreatises on geography and optics. A copy of this latterwork is still preserved in MS. in the Library of UniversityCollege, Oxford. *"With Molyneux , in more recent times, the science ofIreland rose to a level with that of surrounding nations, andthe names Ponce, Boyle, Petty, and Ashe, † serve to fill thecomplement ofthe seventeenth century. In January, 1684,Molyneux succeeded in forming a Philosophical Society atDublin, on the plan of the Royal Society of London. Thefirst meeting of the Society took place on the 28th of January, 1684, when Sir William Petty was chosen President,Under the press mark L. 14. See Bernard's Catalogue, 1697 , p. 5.† Archbishop Ussher was the author of some treatises on sciences and theirhistory, more especially astronomy.72Dr. Charles Willoughby, Director, and Molyneux undertook the combined offices of Secretary and Treasurer.November 1st, All Saints' day, was chosen for the anniversary ofthe Society. On the 1st of November, 1684 , SirWilliam Petty was re- elected President, Molyneux as Secretary, and William Pleydell, Esq. , Treasurer. On the 2nd ofNovember, 1685, Lord Viscount Mountjoy was elected President, George Tollet, Esq. , Treasurer, and St. George AsheSecretary. Inthis year, Molyneux retired from actual office ,but retained his place on the council of the Society. Onthe1st of November, 1686, Lord Viscount Mountjoy was reelected President, George Tollet Esq. , Treasurer, andEdward Smyth, Secretary." The preceding particulars are taken from the originalMinute-book of the Society preserved in the British Museum,MS. Addit. 4811. * The last entry in this book is, theaccount ofthe General Meeting of 1686, and this would leadus to suppose that the Society was dissolved at this period ,although Dr. Hutton assures us, that it was not broken uptill 1688.†"From MS. Addit. 4812, it appears that in the year 1707,an attempt was made to reestablish the Society, but its success was not of any long duration, and this MS. contains aregister ofthe philosophical papers read before the Society,from August 15th, 1707, to March 11th, 1708. The Earl ofPembroke, then Lord Lieutenant of Ireland , presided overthe Society at this revival." In 1686, Molyneux printed at Dublin, his ' SciothericumTelescopium,' containing a description of the structure anduse of a telescopic dial invented by him. In the BritishMuseum is preserved the author's own copy ofthis volume,

• The same volume likewise contains copies of numerous letters and papers on

scientific subjects, addressed for the most part to Molyneux.+ Mathematical Dictionary, vol. ii . p. 117.73enriched with numerous MS. notes, and observations, andwhat is particularly worthy of being noticed, an analysis ofits history. "March 16, (Stated Meeting).SIR WM. R. HAMILTON, LL.D. President, in the Chair.Onthe recommendation of Council, the following gentlemen were elected Honorary Members of the Academy:Professor Adrian, Giessen.Jean B. Dumas, Paris.A. Quetelet, Brussells.J. O. Halliwell, Esq. , Cambridge.The Secretary of Council read the following Report:In conformity with the precedent lately established , the Council, at the expiration of their year of office, beg to offer the Academy a general account of its history and progress during thatinterval.The Council have to report, in the first place, that the publications of the Academy have proceeded with considerable vigour.The first Part of Vol. XIX. of the Transactions has been latelyissued, and the second Part, for which many papers are in readiness,is now beginning to be printed . The first Volume also of theProceedings, containing, along with other ordinary business, anaccount of the communications made to the Academy during thelast four sessions, has just been published. As the quantity remaining on hands ofthefourth Number of the Proceedings wasremarkably small, the Council, on the recommendation of theCommittee of Publication, have ordered 250 copies of that Number to be reprinted, by which means a large stock of completecopies of the first Volume has been made up for the supply offuture demands, and for sale to Members and others at a fixedprice.74The Council are gratified to observe the increasing interestwhich is every day felt in the publication of the Proceedings. Notbeing confined to the mere analysis of elaborate memoirs intendedfor the Transactions, but giving free admission, and occasionallycomplete insertion, to smaller papers of various kinds, the Proceedings serve as a repository for scattered facts, and important notices, which would otherwise be lost. Speedy publication is an additional inducement to authors to communicate such notices; andby the adoption of woodcuts for antiquarian and scientific objects,of which the mere verbal description would be vague and unsatisfactory, the value of the communications is very much enhanced.The expenses of printing and engraving continue, as might beexpected, to press very heavily on the funds of the Academy.With the view, therefore, of practising every possible economy,the Council have entered into an arrangement with Mr. Petrie, bywhich that gentleman has bound himself to print, at his own risk,his Essay on the Round Towers of Ireland , as the twentieth Volumeof the Transactions, engaging to supply the Academy with 450copies of the work at a settled price, the sum which they have already expended for engraving to be deducted therefrom. TheAcademy will thus be furnished with as many copies as they want,and will be saved the additional outlay which would be requisite ifthey were themselves to defray the charge of the whole edition.After the great and unusual delays which have attended the publication of this Essay, the Council are gratified in being able tostate that it has been actually put to press, and that the authorconfidently expects it will make its appearance soon after the secondpart of the nineteenth Volume of the Transactions.Notwithstanding the limited extent of the resources of theAcademy, the Council are of opinion that the formation of a National Museum of Antiquities is an object which the Academyshould continue steadily to pursue, as far as these resources willreasonably permit; and since many articles of great value to theantiquarian are disposed of from time to time by public and byprivate sale, and may never again be met with, if such opportunitiesof procuring them are lost, they have thought it advisable torecommend to the Academy that a sum of money should be en-75trusted to the Committee of Antiquities to enable them to profit bysuch chances. The Academy have accordingly, by a recent vote,placed at the disposal of the Committee the sum of £200, whichwill probably serve the purpose for a considerable period. In themeantime, from the liberality of members and other gentlemen,the Museum is receiving constant accessions, which are regularlyrecorded in the Proceedings, and among which the large donationlately made by Captain Portlock is deserving of especial mention.In touching on this subject, the Council are reminded ofthesevere loss which the Academy have sustained by the decease oftheir late respected Vice- President, the Very Rev. Henry RichardDawson, Dean of St. Patrick's , a gentleman universally lamentedby those who had the pleasure of knowing him in private life, butwhom the lovers of Irish antiquities have peculiar reasons to regret; for he was a zealous preserver and collector of the old memorials of his country, and the treasures of this kind which he hadaccumulated in a period of many years, would have been bequeathedto the Museum now begun withinthese walls, had not his wellknown intentions been frustrated by the suddenness of the strokewhich removed him from amongst us. The Dean having died intestate, his collections will of course be sold; but as they willfetch a price far above what the Academy could afford , a subscription, which it is to be hoped may be successful, has been seton foot, under the management of the Committee of Antiquities ,for the purpose of depositing these valuable remains in the placefor which they were intended by their generous collector.The past year has also deprived us of some other distinguishedMembers, among whom was Thomas Drummond, Esq. , Captain inthe Corps of Royal Engineers, and Under- Secretary of State forIreland. In his professional character, Mr. Drummond was remarkable for combined energy and talent, and for the singularpower which he possessed of making the truths of science availablefor important purposes in practice. Though this was not thecountry of his birth, yet it was here that he spent the most activeperiod of his life. Engaged in the Ordnance Survey, at its commencement in this kingdom, he enriched the practice of geodeticaloperations with some of its most useful instruments, which have76now become indispensable in the observation of distant stations;and it deserves to be remembered, that it was from the summit ofSlieve Snaght, in Donegal, to a party stationed on the hill of Divis,near Belfast, that he first exhibited , across the haze of Lough Neagh,the celebrated Light which bears his name, and which will serve,better than any monument, to perpetuate his memory.In the person of Nicholas Aylward Vigors, Esq. , late Memberof Parliament for the county of Carlow, the Academy and the scientific world have lost one of the best zoologists of his day. Hispapers, in the department of ornithology more especially, are highlyesteemed by naturalists; and the zeal which he felt for the advancement of his favourite science was manifested in the active partwhich he took, along with some other eminent men, in the foundation of the Zoological Society of London.But a very few days have elapsed since the hand of death hasblotted from our roll the honoured name of Laurence Earl ofRosse, one of the original Members of this Academy, and one ofthe ablest vindicators of the ancient literature of Ireland. Oftheillustrious noblemen and gentlemen who founded our Society, whowatched over its infancy, and powerfully promoted its early progress, his Lordship was the last survivor. Hitherto, for more thanhalf a century of our corporate existence, our meetings have beencheered by the presence of some-though a constantly decreasingnumber of those who witnessed their beginning, and who felt, asit were, a paternal interest in our welfare. But now they haveall disappeared from amongst us. Let us endeavour to show thatwe are worthy to succeed them; for so we shall best do honour totheir memory.The other Members whom the Academy has lost by deathwithin the year are:The Earl of Ranfurly.Right Honourable Lord Garvagh.Rev. Sir Francis Lynch Blosse, Bart.Arthur Hamilton, Esq. , L.L.D.Rev. Hosea Guinness.John Crampton, Esq. , M.D.wyAnd the new Members added to the body since the 16th ofMarch, 1840, are:J. Davidson, Esq.Abraham Abell, Esq.J. H. Blake, Esq. , Q. C.G. Wilkinson, Esq.Rev. Henry Barry Knox.Rev. J. West.Thomas Fortescue, Esq. , M.P.Chichester Bolton, Esq.George Willoughby Hemans, Esq. Henry Coulson Beauchamp, M.D.In accordance with the suggestion of the Council of last year,the Council have ordered the compositions received in lieu of annualsubscriptions to be henceforth invested in the Government Funds.The following have been added to the list of Societies withwhom the Academy interchange Transactions:The Bavarian Academy of Sciences.The Institute of Sciences of Milan.The Rotterdam Society of Sciences.In connexion with the subject of Mr. Webber's remarksat the last meeting, Sir W. Betham communicated the following document, giving an account of an order made by KingJames I. for the destruction of wolves in Ireland.Patent Roll, 12 Jac. I. d. R. 17. "The King being givento understand the great loss and hindrance which arose inIreland by the multitude of wolves, in all parts of the kingdom, did by letters from Newmarket, 26th November, 1614,direct a grant to be made by patent to Henrie Tuttesham,who by petition had made offer to repair into Ireland , andthere use his best skill and endeavour to destroy the saidwolves, providing at his own charge men, dogs, traps, andengines, and requiring no other allowance, save only fournobles sterling, for the head of every wolf, young or old,out of every county, and to be authorized to keep four menand twelve couple of hounds in every county, for seven yearsnext after the date of these letters." 12 Jac. s. L. R. 27.The Rev. C. Otway read a letter from Mr. Blacker, onthe origin of the emblem of the shamrock.78Mr. J. M. Ferrall drew the attention of the Academy toseveral drawings, and a preparation, exhibiting a new andbeautiful mechanism belonging to the human eye, anddiscovered by him in April last, while engaged in researcheson certain diseases of the orbit, which the received anatomyof those parts did not appear to him to explain.The new structures consisted of a distinct fibrous tunic,investing the globe of the eye, facilitating its movements,and separating it from all the surrounding tissues.The anatomy of the schools , and of the best authors,from the earliest time to the present, teaches that the ball ofthe eye is in contact with its muscles, and, between them,with a quantity of adipose substance on which it was supposed to be cushioned. It was difficult to conceive , however, why the eye did not manifest any of the symptomsincidental to pressure suddenly endured, whenever thosemuscles were brought into action , since there appeared tobe no provision for its protection. That pressure, suddenly made on the globe of the eye, produces the sensationof a spark or flash of light, is familiarly known as the consequence of a slight blow on the eye.The act of sneezing is frequently followed by a similarphenomenon, and Sir Charles Bell has shown, in a paperpublished in the Philosophical Transactions, that it is occasioned bythe sudden pressure on the ball of the eye, bytheorbicularis palpebrarum or principal muscle of the eyelids,which is suddenly brought into action by the respiratorynerves. The four recti muscles, which move the eye in different directions, being favourably placed, (according to thereceived anatomy) , for exercising such a pressure, it mighthave been expected that a similar phenomenon would haveresulted; but no such coruscations have ever been observedto follow their most rapid actions.The discovery of this tunic, which Mr. Ferrall has ventured to term the TUNICA vagin*LIS OCULI, at once explains79the absence of those phenomena, by showing that a protective provision has always existed to prevent them.Mr. Ferrall went on to state, that the most beautiful portion of this mechanism remained to be described. It wasone ofthose exquisite manifestations of design which aboundin the animal frame.In the anterior portion of this tunic were to be foundsix different well defined openings, through which the tendons ofthe muscles pass to their insertion in the scleroticcoat ofthe eye, and over which they play as over pulleys intheir progress.The annexed engravings, executed from original drawings made in April, 1840, for Mr. Ferrall's clinical lecturesin St. Vincent's Hospital, display this conformation faithfully.Fig. 1 , shows the tendon of the internal rectus, emergingfrom behind the tunic, and passing through its pulley to beinserted in the eyeball.Fig. 2, represents the eyeball drawn downwards, inorder to expose the exit of the tendons of the superior80rectus and superior oblique muscles; the superior rectusplays over its pulley, and the superior oblique passes beneaththe former to reach its insertion in the sclerotic coat.The presence of some such contrivance as is here exhibited might have been inferred from its necessity, and yetit has never been suspected to exist. The four recti musclesrunning from the bottom or apex of the orbit, forward to graspthe eye, must, without it, have had the power of retracting theball ofthe eye, and yet no such retraction has ever been observed in the human eye. Retraction is certainly performedin some ofthe lower classes of animals; but they are providedwith a strong retractor muscle, independent of the four rectimuscles. Again, the rotatory movements of the human eye,which enlarge the sphere of vision , and contribute to expression, are not easily accounted for by the received anatomy ofthe orbit, because the course of the muscles fromthe bottom of the orbit forwards, manifestly gives them apower of retracting rather than of rotating the eye upon itscentre. Thus, then, there appeared to be no provision for81the rotatory movements ofthe ball ofthe eye, which are ofconstant occurrence, and nothing to prevent retraction, whichwe knew did not take place. A knowledge of the existenceof this new and beautiful mechanism reconciles and explainsthese anatomical and physiological contradictions.Mr. Ferrall said, he had found these structures in severalof the lower animals , in whom they appear to enable therecti to antagonize the proper retractor muscles.Several phenomena in diseases of those parts, formerlyobscure, are now easily understood; but Mr. Ferrall refrained, on this occasion, from discussing questions of apractical nature.The Auditors appointed by Council to examine the Treasurer's Account, for the year ending December 31 , 1840, reported as follows:" We have examined the above account, * with the vouchers produced, and have found it to be correct; and we find that there is abalance in Bank of £100 7s. and in the Treasurer's hands, of£110 9s. 4d. making a total balance of 210 16s. 4d.66' (Signed, )" FRANC SADLEIR." SAMUEL LITTON."March, 13th 1841."" The Treasurer reports that there is £1390 17s. 4d. in three percent. consols, and £1526 6s. 1d. in three and a- half per cent. Government Stock, to the credit of the Academy, in the Bank of Ireland;the latter being the Cunningham Fund.66 (Signed, )" THOMAS HERBERT ORPEN.“March 18th, 1841.”The ballot for the annual election having closed , thescrutineers reported that the following gentlemen were dulyelected Officers and Council for the ensuing year:

• Entered in the Treasurer's book.

H82President.Sir Wm. Rowan Hamilton, LL.D.Committee of Science.Rev. Franc Sadleir, D.D., Provost; Rev. HumphreyLloyd, D.D.; James Apjohn, M.D.; James Mac Cullagh,Esq. , LL.D.; Rev. William D. Sadleir, A.M.; Robert Ball,Esq.; Robert Kane, M.D.Committee ofPolite Literature.His Grace the Archbishop of Dublin; Rev. Joseph H.Singer, D.D.; Samuel Litton, M.D.; Rev. William H.Drummond, D.D.; Rev. Charles R. Elrington, D.D.; Rev.Charles W. Wall, D.D.; Rev. Thomas H. Porter, D.D.Committee of Antiquities.Thomas H. Orpen, M.D.; George Petrie, Esq. , R.H.A.;Rev. Cæsar Otway; Rev. James H. Todd, D.D.; Henry J.Monk Mason, Esq. , LL.D.; Aquilla Smith, M.D.; SamuelFerguson, Esq.Officers.Treasurer. -Thomas H. Orpen, M.D.Secretaryto the Academy.-Rev. Joseph H. Singer, D.D.Secretary to the Council. -J. Mac Cullagh, Esq. , LL.D.Secretary ofForeign Correspondence. -Rev. HumphreyLloyd, D.D.Librarian.-Rev. William H. Drummond, D.D.Clerk and Assistant Librarian. -Edward Clibborn.The President appointed under his hand and seal thefollowing Vice- Presidents:His Grace the Archbishop of Dublin; the Provost of83Trinity College; the Rev. Humphrey Lloyd, D.D.; theRev. J. H. Todd, D. D.DONATIONS.Résumé des Observations Météorologiquesfaites en 1839 ,a l'Observatoire Royal de Bruxelles, par A. Quetelet.Second Mémoire sur le Magnétisme Terrestre en Italie,par A. Quetelet.Deuxième Mémoire sur les Variations Annuelles de laTempérature de la Terre a différentes profondeurs , par A.Quetelet.Extraits du Tom. VII. No. 2, des Bulletins de l'A. R. deBruxelles. No. 2. Température de la Terre. No. 3. Magnetisme Terrestre. No. 4. Magnetisme Terrestre. Par A.Quetelet. Presented by the Author.Bulletin de l'Academie Royale de Bruxelles. Nos. 1—8An. 1840. Presented by the Academy.American Almanackfor 1841. Presented by the AmericanPhilosophical Society.Nautical Observations on the Port ofCardiff. By Captain W. H. Smith, R. N., &c . Presented by the Author.Ninth Report of the British Association. Presented bythe Association.A Catalogue of the Miscellaneous Manuscripts in the Library ofthe Royal Society. ByJ. O. Halliwell, Esq. , F.R.S.,&c. Presented by the Royal Society.A Collection of Letters illustrative of the Progress ofScience in England. Edited by J. O. Halliwell, Esq. , F.R.S. ,&c. Presented by the Editor.Proceedings of the Royal Society of Lordon, 1839-40.Nos. 41-44. List of Members of the Royal Society ofLondon, (30th November, 1840) .Philosophical Transactions ofthe Royal Society ofLondonfor 1840. Parts I. and II. Catalogue ofthe Miscellaneous84Manuscripts in the Possession of the Royal Society. Presented by the Society.Remarks on the Classification of Human Knowledge. AnElementary Treatise on the Tides. On the Theory of theMoon. On Currency. By J. W. Lubbock, Esq. Presentedby the Author.An Examination of the ancient Orthography ofthe Jews.Vol. III. By Rev. C. W. Wall, D.D. Presented by theAuthor.The Negroland of the Arabs. By W. DesboroughCooley, Esq. Presented bythe Author.Constitution and By-Laws of the National Institutionforthe Promotion of Science at Washington.Discourse on the Objects and Importance ofthe NationalInstitution for the Promotion of Science. By Joel R. Poinsett, Esq. &c. Presented by order of the Directors.Memoires de la Société Géologique de France. Tome4me. Ire partie. Pesented by the Society.PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1841. No. 29.April 12.SIR WM. R. HAMILTON, LL.D., President, in the Chair.The following gentlemen were elected Members of theAcademy:William Monsell, Esq. , Robert Tighe, Esq. , W. E. Hudson, Esq. , G. Fitzgibbon, Esq. , William Phibbs, Esq. , Rev.James Reid, William Lee, Esq. , F.T.C.D., Robert Jones,Esq., Thomas Wilson, Esq. , Beriah Botfield, Esq. , M.P. ,W. T. Mulvany, Esq.Mr. Ferguson made a communication on the Classificationofancient Military Weapons found in Ireland .DONATIONS.Transactions of the Cambridge Philosophical Society.Vol. II. Part 2; Vol. III . Parts 1 , 2, 3; Vol. IV. Part 1;Vol. V. Part 3. Presented by the Society.Onthe Geological Structure ofthe Northern and CentralRegions ofRussia in Europe. ByR.J. Murchison, F.R.S., &c.Presented by the Author.Proceedings ofthe Geological Society ofLondon. Nos. 74and 75. Presented by the Society.Journal of the Franklin Institute. Vol. XXVI. ( 1840) .Presented by the Institute.The Numismatic Chronicle. No. 12. Presented by theNumismatic Society of London.VOL. II. IACADEMY ,ROYAL IRISH THE ACCOUNT ABSTRACT OF1841 .ENDING MARCH 31,FOR THE YEAR.CHARGE TEGrant Parliamentarysold .TransactionsAcademy the offavour inBalancec.&Taxes ,Rent for warrants TreasuryStock Government ,31500 on£interest year's half Ones.d£300 0146781426d.£S. 7439 Coals ,andles &c. THE DISCHARGE . d£.s 47 ds.£ 61817446142 6half One do. do. half One half One do. do. do. Consols cent ,3pr 5s.8d1367 £ Stock 1526 6s.1d,3£ cent Cosols per 4d.,3175.390 £ 0526102214263 1720Repairs ofHouse ,Furniture &c. Rent ,Taxes and Isurance Books ,Printing and Stationery Salaries ,Servants 'Wages &c. ContingenciesDischarge Theotal favour Blance inofthe Academy568219349 25397 250 971541210455 14599467stable ofrent yar's One Poor Rate ofAllowance 21 081 2222 18 Subscriptions Life 18065 • Entrance do.Annual do. 840014224 474 120The total charge £111462 before Charge asThe £111462.THE BALANCE OFSTATEIreland ofBank Inhands InTreasurer'sBalance asbove• £40 0194£5914Signed , ORPEN ,Treasurer .THOMAS HERBERT87April 26.Rev. H. LLOYD, D. D. , V.P. , in the Chair.Mr. George Downes read a paper " On the Norse Geography of Ancient Ireland." The earlier part consistedof remarks on an " Essay on the earliest Expeditions fromthe North to Ireland," and on a small Map of Ireland accompanying it, as published in the Annals and Memoirs of theRoyal Society of Northern Antiquaries .The author began by adverting to the two provincialnames on the map -Úlaztir (Ulster) , and Kunnáktir (Connaught), —andto two names ofdistricts in Leinster-Dyflinarskíri, or Dublinshire, and Kunnjáttaborg (a part of Meath) .He argued that the local name in Johnstone's edition ofLodbroc's Death-Song, translated " Leinster's," more probably belongs to Lambay, the Avios of Ptolemy, supporting his argument also by a geographical consideration. -Henext proceeded to the estuaries -Jöllduhlaup, supposed tobe Lough Swilly; and Úlfreksfjörðr, or Úlfkelsfjörðr, supposed to be either Lough Foyle or Carlingford Bay, butperhaps an English locality, and, if so, that arm of Morecambe Bay which runs up to Ulverstone.-The townDyflin he stated to be evidently a Norse adaptation of theIrish name of Dublin; Veðrafjörðr, or Waterford, to beundoubtedly Norse, adducing its various derivations, andgiving the preference to veðr “ weather," and fjörðr “ bay; ”and Hlimrék, or Limerick, to be probably a Norse adaptationofthe Irish name Luimneach, notwithstanding its consistingoftwo Norse words, meaning " branch" and " district, " andthe resemblance between the Lower Shannon and the Limfiord, or " branching bay, " in Denmark. Kunnjáttaborg, orKantaraborg, given in the Antiquitates Celto- Scandicæ asKunnaktirborg, and (in the genitive form) Kantaraborgar—the place of Brian Boru's nuptials with Kormlöda, or GormI 288liath he concluded to be Cancora; and then adverted to theminor localities of Iniskillen (perhaps Inisclothran, in LoughRee) , Themar ( Tara) , and Glendelaga (Glendalogh) .The name Smerwick, laid down as Smjörvik on the map,but left unexplained in the essay, was traced by the authorto two sources. The first derivation-from smjör " butter,"and vikbay," or " town"-was supported by the frequencyofthe former word as an element of Norse local nomenclature, and the probability that some trade in butter was carried on between the Northmen and the south-western Irish.A curious tradition, connected with the fortunes of Leif,the son of Hrodmar, was adduced, in which the name mynnthak occurs-that is, meal and butter blended together-aword apparently identical with the Irish móinceaċ " boggy,"and somehow connected with the discovery of butter, or anadipocere resembling it, in the Irish bogs. The second derivation was founded on a tradition current in Munster, thatSmerwick is a contraction of St. Mary's Wick; and a tradition from Olave Tryggvason's Saga was adduced, showingthe probability that, if it be so, the name is due to him.Kaupmannaey, laid down on the map at the entrance ofBelfast Lough, and also left unexplained in the essay, wasshown to be Copeland Island.Mr. Downes prefaced the latter part of his subject bybriefly adverting to the principal countries, in which theNorthmen have left topographical traces of their invasionsnamely, Normandy, Eastland (extending from Mecklenburgh to the White Sea) , and the British Islands—alluding tovarious classes of Norse names occurring in Normandy, a fewsolitary instances inEastland, and dwelling at some length onthose found in Ireland. A minute analysis of the Irish localities, ending in ford, was closed by the inference, that asOdin's Ford, in the county of Carlow, is certainly a Norselocality, so Urlingford, Freshford, and Erke, in the adjacentcounty of Kilkenny, are Norse likewise. Aless minute ana-direct asuu mayou ,son write Pay follow will itColleged.Cainly theomefollow wi ittoGive myнеtomstion tolove Bebe &MyDearسلندimeYouyStart Charles Wolpefouthanting Rememberbarbet say ajainistobedrawn amontfumepardon willfrom message any aboutThethatYoupartientquanسلんhere will ,&Moore Jhn Sir ofBnial the completed have Iinflict itupon your;ou have noonetoblome ,inmining thewo planzer ,thatbut youselyFold youActfor1-INot adrum was heard ,not funeral anoteits his corse the compant wehurried:Soldier discharged his farewell shots .webined thes onwhere grave Per thenight ofdead at,darkly him buried We 2with The sods the By очи bayonets turning .shuphing moonbean's mish ,lghtcansom gun That the Foe way sullenly fixing-89lysis was undertaken with several similar names; after whichthe author proceeded to a rapid scrutiny of names of baronies, townlands, and towns-noticing in particular , as whollyor partly of Norse derivation, Rathgorman, Slaghtmanus,and Ballyvedra, alias Weatherstown, near Waterford. -Thelast class of Irish names analysed was that of islands. Several instances were adduced of insular localities derivablefrom some one of the three Norse words for island-ey,holm, and kalfr-the distinctive meanings of which wereexplained. The name of a locality, in particular, off thesouth coast of Iceland , called " Irishman's Islands," wasexplained from the sequel of the tradition of Leif, beforecited .The author closed his paper by recommending to theantiquary some attention to the neglected literature of theNorth, as a means not only of accumulating information, butof correcting error; and concluded by adducing the following examples of error, corrected by a comparison of specimens found in different countries: —'" The short sword ,or dagger,' with which King, in his account of Richborough,has equipped a Roman bagpiper, would still maintain itsbelligerent masquerade, had not the discovery of a more perfect specimen in Scandinavia proved it to be the more appropriate appendage of a pipe; and certain figures, publishedby Pennant, which were deified in Sweden, might have longenjoyed their sanctity, had not the subsequent discovery ofmore perfect specimens in Denmark desecrated them intoknife-handles. "Dr. Anster, on the part of Dr. Luby, F.T.C.D., read aletter of the late Rev. Charles Wolfe, author of the lines onthe burial of Sir John Moore. The letter, or rather fragment of a letter, had been found by Dr. Luby among thepapers of a deceased brother, who was a college friend ofWolfe and of Mr. Taylor, to whom the letter was addressed .90The part found had the appearance of having been torn offfrom the rest of the letter. It contains the address; a complete copy of the ode; a sentence mentioning to Mr. Taylorthat his praise of the stanzas first written led him to complete the poem; a few words of a private nature atthe end ofthe letter; and the signature. There is no date on the partpreserved; but the post-mark of September 6 , 1816, fixesthe time at which it was sent. Dr. Anster read passagesfrom Captain Medwin's " Conversations of Lord Byron" andArchdeacon Russell's " Remains of Wolfe," in which mention is made of the various guesses as to the author, when thepoem first appeared, without the author's name, in the newspapers and magazines. It was attributed to Moore, to Campbell, to Wilson, to Byron, and now and then to a writer inmany respects equal to the highest of these names, whosepoems havebeen published under the name of Barry Cornwall.Shelley thought the poem likely to be Campbell's; and Medwin believed Byron to be the author. When Medwin's bookappeared in which this was stated, several friends ofWolfe's,among others Mr. Taylor, to whom was addressed the letter,ofwhich an important part has been fortunately found, statedtheir knowledge of Wolfe's having written the ode. Onegratifying result of the controversy was the publication, byArchdeacon Russell , ofthe Remains of Charles Wolfe, with amemoir written with great beauty, and, what constitutes therare charm of the work, describing with entire fidelity thecharacter, and habits, and feelings of one of the mostpureminded, generous, and affectionate natures that everexisted.The question as to the authorship ofthe ode was for everset at rest to any one who had seen either the letters of Mr.Wolfe's friends, at the time of Captain Medwin's publication ,or Archdeacon Russell's book. Were there any doubt on thesubject of authorship, the documentnow produced would completely remove it; but for this purpose it would really not be91worth while to trouble the Academy with the communication,as it would be treating the insane pretensions, now and thenput forward in the newspapers for this person or the other,with too much respect to discuss them seriously, or at all;but another and a very important purpose would be answeredby the publication of this authentic copy of the poem, fromWolfe's autograph, in their Proceedings. The poem hasbeen more frequently reprinted than almost any other in thelanguage; and, an almost necessary consequence of such frequent reprints, it is now seldom printed as it was originallywritten. Every person who has had occasion to comparethe common editions of Milton, or Cowper, or any of ourpoets, with those printed in the life-time of the authors, isaware that no dependence whatever can be placed on the textof the books in common use. Every successive reprint froma volume, carelessly edited , adds its own stock of blundersto the general mass . Wolfe's ode has been, in this way, quitespoiled in many of its best passages. The Academy hadnow the opportunity of correcting these mistakes by publishing an authentic copy ofthe poem. Dr. Anster stated thefitness of this being done by the Academy, not only from itsbeing the natural and proper guardian of every thing relatingto the literature of Ireland, —which alone would seem to hima sufficient reason, -but even yet more, fromthe circ*mstance,that the Academy's Proceedings must command a circulationover the Continent, which it would be in vain to expect forany private publication. The poem has been often translated; and the strange blunders which have got into ourcopies are faithfully preserved in the translations. In a German translation of the ode, three stanzas of a poem, consisting of but eight, are spoiled by the translator's manifestlyhaving read an imperfect copy of the original. In one it isquite plain that the stanza, which closes with the lines-" And we heard the distant and random gunThat the foe was sullenly firing,"9266and in which the word " suddenly" is often substituted forsullenly," was printed falsely in the copy before the Germantranslator. In the second stanza, "The struggling moonbeam's misty light," is lost probably from some similar reason.The general effect of Wolfe's poem is exceedingly well preserved in the translation; but there are several mistakes indetail, most ofwhich, perhaps all, arise from the translator'shaving used an incorrect copy of the original. The translation is printed in the octavo edition of " Hayward's Faust,"p. 304.The Rev. Dr. Todd, V.P., having taken the Chair, Professor Lloyd read a supplement to his paper, " On the Mutual Action of Permanent Magnets in an Observatory,"printed in the Transactions, Vol. XIX. p. 159.This supplement was immediately printed in the samevolume ofthe Transactions.May 10.Sir Wм. R. HAMILTON, LL.D. , President, in the Chair.Oliver Sproule, Esq. , and James Thompson, Esq. , wereelected Members of the Academy,Anote on some new Properties of Surfaces of the secondOrder, by John H. Jellett, Esq. , F.T.C.D., was read .I. Let the points on the focal conic, at which the tangentis parallel to the trace of the tangent plane, be consideredanalogous to foci .II. Let the axis of the surface, perpendicular to the planeof the conic, be considered analogous to the conjugate axis;then, since the square of the distance from focus to centre, ina conic, is equal to the difference between the squares ofthetransverse and conjugate semi-axis, we may consider, as analogous to the transverse semi-axis, the line drawn to the ex-93tremity of the perpendicular axis from the point analogousto the focus .III. Since the square of the semiconjugate diameter isequal to the sum of squares of semiaxes minus the square ofcentral radius vector , let the same be supposed true of theline analogous; i. e. if a be the line analogous to the transverse, and B to the conjugate semi- axis, letAB' = √ A² + B² — A²² Α .Assuming these definitions , we shall have the following theorems analogous to those in plano.1. The sum or difference (according as the focal conic isperpendicular to a real or imaginary axis) of the distancesfrom the points analogous to the foci, to the correspondingpoint on the surface, is equal to 2a.2. The rectangle under them B′².3. The sine of the angle, made by either with the tangentplane, is BB'.4. The rectangle under the perpendiculars from thesepoints on tangent plane = B².5. The sine of the angleAB vector and tangent planevector).Α Β'"between the central radius(A' being the central radius6. The portion of the normal intercepted between the surBface and the plane of the focal conic is . B'.A7. If a plane be drawn perpendicular to the line joiningpoints analogous to the foci , and at a distance from the centreA2Cequal to (c being the distance of one of the focal pointsfrom the centre) , the distance of a point in the surface fromthe corresponding focus will be to its distance from this plane

C: A.

8. Hence, given a focal conic and the perpendicular axis,94wecan find points and tangent planes ad libitum, by the following construction:-Take in the focal conic two diametricallyopposite points; with one as centre, and twice the distancefrom it to the extremity of the perpendicular axis as radius,describe a sphere. Through the other point draw a plane,normal to the focal conic; it will cut the sphere in a certaincircle. Connect any point in this circle with the two points onthe focal conic, and at the middle point of the line connectingit with the second point draw to it a perpendicular plane.This is a tangent plane to the surface, and the point whereit cuts the first connecting line is a point on the surface.Another mode of generating the surface is easily derivablefrom (7).Mr. Petrie gave an account of some ancient Irish inscriptions ofthe sixth century, found in the island of Arran.Dr. Kane made some remarks on the Theory of Types.DONATIONS.Transactions of the Literary and Historical Society ofQuebec. Vols. I. and II.; and Parts 1-4 of Vol. III. Presented by the Society.Report ofthe Directors ofthe Chamber of Commerce atManchester on Import Duties. 11th March, 1841 .Report ofthe Select Committee ofthe House ofCommonson the Import Duties.Proceedings of a Meeting of Members of the House ofCommons, held at the Thatched House Tavern, St. James'sstreet, on the 20th February, 1841. Presented by JosephHume, Esq. , M.P.7TABLE NO.I.-Copper and Zinc .No. of.Experiment2Showing the Chemical and Physical PropChemical Constitution.Composition by Weight Atomic per cent. Weight.Ε εξ ε ε +Specific Gravity. H= 14 51234 LO CONGO aCu. +210 Cu. +100.00 + 0 31.6 8.667 Zn. 9072 + 9.28 348.3 8.6059 Cu. + Zn. 89.80 + 10.20 316.7 8.607TRRR8 Cu. + Zn. 88.60 + 11.40 285.1 8.6337 Cu. +Zn. 87.30 + 12.70 253.4 8.587Cu. +Zn. 85.40 + 14.60 221.9 8.5915 Cu. + Zn. 83.02 + 16.98 190.3 8.4154 Cu. + Zn. 79.65 + 20.35 158.7 8.4483 Cu. + Zn. 74.58 + 25.42 127.1 8.397 10 2 Cu. + Zn. 66.18+ 33.82 95.5 8.299 11 Cu. + Zn. 49.47 + 50.53 63.9 8.230 12 Cu. 2 Zn. 32.85 + 67.15 96.2 8.283 13 8 Cu. 17 Zn. 31.52 + 68.48 801.9 7.721 14 8 Cu. 18 Zn. 30.30 + 69.70 834.2 7.836 15 8 Cu. 19 Zn. 29.17 + 70.83 866.5 8.019 16 8 Cu. + 20 Zn. 28.12 + 71.88 898.8 7.603 17 8 Cu. 21 Zn. 27.10 + 72.90 931.1 8.058 18 8 Cu. 22 Zn. 26.24 + 73.76 963.4 7.882 19 8 Cu. 23 Zn. 25.39 + 74.61 995.7 7.443 20 Cu. +3 Zn. 24.50 + 75.50 128.5 7.449 21 Cu. + 4 Zn. 19.65 + 80.35 160.8 7.371 22 Cu. 5 Zn. 16.36 + 83.64 193.1 6.605 23 + Zn. 0 100.00 32.3 6.895SSASSAAAYR1 Cu. + Sn. 100.00 + 0 31.6 8.667 210 Cu. + Sn. 84.29+ 15.71 374.9 8.561 9 Cu. + Sn. 82.81 + 17.19 343.3 8.462 4 8 Cu. + Sn. 81.10+ 18.90 311.7 8.459 7 Cu. + Sn. 78.97 + 21.03 280.1 8.728 6 Cu. + Sn. 76.29 + 23.71 248.5 8.750 5 Cu. + Sn. 72.80 + 27.20 216.9 8.575 4 Cu. + Sn. 68.21 31.79 185.3 8.400 3 Cu. + Sn. 61.69 38.31 153.7 8.539 10 2 Cu. + Sn. 51.75 + 48.25 122.1 8.416 11 Cu. + Sn. 34.92 + 65.08 90.5 8.056 12 Cu. + 2 Sn. 21.15 + 78.85 149.4 7.387 13 Cu. 3 Sn. 15.17+ 84.83 208.3 7.447 14 Cu. 4 Sn. 11.82 + 88.18 267.2 7.472 15 Cu. 5 Sn. 9.68+ 90-32 326.1 7.442 16 + Sn. 0 + 100.00 58.9 7.291Copper TABLE II.-and TinAbbreviations used in Column 7th to denote character of fracture:-F.C. Fine Cr E. Earthy.The maxima of ductility, malleability, hardness, and fusibility, are = 1 .The numbers in Column 6th denote intensity of shade of the same colour.The atomic weights are those of the hydrogen scale.The specific gravities were determined by the method indicated in Report " On Action The ultimate cohesion was determined on prisms of 0.25 of an inch square, without ha before disruption.The copper used in these alloys was granulated, and of the finest " tough pitch; " the zby oxidation, and the resulting alloy verified by analysis.No simple binary alloy of Cu. + Zn. or of Cu. + Sn. works as pleasantly in turning,Zn. as is known to workers in metals.95May 24.SIR WM. R. HAMILTON, LL.D., President, in the Chair.Mr. Robert Mallet read a paper " On the Physical Properties and Electro- Chemical and other Relations of the Alloys of Copper with Tin and Zinc. "These experiments are collateral to the researches on theaction of air and water on iron , upon which the author hasbeen engaged at the desire of the British Association. Inthe progress of these inquiries, it became necessary to determine the action of solvents on iron in presence of variousdefinite alloys of copper and tin and of copper and zinc.Hence it was requisite to form many such alloys in rigidlyassigned proportions as to their constituents, a matter knownto experimenters to be one of difficulty, especially in the caseof so oxidable and volatile a metal as zinc. The difficultieswere overcome by a peculiar arrangement of apparatus, permitting the metals to be fused and combined in close vessels.The results were verified by assay. Having these alloyswhich belong to the classes of brass or gun metal, of whichmost of our instruments of precision are made, and their constitution being atomic and certain, it seemed useful to determine some of their properties for practical purposes. Theresults are given in the two annexed tables.The author has also determined the numerical conditionsgoverning the rate of solution, or amount of loss sustainedin a given time by equal surfaces of iron in solvent menstrua,when in presence of all these alloys, and of the alloys themselves . Tables of these were presented: the results do notseem to coincide with the law of volta equivalents, which isexplained by showing galvanometrically that the - and+metals of the alloy are often not acted on equally by asolvent; thus, that an alloy of Zn, + Cu, may assume a copper surface after a certain time of reaction. This circ*mstance ,96the author has shown, suggests a method of determining themolecular arrangement of an alloy; and, in general, whetherany alloy be a chemical compound or a mixture.The author also enters into several details as to peculiar,and, in some cases, singular reaction of these and otheralloys upon solutions of the salts of their own metals: thus,certain alloys of lead and zinc decompose solutions of leadas rapidly as pure zinc; while others, containing much zinc,act as lead towards the salts of lead.-In the case of three metals, A, B, C, whereof A is ε + , andC is to B, the author investigates the question as to whatwill be the electro- chemical relation ofthe atomic alloys ofA + C, towards B, in solvent menstrua; and in the classof alloys of copper and zinc, has determined the alloy ofnoaction, with reference to iron; and has also found alloyswhich protect iron in solvents electro- chemically as fully aspure zinc, and yet are not themselves acted on by the solvent.He enters into the subject of the specific gravities of thealloys of Zn + Cu and Sn + Cu minutely, and shows reasonto doubt the accuracy of the published specific gravities ofmost alloys of these and some other classes.Professor Mac Cullagh read a supplement to his paper" Onthe dynamical Theory of Crystalline Reflexion and Refraction. "In his former paper on that subject (see Proceedings,9th December, 1839) the author had given the general principles for solving all questions relative to the propagation oflight in a given medium, or its reflexion and refraction atthe separating surface of two media; but he had appliedthem only to the common case of waves, which suffer nodiminution of intensity in their progress, and in which thevibration may be represented by the sine or cosine of an arcmultiplied by a constant quantity. Some months after that97paper was read, it occurred to him that he might obtain newand important results by substituting in his differentialequations of motion a more general expression for the integral, that is , (as usual in such problems) , by making thedisplacements proportional to the sine or cosine of an arc,multiplied by a negative exponential , of which the exponentshould be a linear function ofthe coordinates. Such vibrations would become very rapidly insensible, and would,therefore, be fitted to represent the disturbance which, inthe case of total reflexion, takes place immediately behindthe reflecting surface; and the laws of this disturbance beingthus discovered, the laws of polarization in the totally reflected light would also become known, by means of thegeneral formulæ which the author had established for allcases of reflexion at the common surface of two media.The present supplement is the fruit of these considerations. It contains the complete theory of the new kind ofvibrations, not only in ordinary media, but in doubly refracting crystals; and also the complete discussion of the laws oftotal reflexion at the first or second surface of a crystal, including, as a particular case, the well known empirical formulæ of Fresnel for total reflexion at the surface of an ordinary medium.The existence of vibrations represented by an expressioncontaining a negative exponential as a factor, had been recognized by other writers, and was indeed sufficiently indicated by the phenomenon of total reflexion; but it wasimpossible to obtain the laws of such vibrations, so long asthe general equations for the propagation of light were unknown.The method of deducing these equations was given inthe abstract of the author's former paper, ( see Proceedings,as above); but as they were not there stated , it may be wellto transcribe them here. Ifthen we putX =dn drdz dy'Y =d αξdx dz'- z =dé dndy dx'-- (1)98and suppose the axes of coordinates to be the principal axesof the crystal, the equations, in question may be thus written:de dz = c² dt2 dydy 2 -dzd²ndx dz = a²c² dt2 dz dx' (2)dr dy ds = b² a²dt2 dx dydr"and if we further put& =dn -da dythey will take the following simple form:d αξι dé dn η Ξ- % = (3) dx dz dy dx'd;;dt2- a²x,d2ndt2d241 b2x,-= c2z,dt2 (4)in which it is remarkable that the auxiliary quantities1, 71, S1, are exactly, for an ordinary medium, the components of the displacement in the theory of Fresnel. In adoubly defracting crystal, the resultant of E1, 1, 1 is perpendicular to the ray, and comprised in a plane passingthrough the ray and the wave normal. Its amplitude, orgreatest magnitude, is proportional to the amplitude of thevibration itself, multiplied by the velocity of the ray.The conditions to be fulfilled at the separating surface oftwo media were given in the abstract already referred to.From these it follows, that the resultant of the quantitiesE1, 1 , 1, projected on that surface, is the same in bothmedia; but the part perpendicular to the surface is not thesame; whereas the quantities E, n, % , are identical in both.These assertions, analytically expressed, would give fiveequations, though four are sufficient; but it can be shownthat any one of the equations is implied in the other four,not only in the case of common, but of total reflexion; which99is a very remarkable circ*mstance, and a very strong confirmation of the theory.The laws of double refraction, discovered by Fresnel,but not legitimately deduced from a consistent hypothesis,either by himself or any intermediate writer, may be veryeasily obtained, as the author has already shown, from equations (2), by assumingp cos a sin , npcos ẞ sin p, p cos y sin p, (5)where2π -• = = (lx + my + nz − st);but the new laws, which are the object of the present supplement, are to be obtained from the same equations bymaking=ε(p cos a sino + q cos a' cos p) ,n = ε(p cos ẞ sin p + q cos ẞ' cos p) ,= (p cos y sin p + q cos y cos 4),where has the same signification as before, andε =e2πγ·( fx + gy † hz);(6)the vibrations being now elliptical, whereas in the formercase they were rectilinear. In these elliptic vibrations themotion depends not only on the distance of the vibratingparticle from the plane whose equation islx + my + nz = 0, (7)but also on its distance from the plane expressed by theequationfx +gy + hz = 0; (8)and ifthe constants in the equation of each plane denote thecosines of the angles which it makes with the coordinateplanes, we shall have λ for the length of the wave, and s forthe velocity of propagation; while the rapidity with which100the motion is extinguished , in receding from the second plane,will depend upon the constant r. The constants p and q maybe any two conjugate semidiameters of the ellipse in whichthe vibration is performed; the former making, with the axesof coordinates, the angles a, ß, y, the latter the angles a',B', y'.As vibrations of this kind cannot exist in any medium,unless they are maintained by total reflexion at its surface,we shall suppose, in order to contemplate their laws in theirutmost generality, that a crystal is in contact with a fluidof greater refractive power than itself, and that a ray isincident at their common surface, at such an angle as to produce total reflexion. The question then is, the angle of incidence being given , to determine the laws ofthe disturbancewithin the crystal .The author finds that the refraction is still double, andthat two distinct and separable systems of vibration are transmitted into the crystal. He shows that the surface ofthecrystal itself (the origin of coordinates being upon it at thepoint of incidence) must coincide with the plane expressedby equation (8) , a circ*mstance which determines the threeconstantsf, g, h. The plane expressed by (7) is parallel tothe plane of the refracted wave; and a normal, drawn to itthrough the origin, lies in the plane of incidence, makingwith a perpendicular to the face of the crystal an angle wwhich may be called the angle of refraction, so that, if i bethe angle of incidence, we havesin w = s sin i,the velocity of propagation in the fluid being regarded asunity.To each refracted wave, or system of vibration, corresponds a particular system of values for r, s, w. These theauthor shows how to determine by means of the index-surface (the reciprocal of Fresnel's wave surface) which he hasemployed on other occasions, (Transactions ofthe Academy,101vol. xvii . and xviii . ) , and the rule which he gives for thispurpose affords a remarkable example of the use of theimaginary roots of equations, without the theory of which,indeed, it would have been difficult to prove, in the presentinstance, that there are two, and only two, refracted waves.Taking a new system of coordinates x' , y' , z' , of which ' isperpendicular to the surface ofthe crystal, and y' to the planeof incidence, while a' lies in the intersection of these twoplanes, put y' = 0 in the equation of the index- surface referred to those coordinates, the origin being at its centre;we shall then have an equation of the fourth degree betweenx' and z', which will be the equation of the section made inthe index surface by the plane of incidence. In this equationput x' sin i, and then solve it for '. When i exceeds acertain angle i' , the four values of z' will be imaginary, andifthey be denoted byu ± v √ − 1 ,-- u' ± v' √-− 1 ,each pair will correspond to a refracted system, and we shallhave, for the first ,sin itan w = s =usin wsin ir = sv; (9)and for the second,tan w' =sin iuS =sin w'sini'"' = s'v'. (10)When i lies between i' and a certain smaller angle i", twoof the roots will be real, and two imaginary. The real rootscorrespond to waves which follow the law of Fresnel; theimaginary roots give a single wave, following the other lawsjust mentioned.Lastly, when i is less than i", all the roots are real, therefraction is entirely regulated by Fresnel's law, and thereflexion by the laws already discovered and published bythe author.VOL. II. K102If the crystal be uniaxal, and all the values of ' imaginary,the ordinary wave normal will coincide with the axis of x';whilst the extraordinary wave normal and the axis of ' willbe conjugate diameters of the ellipse in which the indexsurface is cut by the plane of incidence.When a = b = c, the crystal becomes an ordinary medium; there is then only single refraction, and the refractedwave is always perpendicular to the axis of x'.With regard to the ellipse in which the vibrations areperformed, it may be worth while to observe, that if it beprojected perpendicularly on the plane of incidence, the projected diameters which are parallel to the surface of thecrystal and to the wave plane will, in all cases, be conjugateto each other, and their respective lengths will be in theproportion of r to unity. The vibrations, it is obvious, arenot performed in the plane of the wave, though they takeplace without changing the density ofthe ether.The new laws here announced are, properly speaking,laws of double refraction, and are necessary to complete ourknowledge of that subject. Between them and the laws ofFresnel a curious analogy exists, founded on the change ofreal into imaginary constants.Thelaws ofthe total reflexion, which accompanies the newkind of refraction, need not be dwelt upon in this abstract, asnothing is now more easy than to form the equations whichcontain them. In fact, the difficulties which formerly surrounded the problem of reflexion, even in the simplest cases,have completely disappeared , since the author made knownthe conditions which must be fulfilled at the separating surface oftwo media.In what precedes, it has been supposed that the reflexionand refraction take place at the first surface of the crystal,because this is the more difficult and complicated ofthe twocases into which the question resolves itself. But it willusually happen in practice that a ray which has entered the103crystal will suffer total reflexion at the second surface, whilethe new kind of vibration is propagated into the air without.The refracted wave will then be always perpendicular tothe axis of x'; the two reflected rays, within the crystal,will be plane- polarized , according to the common law, butthey will each undergo a change of phase; and the visviva of the two rays together will be equal to that oftheincident ray, the vis viva being measured by the squareof the amplitude multiplied by the proportional mass.In conclusion, the author states a mathematical hypothesis bywhich both the laws of dispersion, andthose oftheelliptic polarization of rock crystal, may be connected withthe laws already developed.The Rev. Dr. Todd communicated the following particulars concerning an ancient inkstand, contained in a letter fromJoseph H. MonckMason, Esq. , dated Rome, May 4th, 1841:" This relic (described by Mrs. Hamilton Gray, in herTour in Etruria, p. 334) is of coarse terra- cotta, black andill-formed; it is a truncated cone, about eight inches long,about four or five inches round the mouth, and about twelve(not more, I think) round the base; there are about twelvelines of letters written round the upper three- fourths, andone round the very base; they are written from left to right.I repeat it, that, being cramped by the rules and restrictions,I was not entirely particular; and the upper part was dirty,and not very legible without close inspection . I could seeof the last line ( I do not mean that round the base, which hassome Greek capitals, ) about three-fifths; this contained fourteen letters. I saw no omicron or omega. This line mighthave had twenty- four letters; and allowing about twelve, orsay fifteen lines in all , gradually diminishing as on the outside of a cone, there was scarcely room for ba, be, in a second language. I believe them all to be Greek. Aboutthree or four lines up, I remember, there was P (ro , ) andK 2104a little higher, mu, with vowels in order. So much for thiswonder, ifit be the right one; and it was shown to me assuch by one who knew it to be so. "The following Note " On the Force of aqueous Vapourwithin the Range of atmospheric Temperature," was readby James Apjohn, M.D., M.R.I.A., Professor of Chemistryin the Royal College of Surgeons.Having had it in contemplation some time since to investigate by means of an indirect, but I believe a very accurateprocess, the caloric of elasticity of the vapours of severalliquids, I found myself stopped on the threshold of the inquiry by a want of knowledge of the tension of such vapoursat different temperatures; for, with the exception of thevapours ofwater, alcohol, ether, and oil of turpentine, thetension of no others had been made the subject of experiment; and even in the case of the fluids just named, theresults recorded in the books appeared to me very far frombeing of such a nature as to preclude the necessity offurtherresearch.The method which I intended to employ, in order to arrive at the latent heats of vapours, not requiring a knowledgeof their tensions beyond the range of atmospheric temperature, it occurred to me, that the necessary data for the solution of the preliminary problem might be obtained with facility, and, at the same time, with much precision, in thefollowing manner:Let a known volume of dry air be charged with moistureat any given temperature, and let the expansion producedby the moisture be accurately noted . The pressure beingalso measured by an accurate barometer, we have the meansof calculating the force of the vapour which has producedthe expansion. For if v be the volume of the dry air, andv' that of same air when charged with moisture, ƒthe force105of the vapour, and p the existing atmospheric pressure, weshall haveРv = v xfrom which we deducef== ( ) x p.It was not my original intention to make any experiments upon the force of aqueous vapour, believing the tablewhich I have hitherto employed, and which was calculatedby the author of the article " Hygrometry," in Brewster'sEncyclopædia, from the experiments ofDalton, to have beensufficiently exact. But the correctness of this table havingbeen indirectly called in question by so high an authority asMr. Kupffer, who has come to the conclusion, that the tableof the force of aqueous vapour, given by a German meteorologist, of the name of Kämtz, is alone to be relied upon, Iresolved to commence with the vapour of water, in the hopethat I might be able, by the results of direct experiment, tocorroborate a conclusion previously drawn by ProfessorLloyd, from a discussion of some hygrometrical observationsof mine, viz. , that for temperatures within the atmosphericrange, the table of Kämtz is less accurate than that ofDalton, the values given in the former being all too low.The apparatus I have employed in my experiments iscomposed of a glass ball prolonged on the one side into ashort tube, furnished with a cap and stopco*ck, and, on theother, into a long tube of somewhat smaller diameter, divided into 100 equal parts, each being .042 of a cubic inch,or the .001 of the total capacity of ball and tubes down asfar as the division marked 1000.The first step consisted in filling this vessel with dry air,which was done in the following manner into the extremity106of the graduated tubular portion, a cork pierced by a smalltube, open at both ends, was inserted, and this tube wasthen connected with the orifice of a table air-pump usuallyoccupied by a syphon gauge. The stop- co*ck was now connected with one end of a long tube, packed with fragmentsoffused caustic potash, while the other end of this tube wasattached by means of a slip of caoutchouc to a second tubepassing through an air-tight cork fixed in one of the mouthsof the bottle, at present used for the inhalation of chlorine.This bottle being charged with oil of vitriol, and the orificeof the plate ofthe pump being closed, the pump was worked,and a current of air was thus drawn through the glass vesselfor about fifteen minutes, which in passing through the oilof vitriol, and over the fused potash, was deprived of all hygrometric moisture . The included air being now absolutelydry, the stopco*ck was closed, and the small tube connectingthe air vessel with the pump having been drawn out in themiddle, and sealed hermetically by means of a spirit lamp,the air apparatus was separated from the potash tube, andtransferred to a tall jar containing mercury, after which thesealed end of the small glass tube was broken beneath thesurface ofthe quicksilver. The apparatus, however, beingnow completely filled, it became necessary to remove someof the air, and this was done by opening the stopco*ck verygradually, care being taken that during this manipulation theexternal mercury should be higher than its level within thetubular portion. The entire was then placed in a smallroom, the temperature of which was found not to vary morethan one degree Fahrenheit during the twenty- four hours,the stopco*ck having been first attached to one extremity ofa string, which was carried over a fixed pulley placed inthe ceiling, and whose other end carried a counterpoise bywhich the air vessel was kept in a vertical position, and theobserver was enabled readily to bring the mercury within107and without to the same level, before he registered the volume ofthe included air.On the next day, after the apparatus was mounted, andthe four following ones, the volume of the dry air, its temperature, and the existing pressure were accurately noted.This pressure, which was measured by a portable barometerof Newman's, having undergone a variety ofcorrections, forthe capacity of the cistern compared to that of the tube, forthe excess ofthe temperature of the quicksilver over 32º, forcapillarity, and for a constant error by which I found mybarometer affected, when compared with the standard instrument in the Observatory of Trinity College, I reduced bycalculation in each instance the observed volume of air towhat it would be at 32º, and under a pressure of 30, usingfor the expansion of air the corrected coefficient , whichhas resulted from the experiments of Rudberg, and thusobtained the following numbers, which, it will be observed,differ very little from each other.12345• 911.11• 911.85910.21913.30911.72911.64, therefore, the mean of the five observations, maybe assumed as the true volume of the included dry air, at32°, and under a pressure of 30.The volume of the dry air being determined, the nextstep was to charge it with moisture. In order to accomplish this, the air vessel was lifted by means of the string,so as that the mercury within should be about an inchhigher than the external mercury, and distilled water wasthen poured into the upper cavity of the stopco*ck, so ascompletely to fill it. The stopco*ck was now cautiouslyturned, so as to admit the entrance of the moisture guttatim;108and more water being occasionally poured on, this manipulation was repeated until the mercury within came to be covered by a film of water of about one- tenth of an inch inthickness. The stopco*ck was now closed, and the apparatus being lowered, the whole was left to itself until thefollowing day, when the first of a series of observations, continued for twenty successive days, was made, each comprehending the volume of the moist air, the pressure, and thetemperature both of the air and of the mercury in the barometer. To deduce from these by the formulaƒ=хр,v'.-vvthe force of vapour, it was necessary, in the first instance, toapply to p all the corrections already explained, and in addition to raise 911'64, the volume of the dry air, to what itwould be at the temperature and pressure of the moist air,as noted in each observation. But, as this involved tediousarithmetical computations, and as the thermometer duringthe performance of the twenty experiments varied onlyabout 15°, I came to the resolution , being at the time uponthe eve of leaving town for a couple of months, to postponethe calculations until I should be possessed of data applicable to the solution ofthe problem I had undertaken, throughout a more extended range of temperature.Accordingly, in November last, I resumed the subjectwith the very same apparatus, which had been left statu quoin the interval, and succeeded in completing a series offortyfive additional observations, extending nearly as low as 32°,and which I had every reason to expect would lead to satisfactory results. Upon, however, submitting the whole tocalculation, I have been led to the mortifying conviction,that in consequence either of the absorption of the oxygenby the mercury and brass-work, or some accident whichbefel the apparatus during my absence from town, theentire of the latter series of observations is of no value, asthey lead to results for the force of aqueous vapour, which109are certainly greatly below the truth . Upon the presentoccasion, therefore, I can direct attention only to the observations made in July and August last. These are containedin the following table, and, as has been already stated, theyamount to twenty in number, the highest temperaturehaving been 65°, and the lowest 49° 6. The numbers in thelast column represent the bulks which the 911.64 volumesof dry air would have, if reduced to the temperature t, andthe corrected pressure p.TABLE I.v t p observed Tempera- ture ofBarometer.p corrected.911.64 reducedto t and pcorrected.1001 60.4 29.450 59.9 29.430 982.821001.5 59.8 29.364 60.1 29.338 984.77997 60 29.548 60 29.524 978.94984 59.1 29.822 59.5 29.807 967.97977 58.4 29.980 58.6 29.971 961.38984 58.4 29.780 58.9 29.767 967.97991 59 29.624 59.4 29.607 974.33983.5 59.4 29.862 59.8 29.847 967.23979.5 60.2 30.100 60.6 30.086 962.69977.5 61.2 30.132 61.3 30.165 960.35983 61.6 30.05 62.2 30 037 965.18973-3 62.2 30.230 62.4 30.212 960.69978.4 61.6 30.214 62.2 30.197 960.06983.5 63.1 30.156 63.6 30.131 964.93987.5 64.3 30.130 64.7 30.104 968.01991 64.1 30.032 64.6 30.005 970.83994.5 64.8 29.989 65 29.961 973.55994.5 65 29.972 66 29.940 974.61989 65.2 30.152 66.5 30.120 969.121000 64.8 29.834 65 29.306 978.62From the first, last, and second last columns of the preceding table, the force of aqueous vapour has been calculated in the manner already explained. The values thusobtained are exhibited in the second column of Table II.110Column 1 contains the temperatures; column 3 the tensions, as deduced from Dalton's experiments; and column4 the same as given by Kämtz.TABLE II.1 2 3 4Dalton. Kämtz.60°.4 .5345 •5302 •512559.2 ⚫4908 •5197 •502360 . ⚫5348 •5232 •506159.1 .4855 •5077 ⚫489358 .4 •4917 •4960 •476858.4 •4849 •4960 •476859 . ⚫4980 •5060 •487559 ⚫4 •4937 5128 ⚫494960.2 •5169 •5265 ⚫5093.. 61.2 •5292 •5444 •526161 6 ⚫5445 •5517 ⚫534362.2 •5412 •5628 •545861 6 •5660 •5517 ⚫534363.1 •5689 •5798 •561564 .3 •5941 •6033 •586064.1 • 6107 ⚫5993 •582464.8 • 6311 6133 •594965 . •5988 • 6173 •598565 .2 •6054 • 6214 •602964 .8 •6372 .6133 •5949When the corresponding numbers in the three columnsare compared, it will be at once observed, that the values off, investigated by the method just explained , are somewhatless than those extracted from the table I have been hithertoin the habit ofusing; but that they are considerably greaterthan the values of Kämtz, the differences being generallybetter than twice as great in the latter instance as in theformer. This will be more manifest by taking a mean of thedifferent results in column 2, and comparing it with the force111of vapour corresponding to the same temperature as given inthe two other tables. Now, the mean of the temperatures is6163, the quotient got by dividing their sum by twenty.But the corresponding mean value of f, in column 2,must be differently calculated, seeing that the temperatureand the corresponding tensions of the vapour augment at avery different rate. For temperatures, in fact, in arithmetic.progression, the corresponding tensions are in geometricprogression; and, although this is well known to be but anapproximate law, it may be considered as rigorously truefor the limited range of temperature within which my experiments have been made. To calculate, therefore, the meanforce of vapour, as deducible from the numbers in column2, and which must correspond to the temperature 61° 63,it is only necessary to add together the logarithms ofthenumbers in this column, and divide their sum by twenty, andthe quotient will be the logarithm ofthe mean. When thisprocess is gone through, the mean logarithm is found to be73699, and the corresponding number 54575. The following, therefore, are the tensions of aqueous vapour at 61 °.63,as deduced from my experiments, and as extracted from thetables of Dalton and Kämtz.My Experiments.• * 5457Dalton. Kämtz.61°.63,⚫5523 ⚫5349Difference between Dalton's number and mine, +.0066.Difference between Dalton's number and that of Kämtz,= + .0174.It thus appears, that the result at which I have arrivedis somewhat less than the Daltonian number, but considerably greater than that given by Kämtz; and that, therefore,my experiments, as far as they have been discussed, give atleast a prima facie countenance to the opinion , that thevalues of the elastic force of aqueous vapour, as given bythe latter philosopher, are, at and about 61°· 63, below thetruth.112Before, however, this conclusion can be considered asfully established, and before we can judge correctly of theamount of the errors by which his table is affected, it will benecessary to inquire whether the thermometer I have employed be a true one. This essential inquiry I have beenenabled to institute by my friend, Professor Lloyd, who hasput into my possession, for the purpose, a thermometer givenhim by Professor John Phillips , together with a table ofdifferences between it and the standard thermometer belonging to the Royal Society. Upon a comparison ofthe twoinstruments, I find , that at and about 60°, the thermometerI have employed stands 6 of a degree higher than that lentme by Professor Lloyd, while the latter stands 3 of adegree higher than the standard in possession of the RoyalSociety; so that the indications of my instrument are at 60º.9-10ths of a degree higher than the truth. If such be thecase, 5457, instead of being the force of vapour at 61 °.63, isthe force at 61.63 - 0· 9 60° 73; and to compare the resultof my experiments with the tables of Dalton and Kämtz, itis only necessary to extract from these the values of the forceofvapour corresponding to the temperature 60°.73.My Experiments.60°.73 . • * 5457Dalton.

• 5361.

Kämtz.· 5157Difference between Dalton's number and mine — · 0096.Difference between Dalton's number and that of Kämtz+0184.The consideration , therefore, of the error of my thermometer, and the allowance made for it, only strengthens theconclusion already arrived at; and I do not now feel any difficulty in giving it as my deliberate opinion, that the tableofthe force of vapour given by Kämtz is, within the atmospheric range of temperature, erroneous, his values being alltoo low.113Dr. Anster, on the part of the Rev. Dr. Luby, F.T.C.D.,presented to the Academy the original letter of the Rev. C.Wolfe, which he had read at a former Meeting, and of whichafac-simile is published in the present Number of the Proceedings. (See p. 90.)The special thanks of the Academy were voted to DoctorLuby for the donation of this very interesting document.Professor Mac Cullagh presented to the Academy threeadditional ornamented plates belonging to the cross ofCong.When the cross came into his possession, these plates weremissing; but they were lately recovered for him by the exertions of a friend. The front of the cross is now complete,and only one plate is left wanting at the back.DONATIONS.Astronomical Observations made at the Honourable theEast India Company's Observatory at Madras, for the Years1831-39. Vols. I.-V. Presented by the Court of Directors.Journal ofthe Statistical Society. Vol. IV. Part 1. Presented by the Society.Contributions towards the History of Swansea. By LewisW. Dillwyn, F.R.S., &c. Presented by the Author.Mémoires préséntes par divers savants a l'AcadémieRoyale des Sciences de l'Institut de France; Science Mathématiques et Physiques. Tome V.Mémoires de l'Institut Royal de France, Académie desInscriptions et Belles Lettres. Tomes XI. , XII. , XIII. , andXIV.; Part 2.Mémoires de l'Institut de France, Académie Royale desSciences. Tome XIV. -XVII.Séance Publique Annuelle de l'Académie Royale des Inscriptions et Belles Lettres, du Vendredi 25th Septembre,1840.114Comptes Rendus Hebdomadaires des Seances de l'Academiedes Sciences. Premiere Semestre, 1840. Nos. 20-26;Deuxieme Semestre, 1840. Nos. 1-26; Premiere Semestre,1841 , Nos. 1-10. Presented by the Academy.Catalogue des Manuscrits de la Bibliotheque de Chartres.Presented by J. O. Halliwell, Esq. , M.R. I. A.Greenwich Astronomical Observations for the Year 1839.Presented by the Royal Astronomical Society.Report ofthe Tenth Meeting of the British Associationforthe Advancement of Science. 1840. Presented by the Association.Transactions of the American Philosophical Society. Vol.VII. New series. Part 2.Proceedings of the American Philosophical Society.Nos. 14-16. ( 1841 ) . Presented by the Society.On the Composition of Chalk Rocks and Chalk Marl byinvisible organic Bodies; with an Appendix. By ThomasWeaver, Esq., M.R.I.A. Presented by the Author.

PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1841. No. 30.June 14.SIR WM. R. HAMILTON, LL.D. , President, in the Chair.James Patten, M.D. , was elected a member of the Academy.Dr. Aquilla Smith read a paper " On the Irish Coins ofHenry VII."In the preliminary remarks, the author entered at somelengthinto the history ofthe Irish coinage during the reigns ofHenry V. and Henry VI., with the view of facilitating hisinquiries in the subsequent part of his essay. And from theevidence of several Acts of Parliament, which were notknown to previous writers on the coinage of Ireland , he inferred that no legal money was coined in this country byHenry V., and that very few coins are known which can beappropriated to his immediate successor.The coins of Henry VII. , which are very numerous,were divided into three sections, each distinguished by theform ofthe cross on the reverse; and in the last section the author supported Mr.Lindsay's appropriation to Henry VII. ofthe untressured groats which Simon had given to HenryV.Rev. H. Lloyd, V. P. read a " Note on the Mode of observing the vibrating Magnet, so as to eliminate the Effectof the Vibration. "VOL. II. L116The following modification of one of the methods proposed by Gauss, for the attainment of this end, appears tocombine the greatest number of advantages; namely, to takethree readings, at the timest - T, t, t + T;t being the epochfor which the position of the magnet is desired, and T its time of vibration. * In order to show thatthis method is adequate, it is necessary to deduce theequation of motion of a vibrating magnet in a retardingmedium.Let x denote the horizontal part of the earth's magneticforce; q the quantity of free magnetism in the unit of volume of the suspended magnet, at the distance from thecentre of rotation; and 0 the deviation of the magnet fromits mean position. The moment of the force exerted by theearth on the element of the mass, dm, isxqrdm sin 0;and the sum of the moments of the forces exerted upon theentire magnet isxu sin 0;where μ denotes the value of the integral Sqrdm , takenbetween the limits r ± 1, 21 being the length of themagnet.Again, the velocity being small, the resistance may beassumed to be proportional to the velocity. Accordingly, ifw denote the angular velocity, the retarding force due toresistance, upon any element of the surface, ds, at the distance from the centre of motion, is- Kds rw;and the entire moment of this force upon the whole magnet is

• In practice, it is sufficient to take the nearest whole number of seconds,

for the value of T.117Kw Sr²ds =- ΚωSrdmH;dm where H = The ratio, H, is constant for all bodies of dsprismatic form; and for these , therefore, the moment ofresistance isMK -- ω;Hм denoting the moment of inertia Sr²dm.The differential equation of motion is, therefore,do But wdtdw Χμ Ksin 0 - ω.dt M H

and,

0 being small, we may substitute forsin 0. The equation thus becomesd20 KdoΧμ + + 0 = 0.dt2 H dt MKMaking, for abridgment,-HΧμ = 2A, X = B³, the integral is M0 = (c cos √/ B² — A². t +c′ sin √ B² — A³ . t) e¯st.--But, a being small, we have approximatelye-At 1 - At;and, if T denote the time of vibration,√ B² — A² . T = π.-Hence the preceding equation may be put under the formtΠ + c' sin T0 = (1 − st) (c cos π —-~Now, let 0, and 0' denote the values of 0, when t becomesL 2118t-T and T. It will be seen at once, on substitution,that0, +20 + 0 = 0.Hence by combining the three readings according to thepreceding formula, the deviation of the magnet from itsmean position, arising from the vibratory movement, is completely eliminated; and it will readily appear that the sameresult may be attained by any greater number of readings,taken and combined according to the same law.Now, let the value of 0 contain an additional term, +pt,proportional to the time: or, in other words, let us supposethat there is a progressive change of the declination , whichmay be regarded as uniform during the whole interval ofobservation. It is then manifest that 0, + 20 + 0' = 4pt;and accordingly that the quantity1 (0, +20 + 0')will give the mean place of the magnet corresponding to theepoch t.The supposition of a uniform change can, however, beregarded as an approximation to the truth, only when theinterval of time between the first and last reading is verysmall, in comparison with the interval between the successivemaxima and minima, in the fluctuations of the irregularmovement. Hence, we may conclude, that it is important,in the first place, to employ three readings in preference toany greater number; and, secondly, that it is desirable thatthe time of vibration of the magnet itself should be as smallas possible, consistently with the accuracy of its indicationsin other respects.Professor Lloyd read the following extract of a letterfrom the Rev. George S. Smith, containing some facts relative to the storm of May 26th and 27th .119" It appears that the thunder storm commenced on Wednesday night in Tipperary, Clare, Limerick, and Waterford,reaching its greatest violence on Thursday morning at aboutsix. It was on Thursday evening that it was most severe inCarlow and Queen's County, from nine till twelve P.M. ,having, however, been felt in the morning of the same day.On Thursday evening it began in Dublin; but the thunderwas loudest at half- past three A.M. on Friday morning. OnFriday morning, at ten o'clock, A.M. , it raged in the countyMayo."In Windsor forest and the neighbouring country it wasa more furious tempest, and took place on the evening ofThursday the 27th, as in the county Carlow.“ It was reported to me, that there were some remarkable phenomena of the tide in Dublin Bay during the storm;and I accordingly inquired from a variety of persons on thequays and elsewhere, and they concurred in stating, thatabout half- past three the tide, which was then flowing andapproaching to high water, suddenly retired in half an hourto low water mark, and that it rapidly returned and rosetwo feet higher than high water mark, and so quickly thatboats were knocked violently against each other. The coalporters, and dockyard keepers, and various sailors both inthe river and Kingstown, agreed in this statement.66 Further, in the River Foyle, in the North of Ireland,there is an embankment in the course of being formed byThomas Hutton, Esq. , and he states that the tide on Thursday night, or Friday morning, retired so suddenly, that considerable damage was done to his embankment."The concurrence of these phenomena with the storm isa point of some interest; and I write these few lines to invite inquiry, and to ascertain, if possible, whether this extraordinary tide-wave was generally observed, and on what dayand hour, and whether it coincided or not with the storm .120" The newspapers report the occurrence of the storm , asmentioned above; but say nothing of the tide." The course of the storm seems to have been fromsouth to north; but I think a north-east wind was blowing. "A communication by Francis Crawford, Esq. , A.B.," On the Utility of the Irish Language in Classical Studies, "was read.The object of the writer was to show, that, notwithstanding the contempt and ridicule into which the subjecthad fallen in consequence of the rash and unphilosophicviews ofinjudicious advocates, still there existed reasonablegrounds for believing that a careful and sober analysis ofHeathen mythological names would resolve them into Celticelements through the medium of Irish; accordingly he proceeded to give numerous instances of such analysis, at thesame time declaring, that unless supported by such analogies,or other external evidence, as he offered, investigations ofthis sort were by no means to be relied upon.After interpreting, in this manner, the names of some ofthe Syrian deities mentioned by Selden, in his learnedwork "De Dis Syris, " the writer went on to set the wholesubject in a more interesting point of view, by attemptingto show, that even the Bible might receive illustration andconfirmation from such inquiries; to effect this, he undertook to identify the Melchizedek of Scripture with the famousTyrian Hercules; he shewed at some length, that theywere contemporaries in history, that they agreed in character, that tithes were paid to both, and finally that thename of Malcarth, by which the Tyrian Hercules was bestknown, when resolved into its Celtic components mal- ceart,literally signified " Righteous King, " or " King of Righteousness."22The writer, after some further proofs of their identity,121concluded by giving a description of the rites and ceremonies used in the worship of Hercules at Gades, intimatingthat they denoted a purer mode of religious culture thangenerally obtained in the heathen world.DONATIONS.Notes on the United States of North America in 1838 ,1839, 1840. 3 Vols. By George Combe, Esq. , Hon. M.R.I.A. ,&c. Presented by the Author.The Silurian System. By William H. Fitton, Esq.Presented by the Author.Dublin Metropolitan Police Returns of Persons taken intoCustody in 1840. Presented by the Commissioners.Ordnance Survey ofthe County of Galway, in 139 sheets.Presented by his Excellency the Lord Lieutenant.Verhandelingen van het Bataafsch Genootschap der Proefondervindelyke Wysbegeerte te Rotterdam. Vols . I.—XII. ,and New Series, Vols. I.-VIII. Part I.A Collection ofTemperance Medals. Engraved by J. C.Parkes. Presented by the Artist.June 28.SIR WM. R. HAMILTON, LL.D. , President, in the Chair.Mr. Mallet read a paper " On a new Method of raisingShips ofWar out of Water for the Purpose of Repair."Although the author conceived that the objects of theRoyal Irish Academy were rather to investigate principlesthan to apply them in detail, still as any application of these,which proposes to add to our naval power, is of importance,and as on a like subject the Royal Society conferred onSir R. Seppings their highest reward for his application ofdiagonal framing to ships, he did not deem it altogether outof place to bring hismethod of raising ships out of water be-122fore the Academy, with models and drawings to illustrateit. The inventor first gave a rapid description of theseveral methods of taking ships out of water for repair,which have been in use from the earliest times to theday, viz. , by1. Stranding on bilge ways.2. Careening.present3. The machine called the Camel, invented about 1680.4. The graving dock.5. Morton's patent slip.6. The screw dock.7. Thehydraulic dock.Both comparatively recent American inventions, and only usedthere.8. The floating dock of the River Tyne, used at Newcastle.He then pointed out the several disadvantages to whicheach of these is severally liable.These are briefly, in the first case, costliness, tedious- ,ness, straining of the ship, and imperfect access to the hull.In the second, great danger and imperfect access to the hull.The Royal George was sunk by careening her. In thethird case, want of access to the ship-impossibility of exposing the whole hull-straining ofthe framing, and danger.In the fourth or graving dock, great original outlay; greatlabour and loss of time in pumping out water where rise oftide is small; loss of two or three hours of daylight every.day by the sunken position of the ship, and awkwardness inhandling long spars or timber; difficulty of inspection , andunhealthiness of situation to workmen; and, lastly, rottingof timbers, from the constant damp atmosphere of a sunkor graving dock.Morton's slip overcomes most of these evils, but hassome peculiar to itself. Ships can only come on and gooff the slip at high and low water; hence, in large vessels, the loss of one tide is often the loss of a fortnight;123it cannot be used in foul weather, or with the tail ofthe slipin a tideway; the average length of the inclined plane beingabout five hundred feet, and the rate of elevation of a shipfrom three to five feet per minute, the time of taking aship out of water, including the removal of the cradle, occupies from four to six hours; and hence, thoughnominallycheap, this is by loss of time really a dear mode of repair tothe ship-owner-the ship lies on an inclined plane, which isinconvenient in hoisting or lowering heavy parts, particularlyin steam-ships. The hull is always strained, and new coppering is often found wrinkled, by the ship running offtheslip, and receiving unequal support from the water meetingher at an angle to her plane of stable floatation. The vibration of the numerous rollers is also injurious in the sameway.The American screw and hydraulic docks have the advantage, in point of speed , when in use; but are unsafe forlarge ships, and awkward in the posture of the ship'shull.The Newcastle- on-Tyne floating dock possesses all thedisadvantages (except original costliness) of the gravingdock, and is without the safety of the latter.The author then explained the nature of his own method,and exhibited it in action by means of a large workingmodel; without plates it is difficult to describe this combination. The vessel to be raised, floats in over a timberplatform of a suitable size laying at the bottom, and bymeans oftwo very powerful cabstern cranes, actuated by asmall steam engine, and acting on two large flat linkedchains, the platform is raised above the surface of the water,bringing up the vessel along with it, and placing her upona suitable level for the convenience of workmen to get underandround the hull, for which the platform is specially adapted.The two chains spoken of lay horizontally at either sideofthe platform, and above it, and are armed with rollers at1124equal intervals, resting on a hollow iron railway; and fromthese points ofthe chains a number of suspending rods proceed to the platform; at each side below the latter, are anequal number of jointed struts or supports; and the natureof the motion is such, that, when the platform is at thebottom, these struts are nearly horizontal, and the suspending rods vertical, and vice versa when the platform is at itsgreatest elevation; hence, the latter is at all times fully andfirmly supported.The combination is such, that power is to the utmosteconomized, the ratio of the power to the weight increasingas the hull of the vessel leaves the water, and advantagebeing taken of her own floatage power as long as possible.The inventor stated, that a fifty gun frigate, with herstanding rigging up, could be taken out of water, and laiddry and ready for workmen, ins ixteen minutes from thetime she came over the platform, by his arrangement, whichis equally applicable where there is no tide, (as at Malta,&c. , ) as where the rise and fall are considerable. The objectsalso held in view, and he conceives attained, by his method,are equal strain, and wear and tear (by principle) on all theparts-and hence freedom from risk ofaccident-durabilityand facility of repair in the machine itself.A paper by the Rev. Dr. Hincks, " On the EgyptianStèle, or Tablet," was read.Among the Egyptian monuments in museums, there isnone more likely to afford information than the stèles, or funeral tablets, which resemble in form the head-stones in ourgrave-yards, and which appear to have been set up in similarpositions. The object of this paper is to describe the partsof which the inscriptions that these tablets contain usuallyconsist, with such observations as may enable a person, whoshould meet with one of them, to form a judgment as to itsage, and as to the importance of its contents.It commences with some details respecting two tablets125each ofwhich records the dates of the birth and death ofthe deceased person, and also the length of his life . A diligent search should be made for similar tablets, which wouldevidently be of the greatest value in settling the chronologyofthe Egyptian sovereigns . One of these, which is at Florence, records that a person named Psammetich was born inthe third year of Necho, the tenth month and first day; thathe died in the thirty-fifth year of Amasis, the second monthand sixth day; and that he lived seventy-one years, fourmonths, and six days. From this it appears, that the interval between the first year of Necho and the first of Amasiswas forty years; and it follows that the reigns of these kingsmust have commenced in 611 and 571 before our era. Theother tablet, which belongs to Mr. Harris of Alexandria, isthat of a priest named Psherinphthah, who died, aged fortynine years, in the eleventh year of Cleopatra, the eleventhmonth and twentieth day. The chronology of this periodbeing well known from other sources , the dates of the tabletwould be of no value, did not that of the birth contain a royalcartouche, which does not occur elsewhere, and an unknownnumeral character. The cartouche is shown to be that ofPtolemy Alexander, though it does not contain his usual surname; and the unknown character, a bird's head, is provedto stand for twenty. The tablet of Te- imothph, the wife ofthis priest, who was also his half-sister, is in the BritishMuseum; and several circ*mstances in their family history,taken from the two tablets, are collected together. Thebirth of their son Imothph, in the sixth year of Cleopatra,and when the father was turned of forty-three, is recordedon both of them.The most usual form of the inscription on a stèle is tranlated as follows:-" An act of homage to A; he has (or asthe case may be) given B unto C; who says D." The blankat A is filled up with the names and titles of deities; that atB with an enumeration of gifts; that at C with the name anddescription ofthe deceased person; and at D is the speech126attributed to him, in which he sometimes records the leadingevents of his life. Sometimes the tablet is without a speech,the inscription closing at the end of C; and sometimes itbegins with C, containing only the name and description ofthe deceased person and his speech. In a few tablets theprefatory matter is somewhat different from the above; butthe form given above is much the most usual.No record of facts is to be expected in a tablet till wecome to C; the preceding part of the inscription is only valuable, as it may aid us in the study of the language, and asit may lead us to know the age of the tablet, supposing it tobe without a regular date. For this last purpose, a numberof criteria of antiquity are proposed , the result of a carefulexamination of a great many tablets of known ages. Themost remarkable of these is , that in the most ancient tabletsthe sculptured figures are exclusively those of the deceasedperson and his relatives; never these of deities, as in the tablets of the eighteenth dynasty and subsequent ages .At the close of the paper some remarks are made on thechronology of the early Egyptian kings, who are mentionedin the course of it. It is demonstrated that the predecessorof Amenemhe II. , the first king in the series of Abydos, wasOsortasen I.; the latter being the successor of Amenemhe I. ,and not his predecessor, as he has been stated to be by MajorFelix and others, on the supposed authority ofan inscriptionat Beni-Hassan. This completely overturns the hypothesisof Mr. Cullimore, respecting the connexion of a pretendedroyal series at Karnac with the series of Abydos.The phonetic hieroglyphics are represented in this paperby Hebrew characters, in preference to Roman. This hasbeen done on account of the author's peculiar views respecting the extended arm, the crux ansata, and some other characters, which he considers to be equivalent to the HebrewAyin, and by no means " vague vowels," as Champollionsupposed. He regards these characters as essentially dis-127tinct from thefeather, the eagle, and others, with which theyhave been hitherto confounded, and which he represents bythe Hebrew Aleph.The Rev. Charles Graves, F. T. C.D. , read a paperthe Application of Analysis to spherical Geometry."" OuThe object of this paper is to investigate and apply tothe geometry of the sphere, a method strictly analogous tothat of rectilinear coordinates employed in plane geometry.Through a point o on the surface of the sphere, which iscalled the origin, let two fixed quadrantal arcs of great circlesox, oy, be drawn; then if arcs be drawn from y and xthrough any point P on the sphere, and respectively meetingox and oy in м and N, the trigonometric tangents of the arcsOM, ON, are to be considered as the coordinates of the pointP, and denoted by x and y. The fixed arcs may be calledarcs of reference. An equation of the first degree betweenx and y represents a great circle; an equation ofthe seconddegree, a spherical conic; and , in general, an equation ofthe nth degree, between the spherical coordinates x and y,represents a curve formed by the intersection of the spherewith a cone ofthe nth degree, having its vertex at the centreof the sphere.Though it is not easy to establish the general formulæfor the transformation of spherical coordinates, they arefound to be simple.Let x and y be the coordinates of a point referred to twogiven arcs, and let x', y' , be the coordinates of the samepoint referred to two new arcs, whose equations as referredto the given arcs arey - y' = m (x - x'),-·y — y" = m' (x — x'),x", y", being the coordinates of the new origin; then thevalues of xх and y to be used in the transformation of coordinates would be128xy =x (ax' + by' — 1)-px' + qy' — 1y' (cx' +dy' — 1 )px' +qy' - 1In which a, b, c, d, p, and q, are functions of m, m' , x' ,and y'. It is evident that the degree of the transformedequation in x', y', will be the same as that of the originalone in x and y.The great circle represented by the equationax + By = 1 ,- -meets the arcs of reference in two points, the cotangents ofwhose distances from the origin are a and ß; and, if thearcs of reference meet at right angles, the coordinates ofthepole of this great circle are a, and — B.ß. It appears fromthis, that if a and ẞ, instead of being fixed, are connected byan equation of the first degree, the great circle will turn rounda fixed point. And, in general, if a and 3 be connected byan equation of the nth degree, the great circle will envelopea spherical curve to which n tangent arcs may be drawn fromthe same point. Thus, the fundamental principles of thetheory of polar reciprocals present themselves to us in themost obvious manner as we enter upon the analytic geometryof the sphere.A spherical curve being represented by an equation between rectangular coordinates, the equation of the greatcircle touching it at the point x' , y' , is(y — y') dx' — (x — x') dy' = 0;the equation of the normal arc at the same point is(y — y') [dy' + x' (x'dy' — y'dx')]-+ (x − x') [dx' + y' (y'dx' -x'dy') ] = 0.·Now, if we differentiate this last equation with respect to129and y' , supposing x and y to be constant, we should findanother equation, which, taken along with that of the normalarc, would furnish the values of x and y, the coordinates ofthe point in which two consecutive normal arcs intersect:and thus, as in plane geometry, we find the evolute of aspherical curve.Let 2y be the diametral arc of the circle of the spherewhich osculates a spherical curve at the point x, y' , Mr.Graves finds thattan y = ±[dx¹² + dy'² + (x'dy' — y'dx')²]}( 1 +x²² + y²²)§ (dx'd²y' — dy'd²x')'For the rectification and quadrature of a spherical curvegiven by an equation between rectangular coordinates, thefollowing formulæ are to be employed:-andds =

-

√ dx¹² + dy'² + (x'dy' — y'dx')²d (area) =1 + x/2 + y²²ydx(1 + x²) √1 + x² + y²In the preceding equations the radius ofthe sphere hasbeen supposed = 1 .The method of coordinates here employed by Mr. Gravesis entirely distinct from that which is developed by Mr.Davies in a paper in the 12th Vol, ofthe Transactions of theRoyal Society of Edinburgh. Mr. Graves apprehends, however, that he has been anticipated in the choice of thesecoordinates by M. Gudermann of Cleves, who is the authorof an " Outline of Analytic Spherics," which Mr. Graveshas been unable to procure.The President communicated a new demonstration ofFourier's theorem.130A letter was read from Professor Holmboe, accompanying his memoir, " De Priscá re Monetaria Norvegiæ," &c.,and requesting to know from the Academy whether any ofthe coins described in that work are found in Ireland . *July 12.SIR WM. R. HAMILTON, LL.D., President, in the Chair.•Part I. of a " Memoir on the Dialytic Method of Elimination," by J. J. Sylvester, Esq. A. M., of Trinity College,Dublin, and Professor of Natural Philosophy in UniversityCollege, London, was read.The Author confines himself in this part to the treatmentof two equations, the final and other derivees of which formthe subject of investigation.The Author was led to reconsider his former labours inthis department of the general theory by finding certainresults announced by M. Cauchy in L'Institut, March Number, ofthe present year, which flow as obvious and immediate consequences from Mr. Sylvester's own previously published principles and method.Let there be two equations in x,U= a * + b + c 2 + ea −3 + &c. = 0,V = axm +ßxn−1 + λxn−2 + &c.ι= 0,and let n = m + , where is zero or any positive value (asmay be).Let any such quantities as ar U, xeV, be termed augmentatives of Uor V.To obtain the derivee of a degree s units lower than V,we must join s augmentatives of U with s + of V. Thenout of 28 + equations

• The Committee of Antiquities, having been consulted on this point, reported

in the negative.131xº . U = 0,xº . V = 0,x'¹ . U = 0,x¹ . V≤0,x² . U = 0 , . . . . xs - ¹ . U= 0,x² . V = 0, . . .. x² + 8 − ¹, V = 0,we may eliminate linearly 2s + -1 quantities.Now these equations contain no power of a higher thanm + i + s − 1; accordingly, all powers of x, superior toms, may be eliminated, and the derivee of the degree(ms) obtained in its prime form.Thus to obtain the final derivee (which is the derivee ofthe degree zero) , we take m augmentatives of U with n of V,and eliminate (m +n− 1 ) quantities, namely,x, x², x³....... ,up to xm+n- ¹.This process, founded upon the dialytic principle, admitsof a very simple modification. Let us begin with the case.where 0, or m = n. Let the augmentatives of U, betermed Uo, U1, U2, U3, ..... and of V, Vo, V1 , V2, Vs, ....the equations themselves being written-2 Uax² + bxn − 1 + cx² - ² + &c .V = a'x² + b'xn − 1 + c²x² -² + &c .It will readily be seen thata'. U。-a.Vo(b' U。 − bVo) + (a' U₁ − a V₁) ,(c'.U。 −c.Vo) + (b'U₁ − bV₁ ) + (a′U₂ —aV2) ,&c.will be each linearly independent functions of x, x²,am-1, no higher power of x remaining. Whence it follows,that to obtain a derivee of the degree (ms) in its primeform, we have only to employ the s of those which occurfirst in order, and amongst them eliminate m− 1 , xm .rm-s +¹ . Thus, to obtain the final derivee, we must make useof n, that is , the entire number of them.2, ....Now, let us suppose that is not zero, but m = n − 1 .VOL. II. Mι132The equation V may be conceived to be of n instead of mdimensions, if we write it under the form1 0.x + 0.xn − 1 + 0.x² -2 + ..... + 0.xm+1 +axm + ẞxm-1 + &c. = 0.and we are able to apply the same method as above;but as the first し of the coefficients in the equation abovewritten are zero, the first i of the quantities(a'U。 — aVo) , (b' U。 − b Vo) + (a'U₁ — aV₁) , &c.may be read simply-a. Vo, b. Vo a V₁, c Vo - bV₁- aV₂, &c.―― - — —and evidently their office can be supplied by the simpleaugmentatives themselvesιV。0 = 0, V₁ = 0, V₂2 = 0 ..... ………… . V₁₁ = 0;and thus letters, which otherwise would be irrelevant, fallout ofthe several derivees.The Author then proceeds with remarks upon the general theory of simple equations, and shows how by virtue ofthat theory his method contains a solution of the identityX.U Y.V = Dr;where D, is a derivee of the 7th degree of U and V, and,accordingly, X, of the formλ + µx + vx² +.... +0xm-r-1,and Y. ofthe forml + mx + .... + txn - r- 1,and accounts a priori for the fact of not more than (n — 1')simple equations being required for the determination of the(m +n − 2r) quantities λ, µ, v, &c. l, m, n, &c . , by exhibiting these latter as known linear functions of no more than(nr) unknown quantities left to be determined.-133Upon this remarkable relation may be constructed a method well adapted for the expeditious computation of numerical values of the different derivees.He next, as a point of curiosity, exhibits the values ofthe secondary functionsa' . U。0 — aVo,-b'. U。 - bVo +a' . U₁ - aV₁,c' . U。 —c . V。 + b' . U₁ − b V₁ + a' . U₂ — a V2,&c.- 0-under the form of symmetric functions of the roots of theequations U = 0, V = 0, by aid of the theorems developedin the " London and Edinburgh Philosophical Magazine,"December, 1839, and afterwards proceeds to a more closeexamination ofthe final derivee resulting from two equationseach of the same (any given) degree.He conceives a number of cubic blocks each of whichhas two numbers, termed its characteristics, inscribed uponone of its faces, upon which the value of such a block ( itselfcalled an element) depends.For instance, the value of the element, whose characteristics are r, s, is the difference between two products: theone of the coefficient th in order occurring in the polynomial U, by that which comes sth in order in V; the otherproduct is that of the coefficient sth in order of the polynomial V, by that 7th in order of U; so that if the degree ofeach equation be n, there will be altogetherelements .(n + 1 )2suchThe blocks are formed into squares or flats (plafonds) ofn n + 1which the number is 2or 2according as n is even orodd. The first of these contains n blanks in a side, thenext (n - 2) , the next (n - 4), till finally we reach a squareof four blocks or of one, according as n is even or odd.These flats are laid upon one another so as to form a regu-134larly ascending pyramid, of which the two diagonal planes aretermed the planes of separation and symmetry respectively.The former divides the pyramid into two halves, such thatno element on the one side of it is the same as that of anyblock in the other. The plane of symmetry, as the namedenotes, divides the pyramid into two exactly similar parts;it being a rule, that all elements lying in any given line ofa square (plafond) parallel to the plane of separation areidentical; moreover, the sum of the characteristics is thesame, for all elements lying any where in a plane parallelto that of separation.All the terms in the final derivee are made up by multiplying n elements of the pile together, under the sole restriction, that no two or more terms of the said product shalllie in any one plane out of the two sets of planes perpendicular to the sides of the squares . The sign of any such product is determined by the places of either set of planesparallel to a side of the squares and to one another, inwhich the elements composing it may be conceived to lie.The Author then enters into a disquisition relating tothe number of terms which will appear in the final derivee,and concludes this first part with the statement of twogeneral canons, each of which affords as many tests for determining whether a prepared combination of coefficientscan enter into the final derivee of any number of equationsas there are units in that number, but so connected astogether only to afford double that number, less one of independent conditions.The first of these canons refers simply to the number ofletters drawn out of each ofthe given equations, (supposedhom*ogeneous); the second to what he proposes to call theweight of every term in the derivee in respect to each ofthevariables which are to be eliminated .The Author subjoins, for the purpose ofconveying a more135accurate conception of his Pyramid of derivation, examplesof the mode in which it is constructed.When n = 1 there is one flat, When n = 2 there is one flat,viz. viz.1 , 2Let n 3, there will be twoflats:2, 32, 3 2, 42,4 3, 4Let n =34, there will still betwo flats only:2, 3 2, 42, 4 3, 41, 2 1, 3 I, 4 1,51, 2 1, 3 1 , 41, 3 1, 4 1, 5 2,51, 3 1 , 4 2, 41 , 4 1, 5 2, 5 3, 51 , 4 2, 4 3, 41 , 5 2,5 3, 5 4, 5136Let n 5, there will be three flats:3, 42, 3 2, 4 2,52, 4 2,5 3,52,5 3,54, 51 , 2 1, 3 1, 4 1,5 1, 61 , 3 1, 4 1,5 1,6 2,61 , 4 1, 5 1 , 6 2, 6 3,61,5 1 , 6 2,6 3, 6 4, 61, 6 2, 6 3, 6 4, 6 5, 6137Let n = 6, there will be three flats:3, 4 3,53, 5 4, 52, 3 2, 4 2,5 2, 62, 4 2,5 2,6 3, 62,5 2,6 3, 6 4, 62, 6 3, 6 4, 6 5, 61 , 2 1, 3 1 , 4 1,5 1, 6 1, 71, 3 1, 4 1 , 5 1,6 1, 7 2,71 , 4 1, 5 1, 6 1, 7 2, 7 3,71 , 5 1, 6 1, 7 2,7 3,7 4, 71, 6 1,7 2,7 3,7 4,7 5, 71,7 2, 7 3, 7 4, 7 5, 7 6, 7Thus the work of computation reduces itself merely tocalculating n.n + 1elements, or the n (n + 1 ) cross-products138out of which they are constituted, and combining them factorially after that law of the pyramid, to which allusion hasbeen already made.DONATIONS.First Principles of Medicine. 4th Edition. By Archibald Billing, M.D. , &c. Presented by the Author.Bulletin de la Société Geologique de France. Tome XI.(1839 à 1840.) Presented by the Society.O'Halloran on the Air; a Manuscript, presented byMajor-General Sir Joseph O'Halloran, M.R.I.A. , &c.Mémoires de la Société de Physique et d'Histoire Naturelle de Genève. Tome IX. , lere Partie. Presented by theSociety.Calcul de la Densité de la Terre, suivi d'un Memoire surun cas special du Mouvement d'un Pendule. Par L. F. Menabrea. Presented by the Author.Proceedings of the Royal Society of Edinburgh. Nos.16-18.Transactions of the Royal Society ofEdinburgh. Vol.XIV. Part 2; Vol. XV. Part 1. Presented by the Society.Transactions of the American Philosophical Society. Vol.VII. Part 3. (New Series. ) Presented by the Society.PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1841 . No. 31.November 8.SIR WM. R. HAMILTON, LL.D. , President, in the Chair.John H. Jellett, Esq. , F. T. C. D. , was elected a memberof the Academy.A letter was read from Dr. Orpen, stating that increasing ill health would not allow him to continue to dischargehis duties to the Academy, and tendering the resignationof his office of Treasurer, and of his place as a member ofCouncil.RESOLVED, That the Academy have heard Dr. Orpen'scommunication with much regret, and that they deeply lament the cause which deprives them of his valuable services.Professor Mac Cullagh read the following notes on somepoints in the Theory of Light.I.On a Mechanical Theory which has been proposed for theExplanation of the Phenomena of Circular Polarizationin Liquids, and of Circular and Elliptic Polarization inQuartz or Rock-crystal; with Remarks on the corresponding Theory of Rectilinear Polarization.Thetheoryof elliptic polarization , which I feel myselfcalledupon to notice, was first stated by M. Cauchy, and has beenVOL. II. N140made the subject of elaborate investigation by other writers .That celebrated analyst, conceiving (though without sufficient reason, as will presently appear) that he had fully explained the known laws of the propagation of rectilinear vibrations by the hypothesis that the luminiferous ether, in mediatransmitting such vibrations, consists of separate moleculessymmetricallyarranged with respect to each ofthree rectangular planes, and acting on each other by forces which are somefunction of the distance, was led very naturally to imaginethat he would find the laws of circular and elliptic vibrations,in other media, to be included in the more general hypothesisof an unsymmetrical arrangement. Accordingly, in a letterread to the French Academy on the 22nd of February, 1836,a letter to which he attached so much importance that hedesired it might not only be published in the Proceedings,but also " deposited in the Archives" of that body (see theComptes rendus des Séances de l'Académie des Sciences, tom .ii. p. 182) , he gave a precise statement of his more extendedviews, informing the Academy that he had submitted his newtheory to calculation , and that, among other remarkable results , he had obtained ( with a slight variation or correction)the laws of circular polarization, discovered by Arago, Biot,and Fresnel. Referring to his Memoir on Dispersion, published at Prague, under the title of Nouveaux Exercices deMathématiques, he observes, that the results therein contained may be generalised , by " ceasing to neglect" in theequations of motion [the equations marked (24) in § 2 ofthat memoir] , certain terms which vanish in the case of asymmetrical distribution of the ether. He then goes on tosay-"Nos formules ainsi généralisées représentent les phénomènes de l'absorption de la lumière ou de certains rayons,produite par les verres colorés, la tourmaline, &c. , le phenomène de la polarisation circulaire produite par le cristalde roche, l'huile de térébenthine, &c. (Voir les expériences141de MM. Arago, Biot, Fresnel). Elles servent même à déterminer les conditions et les lois de ces phénomènes; ellesmontrent que généralement, dans un rayon de lumière polariseé, une molecule d'éther décrit une ellipse. Mais danscertains cas particuliers, cette ellipse se change en une droite,et alors on obtient la polarisation rectiligne." " Enfin le calculprouve que, dans le cristal de roche, l'huile de térébenthine,&c. , la polarisation des rayons transmis parallèlement à l'axe(s'il s'agit du cristal de roche) n'est pas rigoureusem*nt circulaire , mais qu'alors l'ellipse diffère très peu du cercle. "Thus, to say nothing for the present of the questions ofdispersion and absorption, it appears that M. Cauchy conceived he had completely accounted for the facts of circularand elliptic polarization, and that he had deduced the formulas " which serve to determine the conditions and laws ofthese phenomena. " But neither in this letter, nor in anysubsequent version* of his theory, has he given the formulasthemselves. Nor has he told us the nature of the calculationsby which he was enabled to correct the received opinion,and to prove that the vibrations in a ray transmitted alongthe axis of quartz, or through oil of turpentine, are not rigorously circular, as Fresnel and others have supposed, butslightly elliptical. Now-to take the case of quartz—if weconsider that the vibrations of a ray passing along the axisare in a plane perpendicular to it, and if we admit, as M.Cauchy always does in the case of other uniaxal crystals, thatthere is a perfect optical symmetry all round the axis, weshall find it hard to conceive on what grounds he could have

• From some statements that have been made within the last few days by Professor Powell (Phil. Mag. vol. xix. p. 374) , at the request of M. Cauchy himself,

it appears that the latter republished his views about circular and elliptic polarization, in a lithographed memoir of the date of August, 1836. But I do not find thathe published, either then or since, the detailed calculations which he seems to havemade.N 2142come to the conclusion that the vibrations of such a ray areperformed in an ellipse. For if all planes passing throughthe axis ofthe crystal be alike in their optical properties ,there will be absolutely nothing to determine the position andratio of the axes of the ellipse; there will be no reason why itsmajor axis, for example, should lie in one of these planes,rather than in any other. But, whatever may be thought ofthis case independently of observation , it is manifestly absurd to suppose that the vibrations are elliptical in the caseof a ray passing through oil of turpentine, or any other liquidpossessing the property of rotatory polarization; for , in aliquid , all planes drawn through the ray itself are circ*mstanced alike. Fromthese simple considerations it is evidentthat the theory of M. Cauchy is unsound; but a closer examination will show that it is entirely without foundation , andthat it is directly opposed to the very phenomena which itprofesses to explain. To make this appear, however, inthe easiest way that the abstruseness of the subject willallow, it will be necessary to advert to some former researches of my own, which have a direct bearing on thequestion.The same day on which M. Cauchy's letter was read tothe French Academy, I had the honour of reading to theRoyal Irish Academy, a paper " On the Laws of Double Refraction in Quartz" (see Transactions R. I. A., vol. xvii .p. 461 ) , wherein I showed that every thing which we knowrespecting the action of that crystal upon light is comprisedmathematically in the following equations:d?? d² d³ndt2 dg2 dz³ =A + c 39(1)d2n d²n d³Edt2 dz2 d23'which differ from the common equations of vibratory motionby the two additional terms containing third differential co-143efficients multiplied by the same constant c, this constanthaving opposite signs in the two equations. The quantitiesÉ and ŋ are, at any time t, the displacements parallel to theaxes of x and y, which are supposed to be the principal directions in the plane of the wave, one of them being therefore perpendicular to the axis of the crystal. The constantsA and B are given by the expressionsA = a², B = a² — ( a² —b²) sin² ,where a and b are the principal velocities of propagation,ordinary and extraordinary, and is the angle made by thewave-normal (or the direction of 2) with the axis ofthe crystal. The only new constant introduced is c, which, thoughthe peculiar phenomena of quartz depend entirely on its existence, is almost inconceivably small; its value is determinedin the paper just referred to. The equations are there provedto afford a strict geometrical representation of the facts; notonly connecting together all the laws discovered by the distinguished observers to whom M. Cauchy refers, and including the subsequent additions for which we are indebtedto Mr. Airy, but leading to new results, one of which establishes a relation between two different classes of phenomena, and is verified by the experiments of M. Biot and Mr.Airy. Having, therefore, such conclusive proofs of the truthof these equations, we are entitled to assume them as astandard whereby to judge of any theory; so that any mechanical hypothesis which leads to results inconsistent withthem may be at once rejected .Now I assert that the mechanical hypothesis of M.Cauchy contradicts these equations, and therefore contradicts all the phenomena and experiments which he supposedit to represent. But before we proceed to the proof of thisassertion, it may perhaps be proper to remark, that previously to the date of M. Cauchy's communication , and of myown paper, I had actually tried and rejected this identical144hypothesis, and had even gone so far as to reject along with it.the whole of M. Cauchy's views about the mechanism of light .For though, in my paper, I have said nothing of any mechanical investigations, yet , as a matter of course, before it wasread to the Academy, I made every effort to connect myequations in some way with mechanical principles; and itwas because I had failed in doing so to my own satisfaction,that I chose to publish the equations without comment,* asbare geometrical assumptions, and contented myself withstating orally to the Academy, as I did some months after tothe Physical Section of the British Association in Bristol(see Transactions of the Sections, p . 18), that a mechanicalaccount ofthe phenomena still remained a desideratum whichno attempts of mine had been able to supply. I am not surethat on the first occasion I stated the precise nature oftheseattempts, though I incline to think I did; but I have a distinct recollection of having done so on the second occasion,in reply to questions that were asked me by some Membersofthe Association. Now, my first attempt to explain thoseequations, which was made almost as soon as I discoveredthem, actually turned upon the very idea which about thesame time found entrance into the mind of M. CauchyI mean the idea of an unsymmetrical arrangement of theether. For as it was generally believed , at that period,

• The circ*mstances here related will account for what Mr. Whewell (History of

the Inductive Sciences, vol. ii . p. 449) calls the " obscure and oracular form" inwhich those equations were published . Having, at that time, no good explanationof them to give, I thought it better to attempt none. But in the general view whichI have since taken (see p. 103 of this volume) , they do not offer any peculiar difficulty.At the period of this meeting, M. Cauchy's letter on Elliptic Polarizationhad been published for some months; but I was not then aware of its existence.Indeed the letter appears not to have attracted any general notice; for the theorywhich it contains was afterwards advanced in England as a new one, and M.Cauchy has been lately obliged to assert his prior claim to it, through the mediumofProfessor Powell. - See notes, pp. 141 , 149 .145that the hypothesis of ethereal molecules symmetricallydistributed had led , in the hands of M. Cauchy, to acomplete theory of rectilinear polarization in crystals (seehis Exercices de Mathématiques, Cinquième Année, Paris,1830, and the Mémoires de l'Institut, tom x. p. 293) , thenotion of endeavouring to account for the phenomena ofelliptic polarization, by freeing the hypothesis from any restriction as to the distribution of the ether, would naturallyoccur to any one who was thinking on the subject, no lessthan to M. Cauchy himself. And though, for my own part,I never was satisfied with that theory, which seemed to me topossess no other merit than that of following out in detailthe extremely curious, but (as I thought) very imperfect,analogy which had been perceived to exist between the vibrations of the luminiferous medium and those of a commonelastic solid (for it is usual to regard such a solid as a rigid

• The analogy was suggested by the hypothesis of transversal vibrations, which,

when viewed in its physical bearing, was considered by Dr. Young to be " perfectlyappalling in its consequences," as it was only to solids that a "lateral resistance"tending to produce such vibrations had ever been attributed. ( Supplement to theEncyclopædia Britannica, vol. vi . p. 862: Edinburgh, 1824) . He, admits, however, that the question whether fluids may not " transmit impressions by lateral adhesion, remains completely open for discussion , notwithstanding the apparent difficulties attending it. " As far as I am aware, Fresnel always regarded the ether as afluid. M. Poisson affirms that it must be so regarded, and attributes its apparentpeculiarities to the immense rapidity of its vibrations, which does not allow the lawof equal pressure to hold good in the state of motion ( Annales de Chimie, tom. xliv.p. 432). M. Cauchy calls the ether a fluid , though he treats it as a solid. My ownimpression is, that the ether is a medium ofa peculiar kind, differing from all ponderable bodies, whether solid or fluid , in this respect, that it absolutely refuses, in anycase, to change its density, and therefore propagates to a distance transversal vibrations only; while ordinary elastic fluids transmit only normal vibrations, and ordinary solids admit vibrations of both kinds. This hypothesis also includes thesupposition that the density of the ether is unchanged by the presence of ponderable matter. As to M. Cauchy's third ray, with vibrations nearly normal to the wave,there is no reason to believe that it has even the faintest existence; but it is necessarily introduced by his identification of the vibrations of light with those of an indefinitely extended elastic solid.116system of attracting or repelling molecules, and M. Cauchyhas really done nothing more than transfer to the luminiferous ether both the constitution ofthe solid and differentialformulas of its vibration), still I should have been glad, inthe absence of anything better, to find my equations supported by a similar theory, and their form at least countenanced by the like mechanical analogy. Besides , I recollected that Fresnel himself, in his Memoir on Double Refraction, had indicated a " helicoidal arrangement, " or something of that sort, as a probable cause of circular polarization (Mémoires de l'Institut, tom. vii. p. 73); and as thiswas an hypothesis of the same kind as the other, only notso general, I was prepared to find that the supposition ofan arbitrary arrangement, whatever might be thought of itsphysical reality, would lead to equations of the same formas those which I had assumed. Upon trial , however, thevery contrary proved to be the case, for though it was possible to obtain additional terms, containing differential coefficients of the third order, multiplied by the same constantC, yet this constant always came out with the same sign inboth equations , whereas a difference of sign was essentialfor the expression ofthe phenomena. I had no sooner arrived at this result, than I perceived it to be fatal to thetheory of M. Cauchy, and to afford a demonstration of itsinsufficiency, not only in the particular application which Ihad made of it, but in all its applications. For the hypothesis which I used was, in fact, identical with that theory,in the most general form of which it is susceptible , when unrestricted by any particular supposition as to the arrangement of the ethereal molecules; and therefore the fundamental conception of the theory could not be true, as it notmerely failed to explain a large and most remarkable class ofphenomena- those of circular and elliptical polarization-butabsolutely excluded them, and left no room for their existence. It followed from this, that the mechanical explanation ,147which the same theory was supposed to have given, of thephenomena of rectilinear polarization and double refractionin crystals , could not be well founded; indeed, as I havesaid, I had always distrusted it, and that for various reasons, of which one has been already mentioned, and anotherwas suggested by the forced relations which M. Cauchy hadfound it necessary to establish among the constants of histheory, and by which he had compelled, as it were, his complicated formulas to assume the appearance of an agreement(though, after all, a very imperfect one) with the simple lawsof Fresnel.Such were the conclusions at which I arrived , and thereflections which they forced upon me, nearly six years ago.They have been frequently mentioned in conversation tothose who took an interest in such matters, and their generaltenor may be gathered from what I have elsewhere written(Transactions of the Academy, vol. xviii. p. 68); but I did notthink it worth while to publish them in detail, because it seemedprobable that juster notions would prevail in the course of afew years, and that the ingenious speculations to which Ihave alluded would gradually come to be estimated at theirproper value. But from whatever cause it has arisen- whether from the real difficulties of the subject, or the extremevagueness of the ideas that most persons are content to formofit, or from deference to the authority of a distinguishedmathematician- certain it is that the doctrines in questionhave not only been received without any expression ofdissent,but have been eagerly adopted , both in this country and abroad ,by a host offollowers; and even the extraordinary error, whichit is my more immediate object to expose, has been continuallygaining ground up to the very moment at which I write, andhas at last begun to be ranked among the elementary truths ofthe undulatory theory oflight. Notwithstanding my unwillingness, therefore, to be at all concerned in such discussions,I do not think myself at liberty to remain silent any longer.148There are occasions on which every consideration ofthis kindmust give way to a regard for the interests of science.To show that the principles of M. Cauchy contradict, instead of explaining , the phenomenon of elliptic polarization,let us take the axes of coordinates as before; and let us suppose, for the sake of simplicity, and to avoid his third ray,that the normal displacements vanish . Then his fundamentalequations take the formd°Edt2 = ΣƒAE + ΣhAn,d²n = EgAn + EhAĘ,dt2(2)where f, g, h are quantities depending on the law offorceand the mutual distances of the molecules. * If, therefore,I have not thought it necessary to transcribe the original equations of M.Cauchy, which are rather long. He has presented them in different forms; but thesystem marked ( 16) at the end of § 1 of his Memoir on Dispersion, already quoted,is the most convenient, and it is the one which I have here used . The directionsof the coordinates being arbitrary, I have supposed the axis of ≈ to be perpendicular to the wave- plane. Then, on putting = 0 , A = 0 , in order to get rid ofthe normal vibration, the last equation of the system becomes useless, and the othertwo are reduced to the equations (2 ), given above; the letters f, g, h, being written in place of certain functions depending on the mutual actions of the molecules.It will be proved, further on , that this simplification does not at all affect the argument. As the directions of x and y still remain arbitrary , I have made them parallel to the axes of the supposed elliptic vibration.It may be right to observe, for the sake of clearness, that, when the medium isarranged symmetrically, it is always possible to take the directions of x and y suchthat the two sums depending on the quantity h may disappear from the equations(2 ) , and then the vibrations are rectilinear. But when the arrangement is unsymmetrical, this is no longer possible.The equations (2 ) are precisely the same as those which have been employedby Mr. Tovey and by Professor Powell, the latter of whom, in his lately publishedwork, entitled, " A General and Elementary View of the Undulatory Theory, as applied to the Dispersion of Light, and other Subjects,” has dwelt at great length onthe theory of elliptic polarization , which they have been supposed to afford, andwhich he regards as a most important accession to the Science of Light. ProfessorPowell has also made some communications on the subject to the British Asso-149we assume that each molecule describes an ellipse, the axesofwhich are parallel to those of x and y; that is to say, if wemake= pcos p, nqsing,and consequently2п4 = 2T (st — ≈),-(3)A = p (sin 20 sin - 2 sin 20 cos p),where 0Ang(sin 20 cosTAS+2 sin 20 sin ),= we shall find, by substituting these values in λthe equations (2) , which must hold good independently of p,C's² = A' + c'k, s2 = B' -k'Σfsin 20 -2khsin 200,(4)2Eg sin 20+ sin 20 = 0,kwherein k = expresses the ratio ofthe semiaxes of the elΡliptic vibration, and12 12 A =2π2Efsin 20,B' =272 Eg sin 20,124π2c'h =sin 20.ciation, and has written two papers about it in the Philosophical Transactions ( 1838,p. 253; and 1840, p. 157) , besides several others in the Philosophical Magazine.He, however, always attributed this theory of elliptic polarization to Mr. Tovey,until his attention was directed, by a letter from M. Cauchy, to some investigations of the latter which he had not previously seen ( Phil. Mag. vol . xix. p. 374) .Mr. Tovey set out with the principles of M. Cauchy, and therefore naturally struckinto the same track, in pursuit of the same object, apparently quite unconscious thatany one had preceded him. It was, indeed, an obvious reflection , that these principles, when generalised to the utmost, ought to include, not only the laws ofelliptic polarization, but (as really has been thought by M. Cauchy and his followers) of dispersion and absorption , and, in short, of all the phenomena of optics.150Equating the two values of s², we get, for the determinationof k, the following quadratic:-k² +A' B'c'k + 1 = 0. (5)Now making the substitutions (3) in equations ( 1 ) , page 142,we have2π 2п с82 =A ck, -(6)λ X k'and thenceλk2 -- (7)πε· (A − B) k − 1 = 0,a result which is perfectly inconsistent with the former, sincethe two roots of( 5) have the same sign, if they are not imaginary, while those of ( 7) have opposite signs, and cannot beimaginary. If, therefore, one equation agrees with the phenomena, the other must contradict them. The last equationindicates that, in the double refraction of quartz, the twoelliptic vibrations are always possible, and performed in opposite directions, which is in accordance with the facts;whereas the equation (5) , deduced from M. Cauchy's theory,would inform us that the vibrations of the two rays areeither impossible or in the same direction. *To apply the results to a particular instance, let us conceive a circularly polarized ray passing along the axis ofquartz, or through one of the rotatory liquids, such as oil ofturpentine; the position of the coordinates x and y, in theplane of the wave, being now, of course , arbitrary. In eachofthese cases we have k = ± 1 , and A = Ba², so that thevalue of s² in equation (6) is expressed by the constant a²,plus or minus a term which is inversely proportional to the

• This conclusion , which shows that M. Cauchy's Theory is in direct opposition

to the phenomena, might have been obtained without any reference to the equations ( 1 ). But these equations are necessary in what follows.151wave-length; the sign of this term depending on the direction of the circular vibration . Now it will not be possibleto obtain a similar value of s² from the formulas (4) , unlesswe suppose A'B' a², since it is only in the expansion.of c' that a term inversely proportional to λ can be found;but on this supposition the formulas are inconsistent witheach other, nor can they be reconciled by any value of k.Indeed, when A'B', the equation (5) gives k = ± √ − 1 .Thus it appears that circular vibrations, such as are knownto be propagated along the axis of quartz, and through certain fluids, cannot possibly exist on the hypothesis of M.Cauchy. It was probably some partial perception of thisfact that caused M. Cauchy to assert that the vibrations,in these cases, are not exactly circular, but in some degreeelliptical; a supposition which, if it were at all conceivable,which we have seen it is not (p. 142) , would be at once setaside by what has just been proved; for no assumed valueof k, whether small or great, will in any way help to removethe difficulty.But this is not all. Rectilinear vibrations are excludedas well as circular; for we cannot suppose k = 0 in the equations (4) , so long as the quantity c', resulting from the hypothesis of unsymmetrical arrangement, has any existence .Thus the inconsistency ofthat hypothesis is complete, and theequations to which it leads are utterly devoid of meaning.The foregoing investigation does not differ materiallyfrom that which I had recourse to in the beginning of theyear 1836. To render the proof more easily intelligible,and to get rid of M. Cauchy's " third ray," which has noexistence in the nature of things, I have suppressed thenormal vibrations; a procedure which is not, in general, allowable on the principles of M. Cauchy. It will readily appear, however, that this simplification still leaves the demonstration perfectly rigorous in the case of circular vibrations,152-- 1.and does not affect its force when the vibrations are elliptical. For in the rotatory fluids it is obvious that the normalvibrations, supposing such to exist, must, by reason ofthesymmetry which the fluid constitution requires, be independent ofthe transversal vibrations, and separable from them,so that the one kind ofvibrations may be supposed to vanishwhen we wish merely to determine the laws of the other.The equations ( 2) are , therefore, quite exact in this case;and they are also exact in the case of a ray passing alongthe axis of quartz, since such a ray is not experimentally distinguishable from one transmitted by a rotatory fluid, andits vibrations must consequently be subject to the same kindof symmetry. In these two cases, therefore , it is rigorouslyproved that the values of k, which ought to be equal to plusand minus unity, are imaginary, and equal to ± √And if we now take the most general case with regard toquartz, and suppose that the ray, which was at first coincident with the axis of the crystal, becomes gradually inclinedto it, the values ofk must evidently continue to be imaginary,until such an inclination has been attained that the two rootsofequation (5) become possible and equal, in consequence ofthe increased magnitude of the co-efficient of the secondterm . Supposing the last term of that equation to remainunchanged, this would take place when the co- efficient of k(without regarding its sign) became equal to the number 2,and the values of k each equal to unity, both values beingpositive or both negative. The vibrations which before wereimpossible, would, at this inclination , suddenly become possible; they would be circular, which is the exclusive property of vibrations transmitted along the axis; and theywould have the same direction in both rays, which is not aproperty ofany vibrations that are known to exist. At greaterinclinations the vibrations would be elliptical, but they wouldstill have the same direction in the two rays. These results would not be sensibly altered by regarding the equa-153tion (5) as only approximate in the case of rays inclined tothe axis; for the last term of that equation, if it does not remain the same, can never differ much from unity; since it mustbecome exactly equal to unity, whatever be the direction ofthe ray, when the crystalline structure is supposed to disappear, and the medium to become a rotatory fluid .That a theory involving so many inconsistencies shouldhave been advanced by a person of M. Cauchy's reputation ,would, perhaps, appear very extraordinary, if we did not recollect that it was unavoidably suggested by the generalprinciples which he had previously adopted , and which weresupposed, not merely by himself, but by the scientific worldgenerally, to have already afforded the only satisfactory explanation of the laws of double refraction in the commonand well-known case where the vibrations are rectilinear.This supposed explanation was obtained, as has been said ,by restricting the application of M. Cauchy's principles tothe hypothesis of a vibrating medium arranged symmetrically,in which case it was shown that the vibrations were necessarily rectilinear; and of course the removal of this restriction was the only way in which it was possible, on thoseprinciples, to account for the existence of circular and elliptical vibrations . Accordingly, when M. Cauchy perceivedthat, onthe hypothesis ofunsymmetrical arrangement, the existence of rectilinear vibrations became impossible, and thatof elliptic vibrations, generally speaking, possible, he foundit very easy to persuade himself that he had obtained anew proof of the correctness of his views, and a new andmost important application of the fundamental equationsby which his general principles were analytically expressed.To have supposed otherwise would have been to admitthat his general principles were false. If the elliptical orquasi-circular vibrations which he was now contemplatingwere not capable of being identified with those which hadbeen recognized in the phenomena presented by quartz and154the rotatory fluids -if their laws were essentially or veryconsiderably different-his theory would be inconsistentwith a wide range of well known facts, and, notwithstanding its so- called explanations of other laws, should befinally abandoned . Under these circ*mstances, therefore,he very naturally supposed that his new results must bein complete harmony with the phenomena discovered byM. Arago, and analysed so successfully by MM. Biot andFresnel; although, had he taken the precaution of acquiringsuch a clear notion ofthe phenomena as would have enabledhim to translate them into analytical language, he must haveperceived that they were entirely opposed to his results, andthat this opposition furnished an argument which swept awaythe very foundations of his theory . For, if the constitutionof the luminiferous medium were such as M. Cauchy supposes, the well-known phenomena of circular and elliptic polarization would, as we have seen, be absolutely impossible.Thus the argument which overturns the particular theoryof elliptical polarization destroys at the same time all theother optical theories of M. Cauchy, because they are allbuilt on the principles which we have now demonstrated to befalse. But though the principles of M. Cauchy are now, forthe first time, formally refuted, they were objected to, ongeneral grounds, so long ago as the year 1830, by a personwhose opinion, on a question of mechanics, ought to have hadconsiderable weight. This was M. Poisson, who, having deduced from the equations of motion of an elastic solid the consequence that such a body admitted vibrations perpendicular to the direction of their propagation, thought it right toremark that this conclusion could not be supposed to accountfor transversal vibrations in the theory of light, because (ashe expressed himself) " the same equations of motion couldnot possibly apply to two systems [ of molecules] so essentially different from each other" as the ethereal fluid and155an elastic solid . * (See the Annales de Chimie, tom. xliv.p. 432). The remark, however, did not meet with muchattention from mathematicians, who were, perhaps, not disposed to scrutinize too closely any hypothesis which gavetransversal vibrations as a result. Besides, the hypothesisappeared to go much further, as it offered primá facieexplanations of a great variety of phenomena; it was oneto which calculation could be readily applied , and therefore it naturally found favour with the calculator; and asto M. Poisson's objection, it was easily removed by a changeof terms, for when the elastic solid was called an " elasticsystem," there was no longer anything startling in the announcement that the motions of the ether are those of sucha system. The hypothesis was therefore embraced by agreatnumber of writers in every part of Europe, who reproduced,each in his own way, the results of M. Cauchy, though sometimes with considerable modifications. Every day saw somenew investigation purely analytical-some new mathematicalresearch uncontrolled by a single physical conception- putforward as a " mechanical theory" of double refraction, ofcircular polarization , of dispersion, of absorption; until atlength the Journals of Science and Transactions of Societieswere filled with a great mass of unmeaning formulas . Thisstate of things was partly occasioned by the great number ofdisposable" constants entering into the differential equationsofM. Cauchy and their integrals; for it was easy to introduce,among the constants, such relations as would lead to any desired conclusion; and this method was frequently adopted byM. Cauchy himself. Thus, in his theory of double (or rathertriple) refraction , given in the works already cited (p. 145) , hesupposes three out of his nine constants to vanish, and assumes ,66

• As the theory of M. Cauchy (Mem. de l'Institut, tom. x. ) had been communicated to the Academy of Sciences some months before the period (October, 1830)

at which M. Poisson wrote, there can be no doubt that M. Poisson's remark wasdirected against that theory, though he did not expressly mention it.VOL. II.156among the other six, three very strange and improbable relations, by means of which each of the principal sections ofhis wave-surface (considering only two out ofits three sheets)is reduced to the circle and ellipse of Fresnel's law; andthe three principal sections being thus forced to coincide, itwould not be very surprising if the two sheets were foundto coincide in every part with the wave- surface of Fresnel.The coincidence, however, is only approximate; but M.Cauchy is so far from being embarrassed by this circ*mstance ,that he does not hesitate to regard his own theory as rigorously true, and that of Fresnel as bearing to it, in point ofaccuracy, the same relation which the elliptical theory of theplanets, in the system of the world, bears to that of gravitation (Mémoires de l'Institut, tom. x. p. 313) . Nor is he atall embarrassed by the supernumerary ray belonging to thethird sheet of his wave- surface; he assumes at once thatsuch a ray exists, though it was never seen, and promises,for the satisfaction ofphilosophers, to make known the meansof ascertaining its existence (Ibid. p. 305). But he afterwardscontented himself with observing that as its vibrations are inthe direction of propagation they probably make no impression on the eye, and he then gave it the name of the " invisibleray." (Nouveaux Exercices, p. 40).In these investigations, the suppositions which M. Cauchyhad made respecting the constants led to the result that thevibrations of a polarized ray are parallel to its plane of polarization; but in the year 1836 he changed his opinion on thispoint, and then, by reinstating the constants that he had before supposed to vanish, and establishing proper relationsamongst them and the rest, he arrived at the conclusion thatthe vibrations are perpendicular to the plane of polarization(Comptes Rendus, Tom. ii . p. 342). All his other results, ofcourse, underwent some corresponding change; and it is thisnew theory which must now be regarded as rigorous, whilethat of Fresnel is to be looked on as approximate. But it is157needless to say, that if the accuracy of Fresnel's law ofdouble refraction is to be disputed, it must be on much bettergrounds than these; and the results of M. Cauchy are certainly too far removed from that law to have any chance ofbeing consonant with truth. Although, for example, his newviews respecting the direction of the vibrations agree, in ageneral way, with those of Fresnel, there is yet, in one particular, an important difference between them; for according to Fresnel, the vibrations are always exactly in the surface of the wave, while, according to M. Cauchy (in his oldtheory as well as the new) , they are only so in ordinary media.In a biaxal crystal he finds-and this is one of the ways inwhich the " invisible ray" manifests its influence that thedirection of vibration , in each ofthe two rays that are visible,is inclined at a certain angle to the wave- plane; but thisangle, though small, is by no means inconsiderable, as M.Cauchy seems to intimate, overlooking the fact, which appearsfrom his own equations, that it is of the same order of magnitude as the quantities on which the double refraction depends. It is true, the deviation measured by this angle cannot, if it exists, be directly observed in the refracted light;but its indirect effects on reflected light ought to be verygreat, since the action of the crystal on a ray reflected at itssurface differs fromthat of an ordinary medium by a quantityof the same order merely as the aforesaid angle; and as theproblem of crystalline reflexion has been already solved( Trans. R. I. A. vol . xviii. , p. 31 ) on the supposition (whichis an essential one in the solution) that the vibrations are exactly in the plane of the wave, it is highly improbable, considering the complex nature of the question , that it will besolved, in any satisfactory way, on a supposition so differentas that which is required by the theory of M. Cauchy. However, as the laws of such reflexion are now well known, bymeans ofthe solution alluded to, it is possible that M. Cauchymay, as in the case of double refraction, succeed in deducing02158the same laws, or, if not the same, what may seem to be moreexact laws, from certain principles of his own, helped out,if need be, by proper relations among his constants; especially if, to allow greater scope for such relations, the numberof constants be increased by the hypothesis of two coexist-

• In applying these principles to the question of reflexion and refraction at the

surface of an ordinary medium ( Comptes Rendus, Tom. ii . p. 348) , M. Cauchy hasarrived at the singular conclusion, that light may be greatly increased by refractionthrough a prism, at the same time that it is almost totally reflected within it. Supposing the refracting angle of the prism to be very little less than the angle of total reflexion for the substance of which it is composed, a ray incident perpendicularly on one of the faces will emerge making a very small angle with the otherface; and as the reflexion at the latter face is nearly total , it is self- evident thatthe intensity of the emergent light, as compared with that of the incident, must bevery small. M. Cauchy, however, finds, by an elaborate analysis, that a prodigiousmultiplication of light [ " une prodigieuse multiplication de la lumière"] takes place,the emergent ray being nearly six times more intense than the incident when theprism is made of glass, and nearly nine times when the prism is of diamond. Thisresult was, in a general way, actually verified experimentally by himself and another person; so easy it is, in some cases, to see anything that we expect to see. Hadthe result been true, it would have been a very brilliant discovery indeed; for thenwe should have been able, by a simple series of refractions, to convert the feeblestlight into one of any intensity we pleased; but the very absurdity of such a supposition should have taught M. Cauchy to distrust both his theory and his experiment. Far from doing so, however, he considers the fact to be perfectly established, and to afford a new argument against the system of emission. " Ici, " sayshe, " un rayon, réfléchi en totalité, est de plus transmis avec accroissem*nt delumière; ce qui est un nouvel argument contre le système d'émission."The system of emission has at least this advantage, that by no possible error could such aconclusion be deduced from it. For if all the particles of light be reflected, certainly none of them can be refracted.The truth is, that M. Cauchy mistook the measure of intensity in the hypothesis of undulations, supposing it to be proportional simply to the square of theamplitude of vibration; whereas it is really measured by the vis viva, or by thatsquare multiplied by the quantity of ether put in motion , a quantity which in thepresent case is evanescent, since the corresponding volumes of ether, moved by theray within in the prism and by the emergent ray, are to each other as the sine oftwice the angle of the prism to the sine of twice the very small angle which theemergent ray makes with the second face of the prism. The intensity ofthe emergent light is therefore very small, as it ought to be, though the amplitude of itsvibrations is considerable.159ing systems ofmolecules , an hypothesis which M. Cauchy hasalready considered with his usual generality, but withoutmaking any precise application of it. (Exercices d'Analyseet de Physique Mathématique, Tom. i . p. 33.)Perhaps one cause why M. Cauchy's views on the subjectof double refraction have met with such general acceptance,may be found in the fact, that a theory setting out from thesame principles , and leading, by the same relations amongconstants, to formulas identical in every respect with hisearlier results, was advanced independently, and nearly atthesame time, by M. Neumann of Königsberg (Poggendorff'sAnnals, vol. xxv. p. 418) . A coincidence so remarkablewould be looked upon, not unreasonably, as a strong argument in favour ofthe theory; though it must be allowed that,in the effort to extend the knowledge of any subject, there isa tendency in different minds to adopt the same errors respecting it, as well as the same truths; a fact of which wehave seen other examples in the course of the presentarticle.According to M. Neumann (ibid. p. 454) , the " thirdray," not being perceived as light, must manifest its existenceas radiant heat, or as a chemical power, or as some otheragent [" als strahlende Wärme, oder chemisch wirkend, oderals irgend ein anderes Agens" ] , and he thinks that the natureofthis ray will be more easily investigated , if the laws of reflexion shall be deduced from the aforesaid theory. But wehave seen that the laws of reflexion are, to all appearance, atvariance with the theory, and they take no account whateverof the third ray. Besides, the discoveries which have beenmade of late years respecting the polarization ofradiant heat,and the strong analogies that have been traced between itand light, amount to a demonstration that its vibrations aretransversal, and of course essentially different from thoseof the supposed third ray, which are normal, or nearly so.There is every reason to believe that the vibrations ofthe160chemical rays are also transversal; and we may confidentlyassert, that the three species of rays-those of light andheat, and the chemical rays, -are produced not only by vibrations of the same medium, but by the same kind of vibrations, propagated with nearly the same velocities. If, therefore, the third ray of MM. Cauchy and Neumann has anyexistence, it must be referred to " some other agent," thenature of which it is impossible to conjecture.Enough has now been said to show that the optical theorywhich we have examined, and which has passed current inthe scientific world for a considerable period , is quite inadequate to explain the leading phenomena of light, and that itis based upon principles which are altogether inapplicable tothe subject. M. Cauchy states, in the memoir so oftenquoted (Mem. de l'Institut, Tom. x. p. 294) , that the first application which he had made of his principles was to thetheory ofsound, and that the formulas which he had deducedfrom them agreed remarkably well with the experiments ofSavart and others on the vibrations of elastic solids . As Ihave already intimated , it is in the solution of such questions (which, however, have long been familiar to mathematicians) that the fundamental equations of M. Cauchy may bemost advantageously employed; and had he pursued his researches in this direction , his labours would doubtless havebeen attended with more success, and with greater benefitto science.II.On Fresnel's Formula for the Intensity of ReflectedLight, with Remarks on Metallic Reflexion.When Mr. Potter discovered , by experiment, that morelight is reflected by a metal at a perpendicular incidencethan at any oblique incidence (at least as far as 70° ) , the factwas looked upon, by himself and others , as contrary to all received theories; and certainly the universal opinion, up tothat time, was, that the intensity ofreflexion always increases161with the incidence. It may therefore be worth while to remark, that the formula given by Fresnel for reflexion at thesurface of a transparent body, though not of course applicable, except in a very rude way, to the case of metals, wouldyet lead us to expect, for highly refracting bodies as themetals are supposed to be, precisely such a result as thatobtained by Mr. Potter. For when the index of refractionexceeds the number 2 + √3, or the tangent of 75°, the expression for the intensity of reflected light will be found tohave a minimum value at a certain angle of incidence; whilefor all less values ofthe refractive index the intensity will beleast at the perpendicular incidence.Let i and ' be the angles of incidence and refraction,and putM=sin isin ¿'M =cos icos i'then if I be the intensity of the reflected light, when commonlight is incident, Fresnel's expression1 = {}{+( sin² (ii) tan²(ii)sin² (i + ¿') tan²(i + i')9in which the intensity of the incident light is taken for unity,may be put under the formI=( − µ) ² + (~ − ×) ²+ μ ++M22( + + + x ) * 'which has a minimum value when1μ+μ= M +the value of I being in that caseM21-МM M +M(x - M4) = 4 ( + ) - 82M M= 22(M − 1 ) ³ − 2(x + 1 ) ³ — 8'-- M 9( x M162and the corresponding angle of incidence being given by theformula2 Msini =ε + √ 2where & = M +M1Since μ +-μcannot be less than 2, it is easy to see that, whenthere is a minimum, M +1cannot be less than 4, and there- M--fore м cannot be less than 2 + √3, or 3.732.1As an example, let м + 6. Then, at a perpendicu- Mlar incidence, one- half the incident light will be reflected.The minimum will be when i = 65° 36', and at this angleonly of the incident light will be reflected. The valuehere assumed for the refractive index is that which Sir J.Herschel (Treatise on Light, Art. 594), assigns to mercury;but if my ideas be correct, it is far too low for that metal.The only person who supposes that the refractive indexofa metal is not a large number, is M. Cauchy. It has alwaysbeen held as a maxim in optics , that the higher the reflectivepower ofany substance, the higher also is its refractive index .But M. Cauchy completely reverses this maxim; for, as Ihave elsewhere shown (Comptes Rendus, tom. viii . p. 964) , itfollows from his theory that the most reflective metals are theleast refractive, and even that the index of refraction, whichfor transparent bodies is always greater than unity, may formetals descend far below unity. Thus, according to his formula, the index of refraction for pure silver is the fraction ,so that the dense body of the silver actually plays the partof a very rare medium with respect to a vacuum. It appearsto me that such a result as this is quite sufficient to overturnthe theory from which it is derived . The formulas, however,which he gives for the intensity of the reflected light, areidentical with the empirical expressions which I had givenlong before, and are at least approximately true.In framing my own empirical theory (see Proceedings,163vol. i . p. 2), two suppositions relative to the value of therefractive index presented themselves. Putting м for themodulus, and x for the characteristic, I had to choose between the values McOS X and Mcos X• The latter value is thatwhich I adopted; the former , which is M. Cauchy's, was rejected because I saw that it would lead to the result abovementioned.Another result of M. Cauchy's, which he has given twicein the Comptes Rendus ( tom. ii. p. 428, and tom. viii . p. 965)requires to be noticed . When a polarized ray is reflectedby a metal, the phase of its vibration is altered , and if the incidence be oblique, the change of phase is different, according as the light is polarized in the plane of incidence , or inthe perpendicular plane. But when the ray is reflected at aperpendicular incidence , it is manifest that the change is aconstant quantity, whatever be the plane of polarization. Infact, the distinction between the plane of incidence and theperpendicular plane no longer exists, and the phenomenamust be the same in all planes passing through the ray.Yet M. Cauchy, in the two places above quoted, asserts it tobe a consequence of his theory, that in this case the alterations of phase are different for two planes of polarization atright angles to each other, and that the difference of the alterations amounts to half an undulation . The same singularhypothesis had been previously made by M. Neumann (Poggendorff's Annals, vol. xxvi . p. 90) , whom M. Cauchy appearsto have followed; but M. Neumann has since admitted it tobe erroneous (Ibid. vol. xl. p. 513) .Mr. J. Huband Smith communicated to the Academy someparticulars connected with the recent discovery of a cairncontaining cinerary urns , which appears to have been accompanied by some circ*mstances not unworthy of notice.It took place at Loughanmore, in the county of Antrim,164the seat of Mr. Thomas Adair, in a field which was beingploughed, in the spring of 1840. After a few urns had beenfound, there being some difficulty in preserving them entire , Mr. Adair, with a commendable desire to avoid the destruction of remains so full of interest, caused the cairn , inwhich these urns were found, to be closed carefully, and restored the ground to its former state as nearly as might be, inorder to leave it to some skilful and experienced antiquary toexplore the entire in a more deliberate and scientific manner.The discovery was occasioned by one ofthe horses whichwere in the plough suddenly stumbling, one of his legshaving sunk nearly up to the knee in a deep hole. On examination it was found he had put his foot into a fine sepulchral urn, which, it need hardly be stated, was broken intoshivers.On a slight further search a second urn was discovered .Every effort was made to preserve this one entire, but invain; it fell to pieces in the hands of the person who took itup. A third urn was then exposed, when Mr. Adair findingit impossible to save them, put a stop for the time to the further opening of the cairn.The cairn in which these urns were found is situatedin the townland of Loughanmore, and not far from theLoughan or lake (now drained) from which the townland derives its name. It lies within a field called the cove- park,there being one or more artificial caves, or coves (as theyare termed by the Antrim peasantry) , within it . And froma hollow sound which the ground gives, other caves, as yetunopened, are confidently supposed to exist near where theurns were found .The cairn in question is indicated by so very slight anelevation of the surface, thatit was in course of being ploughedover without any particular notice, till the finding of the urnsdrew Mr. Adair's attention to it. This elevation was thenobserved to have a circumference of some twelve or fourteen165feet, perhaps a little more; and on closer examination provedto be composed of loose field- stones mixed with earth, apparently laid in, upon, and around the urns, with just somuch care as not to break them.It will not fail to be noticed, that in this latter circ*mstance this cairn seems to differ remarkably from most others,for instance Deveril Barrow in Dorsetshire, which has beenthought worthy of an elegant descriptive work, and manyother of the Wiltshire Barrows, so carefully and scientificallyopened by an eminent and accomplished English antiquary,the late Sir Richard Colt Hoare; and also from the veryimportant cairn opened at Mount Stewart, near Grey- Abbey,in the county of Down, about the year 1807. In these theurns have almost invariably been protected by a kist or stonechest formed of flags, enclosing a considerable space. Wehave the authority of our distinguished Irish antiquary,Mr. George Petrie, for saying that " the sepulchral urns ofIreland are superior in ornament to any found in England .The ornaments of gold frequently found in them are richerand more numerous." And he does not hesitate to inferfrom these and other facts, that " the pagan Irish were superior in the arts of civilized life to their British neighbours."These urns found at Loughanmore were found to havebeen all placed with the mouth downwards. Theylay ratherclosely together, scarce eighteen inches apart from eachother, the smaller urns appearing to surround the larger one,which was that broken by the horse.The two smaller sized urns were of the same size, andwould hold probably eight or nine quarts of liquid each.No metallic remains of brass or bronze; no flint arrowheads, stone adzes, or any other remains were found . Everyprobability exists of future discoveries of a most interestingdescription being made on a stricter examination of thiscairn.Opportunities such as this daily offer themselves in this166country, of pursuing an inquiry of deep historical interest;which if they were to occur at the other side of the Irishchannel, would be grasped at with avidity by the untiringzeal of many an English antiquary, who, while he cultivatesassiduously, and under circ*mstances of extreme difficulty,the meagre opportunities which England affords to thestudy ofancient British and Celtic remains , cannot but lookwith a feeling of astonishment (akin perhaps to contempt) ,on the apathy with which in Ireland we suffer daily the tangible and unquestionable proofs of the early civilization ofour country, to which we have long proudly laid claim, actually to perish before our eyes, from the most disgracefulnegligence.The Chair having been taken, pro tempore, by the Rev.J. H. Todd, D. D. , V. P. , the President communicated thefollowing proof of the known law of Composition of Forces.Two rectangular forces, x and y, being supposed to beequivalent to a single resultant force p, inclined at an anglev to the force x, it is required to determine the law of thedependence of this angle on the ratio ofthe two componentforces x and y.Denoting by p' any other single force, intermediate between x and y, and inclined to a at an angle ' , which weshall suppose to be greater than v; and denoting by x' andy' the rectangular components of this new force p' , in thedirections of x and y, we may, by easy decompositions andrecompositions, obtain a new pair of rectangular forces, x"and y", which are together equivalent to p' , and have forcomponentsx"[]y+ = y';XCy" = =y'-yΡ167the direction of a" coinciding with that of p' , but the direction of y" being perpendicular thereto. Hence,that is,tanor, finally,<-1y" xy' -yx'x" xx' +yy' '=y"'x"tan 1 yx'- tan yXƒ(v' — v) = ƒ(v′) —ƒ( v), (A)at least for values of v, v ' , and '- v, which are each greaterπthan 0, and less than; ifƒbe a function so chosen that theequationy= tanƒ(v)expresses the sought law of connexion between the ratioyXand the angle v. The functional equation ( A) givesmƒ(mv) = mf(v) ==ƒ(nv) ,m and n being any whole numbers; and the case of equalcomponents gives evidentlyhenceπ=M π=n 4 n 4 'and ultimately,f(v) = v, (B)πbecause it is evident, by the nature of the question, thatwhile v increases from 0 to the function f(v) increasestherewith, and therefore could not be equal thereto for allvalues of v commensurable with , unless it had the sameproperty also for all intermediate incommensurable values.We find, therefore, that for all values of the ' componentforces a and y, the equation168y= tan vX(c)holds good; that is, the resultant force coincides in directionwith the diagonal of the rectangle constructed with lines representing x and y as sides .The other part of the known law of the composition offorces, namely, that this resultant is represented also in magnitude by the same diagonal, may easily be proved bytheprocess of the Mécanique Céleste, which, in the present notation, corresponds to makingx' = x, y' = y, x" = p,and therefore givesx² + y²y²,p = p² = x² + y².ΡBut the demonstration above assigned for the law ofthedirection of the resultant, appears to Sir William Hamiltonto be new.It was resolved, on the recommendation of the Council,to present a congratulatory address to His Excellency theLord Lieutenant; whereupon, the Academy having adjourned for a short interval, an address was prepared, which wasafterwards agreed to.A letter was read from M. Moreau de Jonnés, presenting to the Academy two volumes of the Agricultural Statisticsof France.DONATIONS.Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences. Premier Semestre . 1841. Nos. 17-24.Ordnance Map of the Queen's County, in 39 sheets, including Title and Index. Presented by His Excellency theLord Lieutenant.Journal ofthe Franklin Institute. Vol. I. Third Series.( 1841) .169Det Kongelige Danske Videnskabernes Selskabs Naturvidenskabelige og Mathematiske Afhandlinger. 8de Deel.( 1841) .Commentationes Societatis Regia Scientiarum Gottingensisrecentiores. Vol. VIII. ( 1832-1837) .Esop's Fables in Chinese. Presented by the Rev. DavidThom.An Account of the Magnetic Observations made at Harvard University. (U. S.) Presented by the AmericanAcademy.Résumé des Observations sur la Meteorologie, sur le Magnetisme, &c. , faites a l'Observatoire Royal de Bruxelles en1840. Par le Directeur A. Quetelet. Presented by theAuthor.Memoire sur la Diathermansie Electrique des CouplesMetalliques:Des Travaux et des Opinions des Allemands sur la PileVoltaique:Essai Historique sur les Phénoménes et les Doctrines del'Electro- Chimie. Par Professeur C. F. Wartmann. Presented by the Author.Oversigt over det Kongelige Danske Videnskabernes Selskabs Forhandlinger og dets Medlemmers Arbeider. 1 Aaret,1839-40.Report ofthe Council ofthe Zoological Society of London. April 29, 1841 .Report on the Observations by the self-registering Anemometer, in 1837-40. By A. F. Osler, Esq. Presented bythe British Association.Abstract ofthe Magnetic Observations made at the Travandrum Observatory in May, 1841. By John Caldecott,Esq. Presented by the Author.Extrait du Tom. VIII. No. 6, des Bulletins de l'AcademieRoyale de Bruxelles. (" Physique du Globe.") Presentedby M. Gudele.170Rapport Decennal des Travaux de l'Academie Royalede Bruxelles depuis 1830. Par M. A. Quetelet, Hon. M.R. I. A., &c. &c.Annuaire de l'Academie Royal de Bruxelles . 7me année.Annuaire de l'Observatoire Royale de Bruxelles, pourl'An 1841. Par M. Quetelet. Presented by the Author.Des Moyens de soustraire l'Exploitation des Mines deHouille aux Chances d'Explosion. Recueil de Memoires etde Rapports publié par l'Academie Royale de Bruxelles .Presented by the Academy.Traité élémentaire des Fonctions Elliptiques. Par P. F.Verhulst. Presented by the Author .Statisque de la France (Agriculture) . Tom. I. II. ParM. De Jonnés. Presented by the Author.First Publication of the Irish Archeological Society.Presented by the Society.Memoires couronnes de l'Academie Royale de Bruxelles.Tome XIV. me Partie ( 1839–40) .Nouveaux Memoires de l'Academie Royale de Bruxelles.Tome XIII. ( 1841) .Bulletins de l'Academie Royale de Bruxelles. Nos. 9, 12( 1840). Nos. 1 , 6 ( 1841 ) .Transactions of the Zoological Society of London. Vol.II. Part 5 .Meteorological Observations made in Dublin. By ThomasH. Orpen, M. D., M. R. I. A. Presented by the Author.Journal ofthe Statistical Society of London. Vol. IV.Part 3.Seventh Annual Report of the Poor-Law Commissioners( 1841 ).Report ofthe Poor- Law Commissioners on Medical Charities in Ireland. ( 1841 ) . Presented by George Nicholls,Esq.Abhandlungen der Königlichen Akademie der Wissenschaften zu Berlin. (1839) .PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1841.November 30. (Stated Meeting. )No. 32.SIR WM. R. HAMILTON, LL.D., President, in the Chair.The following communication " on the Compound Nature of Nitrogen," by George J. Knox, Esq. , was read byDr. Kane.Soon after the discovery ofthe bases of the alcalies andearths by Sir Humphrey Davy, the compound nature of nitrogen began to be a subject of discussion amongst chemists;but the arguments in favour of this supposition, deducedprincipally from the nature of the ammoniacal amalgam, ledto no satisfactory physical results.The experiments of Sir Humphrey Davy on the ammoniacal nitruret of potassium, and those of Despretz andGrove on the compounds of nitrogen with iron, copper, &c.,have shown that the metals singly (even when aided by themost powerful electrical induction) have not the power ofdecomposing nitrogen. There is one experiment, however, bySir Humphrey Davy, from which one might deduce its compound nature.Upon heating ammonia- nitruret of potassium in an irontube, he obtained more hydrogen, and less nitrogen, thanthe ammonia ought to have given.Again on mixing this substance with a greater proportion of potassium, he obtained still more hydrogen, andVOL. II. P172less nitrogen; whereas, on heating the same substance in atube ofplatinum, the potassium alloyed with the platinum, andthe ammonia was given off almost entirely undecomposed.How can these experiments be explained except uponthe supposition that the potassium and the iron had conjointly decomposed the nitrogen? The latest experimentswhich bear upon this subject, and from which I received theidea which led me to this investigation, are those of DoctorBrown, " upon the conversion of Carbon into Silicon," anexplanation of phenomena which appears to me most unreasonable, and contrary to all chemical analogy; whilst thesupposition of the carbon having reduced the nitrogen is notonly a simple but an unavoidable conclusion to arrive at, ifnitrogen be a compound substance. To determine, by experiment, the correctness or incorrectness of this idea, it wereonly necessary to reduce nitrogen by some other substancethan charcoal; and should silica result from its decomposition,the problem might be considered to be solved.Exp. I. -A considerable quantity of ammonia- nitruret ofpotassium was formed , by passing ammonia over potassiumheated in an iron tube; the part which had not been in contact with the tube, having been examined for silica, containednone.Exp. II.-Ammonia was passed for several hours overpure iron, heated to a dull red heat; examined for silica, itcontained none.Exp. III .-Ammonia- nitruret of potassium was heatedwith pure iron in an iron crucible, for one half hour, over alarge Rose's lamp; the contents of the crucible, on examination, gave silicon and silica, the weight of which was not registered, as it might have been said to have derived a portionof silica from the inner surface of the crucible.Exp. IV. Twenty grains of ammonia-nitruret of potassium were heated with twenty grains of pure iron in thesame iron vessel for one half hour; when treated with nitric173and muriatic acids there remained insoluble a small quantityof a brownish colour, which, when fused with carbonate ofpotash, gave of silica 0.10. The solution, supersaturatedwith potash, filtered , neutralized, evaporated to dryness,gave of silica 1.450; sum total of silica 1.550 .From these experiments, together with those of Sir Humphrey Davy mentioned above, one might infer that nitrogenis either a compound of silicon and hydrogen, or of silicon,hydrogen, and oxygen; to determine which, synthetically, acurrent of dry muriatic acid gas was passed over siliciuretof potassium (formed by heating silica with potassium),placed in a bent tube of Bohemian glass, the extremity ofwhich dipped into a cup of mercury, lying on the bottom ofa vessel filled with water. The atmospheric air had beenpreviously expelled from the apparatus by a current ofhydrogen.The gases insoluble in water having been collected , werefound, on examination, to be hydrogen and nitrogen, therelative proportions of which varied in different experiments.In two experiments the proportions of hydrogen to nitrogen were four of the former to one ofthe latter.In a third experiment, as six of hydrogen to one ofnitrogen.In a fourth, as five of hydrogen to four of nitrogen.Observation. White fumes appeared occasionally in thetube, indicating the presence of muriate of ammonia.Professor Lloyd exhibited a specimen of Rock from TerreAdele.Professor Mac Cullagh communicated to the Academy avery simple geometrical rule, which gives the solution oftheproblem of total reflexion, for ordinary media and for uniaxal crystals.P 2174First, let the total reflexion take place at the commonsurface oftwo ordinary media, as between glass and air, andlet it be proposed to determine the incident and reflectedvibrations, when the refracted vibration is known. It is tobe observed, that the refracted vibration ( which is in generalelliptical) cannot be arbitrarily assumed; for, as may beinferred from what has been already stated ( Proceedings ofthe Academy, vol. ii . p. 102) , it must be always similar to thesection of a certain cylinder, the sides of which are perpendicular to the plane of incidence, and the base of which isan ellipse lying in that plane and having its major axis perpendicular to the reflecting surface, the ratio of the major tothe minor axis being that of unity to the constant r. Thevalue of r, as determined by the general rule in p. 101 , isr = √11n2 sinwhere i is the angle of incidence, and n the index of refraction out ofthe rarer into the denser medium. The ellipse isgreatest for a particle at the common surface of the media;and for a particle situated in the rarer medium, at thedistance from that surface, its linear dimensions are proportional to the quantity e λ; so that for a very small value2πτ7of the refracted vibration becomes insensible.Now, taking any plane section of the aforesaid cylinderto represent the refracted vibration for a particle situated atthe common surface ofthe two media, let op and oo be thesemiaxes ofthe section, and let them be drawn, with theirproper lengths and directions, from the point of incidence o;through which point also let two planes be drawn to represent the incident and reflected waves. Then conceive aplane passing through the semiaxis op, and intersecting thetwo wave- planes , to revolve until it comes into the positionwhere the semiaxis makes equal angles with the two intersections; and in this position let the intersections be madethe sides of a parallelogram, of which the semiaxis op is the175diagonal. Let oa and oa', which are of course equal in length,denote these two sides. Make a similar construction for theother semiaxis oQ, and let OB, OB' , which are also equal, denotethe two sides of the corresponding parallelogram . Then willthe incident vibration be represented by the ellipse of whichOA and OB are conjugate semidiameters, and the reflected vibration by the ellipse of which оA' and Oв' are conjugate semidiameters. And the correspondence of phase in describingthe three ellipses will be such that the points A, A', P will besimultaneous positions, as also the points B, B', Q.The same construction precisely will answer for the caseof total reflexion at the surface of a uniaxal crystal, which iscovered with a fluid of greater refractive power than itself.It is to be applied successively to the ordinary and extraordinary refracted vibrations, and we thus get the uniradial incident and reflected vibrations, or rather the ellipses which aresimilar to them. And as any incident vibration may be resolved into two which shall be similar to the uniradial ones,we can find the reflected vibration which corresponds to it,by compounding the uniradial reflected vibrations.It may be well to mention that, in a uniaxal crystal, theplane of the extraordinary refracted vibration is always perpendicular to the axis, and therefore the ellipse in which thevibration is performed may be easily determined by the remark in p. 102. The plane of the ordinary vibration has nofixed position in the crystal; but if we conceive the auxiliary quantities 1 , 71, 1 , (p. 98) to be compounded into an ellipse (as if they were displacements) , the plane of this auxiliary ellipse will be perpendicular to the axis of the crystal.Whether the preceding very simple construction , for finding the incident and reflected vibrations by means ofthe refracted vibration , extends also to the case of biaxal crystals,is a point which has not yet been determined, on account ofthe complicated operations to which the investigation leads,at least when attempted in any way that obviously suggestsitself.176Joseph Huband Smith, Esq. was elected a Member of theCommittee of Antiquities, and Dr. Aquilla Smith was electedTreasurer of the Academy, in the room of Dr. Orpen, resigned .The following Address was presented on the 13th November to the Lord Lieutenant:" To His Excellency the Right Hon. Thomas Philip Earl DeGrey, Lord Lieutenant- General and General- Governor ofIreland." MAY IT PLEASE YOUR EXCELLLENCY," We, the President and Members of the Royal IrishAcademy, have the honour to present to your Excellency ourvery sincere congratulations on your arrival in our metropolitan city, as the representative of our most gracious Sovereign." It has been the pleasure of her Majesty to declare herself the Patron of the Institution of which we are members;and, in virtue of the charter which was granted to us by one.ofher royal predecessors, King George the III., the office ofVisitor ofthe Academy has become vested in your Excellency, as Lord Lieutenant of Ireland ." We cannot but think ourselves fortunate in an officialconnexion with a nobleman who, in his private career, hasshown himself so much attached to arts and letters as yourExcellency is known to be." The objects of the Royal Irish Academy are Science,Polite Literature , and Antiquities; and in the tranquil pursuitof these objects, the importance of which is appreciated byyour Excellency, we have had the pleasure of seeing fostered within our body those feelings of mutual good- will,which are, perhaps, scarcely less highly to be prized than thepursuit of knowledge itself.(Signed)" WILLIAM ROWAN HAMILTON, President."177To which His Excellency was pleased to return the following answer:" MR. PRESIDENT, AND MEMBERS OF THE ROYALIRISH ACADEMY," I thank you for your congratulations on my arrival inIreland." It is a source of pleasure to me to feel that a part ofmypublic duty, as the Representative of her Majesty, will bringme into such immediate connexion with the body of scientific and learned gentlemen forming the Royal Irish Academy." The duties of a visitor lose the austerity of official character, and merge into those of friendship and association,whenthe person who is invested with them has the honour ofbeing received with the warmth which has distinguished yourreception of myself." You are pleased to estimate my fitness and talents beyond their value; but I can assure you that you cannot attachmore importance than I do to the welfare and prosperity ofsuch institutions as yours. As you justly observe, the pursuit of the objects principally cultivated by the Royal IrishAcademy enables you to foster within your body feelings ofmutual good-will; and when I see enrolled amongst yourmembers those who conscientiously entertain a difference ofopinion upon points ofthe very highest importance, I cannotwithhold my conviction of the public utility of a society whichaffords them a point of union, and holds out to them an object upon which they can honestly coincide."DONATIONS.Bericht über die zur Bekanntmachung geeigneten Verhandlungen der Königl. Preuss. Akademie der Wissenschaften zu Berlin. VomJuli 1840 bis Juni 1841.Transactions of the Cambridge Philosophical Society.Vol. VII. Part. 2.178Astronomische Nachrichten. Nos. 413–432.Magnétisme terrestre. Par M. Quetelet. Extrait du tom.VIII. No. 9, des Bulletins de l'Academie Royale du Bruxelles . Presented by the Author.Nouveaux Memoires de l'Academie Royale des Scienceset Belles-Lettres de Bruxelles. Tome. XIV.Memoires Couronnés par l'Academie Royale des Scienceset Belles-Lettres de Bruxelles. Tome XV. 1ere partie1840-41 .Memoire sur différens Procédes d'Integration, par lesquelson obtient l'attraction d'un ellipsoïde hom*ogene dont les troisaxes sont inégaux, sur un point extérieur. Par M. J. Plana.Presented by the Author.The Fishes ofthe Dukhun. By Lieut.- Col. W. H. Sykes,F. R. S. Presented by the Author.Notes on India before the Mahommedan Invasion. ByLieut.-Col . W.H. Sykes, F. R. S. Presented by the Author.Proceedings of the Royal Society. Nos. 44-48. 1840-41.Supplemental Instructions for the Use ofthe MagneticalObservatories. Presented by the Royal Society.On the Character of Sir John Falstaff. By James O. Halliwell, Esq . Presented by the Author.APlan ofMedical Reform and Reorganization oftheProfession. By Richard Carmichael, Esq. Presented by theAuthor.December 13.SIR WM. R. HAMILTON, LL.D., President, in the Chair.The President read the following letter from the RightHon. Sir John Newport, Bart. , presenting to the Academya manuscript containing an account ofthe Loans of Moneyto King Charles I.179" New Park," 12th November, 1841 ." I desire, Sir, to offer for acceptance of the Royal IrishAcademy, of which I have, during many years , had thehonour of being a member, a volume, which, as it respects amost interesting period of British history, and materiallytends to elucidate transactions which had a powerful influence in producing the calamitous results, in the reign ofCharles the First, that immediately succeeded, may bedeemed not unworthy of admission into the Library of theInstitution." The volume contains correct copies of the orders oftheLords of the Council, and letters addressed to the LordLieutenants ofthe counties ofEngland, and others, directingthe assessment and collection of what was called a voluntaryloan, according to the annexed lists, from the several landholders, merchants, and merchant strangers of England, andthe citizens of the cities and towns therein, including thejudges and law officers, but specially excluding all membersof the peerage, with whom it was not purposed to deal forthe present.'"" The original documents, of which this volume is a transcript, were found during the period whilst I held the officeofComptroller- General of the Exchequer, amongst a largecollection of papers deposited in the Pells Office; and as Iconsidered them to afford interesting materials to elucidatethe history of that eventful period, I directed two copies tobe made ofthem; one of these I sent to the British Museum,and now offer the other to the acceptance of the Royal IrishAcademy." The great inequality ofthe extent ofthe demand on theseveral parties thus assessed, varying in a great degree withtheir capacity of resistance to its enforcement, will be quiteapparent on examining the lists; as will also the urgency ofthe measure, from the repetition of the letters from the Lords180of the Council, at a short interval of time, deprecating furtherdelay, and censuring what had already occurred.One name in the list of contributors from the town ofCambridge, that of Hobson the carrier, celebrated by somelines of Milton, has , from that circ*mstance, attracted attention, from the sum demanded and the nature of his occupation." The original papers have been injured by damp, andrendered in some degree, but not materially, defective ." In order to render the papers more accessible forperusal, I have sketched out a table of reference which Ienclose, and avail myself of the kindness of my valuedfriend, the Lord Bishop of Cashel, for their transmission toDublin." Sir William R. Hamilton,President R. I. Academy,&c . &c. &c."" I am, Sir," Your obedient Servant," JOHN NEWPORT.The special thanks of the Academy were voted to SirJ. Newport.A paper was read by William Roberts, Esq. , F. T. C. D.," on the Rectification of Lemniscates and other Curves."Let a curve be traced out by the feet of perpendicularsdropped from a fixed origin upon the tangents to a givencurve: and from this new curve, let another be derived by asimilar construction, and so on. Also let a curve be imaginedwhich is constantly touched by perpendiculars to the radiivectores of the given curve, drawn at the points where it ismet by these radii, and from this let another be derived by asimilar mode of generation, and so on.Then if sn denote the arc of the curve which is nth inorder in the former series, and s_n that of the nth in the latter, we shall have181d2w + nrdr.2 (1 ±n)drdw dw3 +22dsndr.3(1 +redw² ±n +1dw ± n- 1dr rdr,2dr.2F (r, w) = 0 being the polar equation of the given curve .It is convenient to distinguish the curves ofthe two seriesby calling those of the former positive, and those of the latter negative; we may also generally denote their polar coordinates by the symbols + w±n°Ifthe given curve, which may be denominated the baseof either system, be an ellipse whose centre is the origin, itwill be found, by applying the above formula, that the negative curves will in general have their arcs expressible byelliptic integrals of the first and second kinds, whose modulusis the eccentricity of the base-ellipse. The arc of the firstwill involve only a function of the first kind: a result whichhas been given by Mr. Talbot in a letter addressed to M.Gergonne, and inserted in the Annales des Mathematiques,tom. xiv. p. 380.A function of the third kind , with a circular parameter- 1 + b², where b is the semiaxis minor of the ellipse, itssemiaxis major being unity, and the modulus of which is theeccentricity, enters into the arcs of all the positive curves;and their general rectification depends only on that of theellipse, and of the first derived, both positive and negative.The quadrants of the ellipse, and of the first two curves,positive and negative, are connected by the following relation:(S-1S1) S -1 (3s - s- 2) (2s — S2).It is worthy of notice, that if the eccentricity be √5–1 2the functions of the third kind disappear, and the rectification of both series depends only on that of the ellipse and ofthe first negative curve.182If the base curve be a hyperbola, whose centre is theorigin, the arcs of all the curves of the negative series willdepend only on elliptic functions ofthe first and second kinds.But the general expression for the arc in the positive seriescontains a function of the third kind , the parameter of whichis alternately circular and logarithmic: the curves of an oddorder involving the same function of the circular kind , andthose ofan even order the same of the logarithmic kind, ifthe real axis of the base- hyperbola be greater than the imaginary, and vice versa.Mr. Roberts also shows, that besides the case of theequilateral hyperbola, in which the first positive curve is thelemniscate of Bernouilli, and which has been the only onehitherto noticed , at least as far as he is aware, there are twoothers, in which the arc ofthe first positive curve can be expressed by a function of the first kind, with the addition ofa circular arc in one case, and of a logarithm in the other.The first of these occurs when the imaginary semiaxis isequal to (the distance between the centre and focusbeing unity), and this fraction is the modulus of the function.The other case is furnished by the conjugate hyperbola, andthe modulus is complementary. In both these cases functions of the third kind disappear from the arcs of the positivecurves.√5-12If the hyperbola be equilateral, and its semiaxis be supposed equal to unity, the general equation of the derivedcurves of both series may be presented under the form+n2+2n-1 2w+n= COS ± 2nThe successive curves represented by this equation are verycuriously related to each other. The following property appears worthy of remark:Let P - 1 , Pn, Pa+1 be corresponding points on the183(n − 1)th, nth, and (n + 1 )th curves of the positive series respectively, and v their common vertex, which is also that of thehyperbola, then willarc VP -1 + right line Pn- 1 Pn =2n 12n +1--arc VPn +1Mr. Roberts states that he has demonstrated the propertyin a manner purely geometrical.This equation shows that the arcs of all the curves of anodd order will depend only on that of Bernouilli's lemniscate ,or the function F { √√, } , and those of an even order onlyon the arc of the second of the series. This latter arc isthree times the difference between the corresponding hyperbolic arc and the portion of the tangent applied at its extremity, which is intercepted between the point of contact andthe perpendicular dropped upon it from the centre: and theentire quadrant is three times the difference between theinfinite hyperbolic arc and its asymptot.Also, Sn, Sn +1 , denoting the quadrants of the nth, and(n + 1 )th curves, the following very remarkable relation existsbetween them,Sn Sn+1 = (2n + 1 )πThe curves of the negative series enjoy analogous properties.Lastly, let the base curve be a circle , the origin beingwithin it and it appears that the rectification of the curvesof both series, which are of an even order, can be effectedby the arcs of circles; and that those of an odd order, whichbelong to the positive series, will involve elliptic integrals ofthe first and second kinds in their arcs. The negative curvesof an odd order contain a term depending on a function ofthe third kind, which is however reducible to a function ofthe first kind and a logarithm.By the particular consideration of the first negative curvein this case, Mr. Roberts was led to a very simple demon-184stration of the equation which results from the application ofLagrange's celebrated scale of reduction to elliptic functionsof the second kind, and which is nothing more than theanalytical expression of Landen's theorem .Professor Mac Cullagh exhibited to the Academy someRoman Denarii, from the collection of Mrs. Alexander ofBlackheath (Coleraine) .These coins (twenty-eight in number) were found inthe year 1831 , along with an immense quantity of othersof the same kind, weighing altogether about eight pounds,by a labourer who was digging in a field on the FaughMountain, near Pleaskin, one of the headlands of theGiant's Causeway. According to an account publishedat the time in the Belfast News' Letter (June, 1831 ) , andcommunicated to the Academy by the Rev. Dr. Drummond,they were found under a flat stone which was turned up bythe spade. Nearly 200 of them ( says this account) were soldfor a trifling sum to an English gentleman at Coleraine, andsome ofthe remainder were bought by the Rev. R. Alexander.Ofthe twenty-eight coins that were exhibited , only seventeenhave their legends legible, and these are of the times of theemperors, from Vespasian to the Antonines. The followinglist of them has been supplied by Dr. Aquilla Smith, withreferences to the catalogue of the University Cabinet, published by the Rev. J. Malet, F. T. C. D.1. Vespasian,2. Vespasian,3. Domitian,Malet, 384.Reverse, a winged Caduceus.Malet, 452.4. Domitian,5. Nerva,6. Trajan,7. Trajan, S8. Trajan,9. Trajan,10. Hadrian,•• Reverse, Minerva.• Malet, 467.• Malet, 513.Reverse, Minerva.Reverse, a Female seated.Malet, 548.18511. Hadrian,12. Antoninus Pius,13. Antoninus Pius,14. Antoninus Pius,15. Antoninus Pius,••16. Faustina the Elder,Malet, 552,• Malet, 615.• Malet, 621.Malet, 623.Re. aFemale holding a Cornucopia.Malet, 670.17. FaustinatheYounger, Malet, 723.Dr. Smith remarks, that the coin of Hadrian, No. 11 , isinteresting, as having on the reverse a star and crescent,resembling those on the Irish coins of King John.The Rev. Dr. Drummond then gave an account of otherRoman coins that had been found in Ireland; and in somepreliminary observations he dwelt on the utility ofpreservinga knowledge even of such an insulated fact as the discoveryofa coin, for though of little importance in itself, it mightprompt to farther research, and lead both the historian andantiquary to consequences which could scarcely have beenanticipated .In England, almost every year is bringing to light variousmonuments of Roman antiquity, but in Ireland they are exceedingly rare; though, perhaps, ofmore frequent occurrencethan is generally known. Ancient coins and other articleshave been repeatedly found by persons ignorant of their realvalue, and sold as mere metal by their weight, without regard to their age and character. Thus, we read in Mason'sParochial Survey, that in the parish of Dunaghy were founda number of silver coins, which were sold at Ballymena before any one had an opportunity of examining or describingthem. Again, the Rev. Alexander Ross informs us, thata person on whose veracity he could depend, assured him,that about thirty years prior to the time of his writing, twoor three men, in digging an old fort near Cashel, found anearthen pot, which might contain four or five quarts, filledwith gold coins of different sizes ( Par. Survey, II . p. 304) .186The same writer states that " a fine copper coin of the Emperor Nero was found some years ago, and is now in Mr. A.Ogilby's collection , the head finely relieved , and in perfectpreservation." In the collection of the Royal Dublin Societyare three Roman copper coins of the Cæsars, dug up in Fermanagh, and presented by Sir C. Coote. But the most curious fact in connexion with the coins exhibited by Mr. MacCullagh, is that of a Roman gold coin being found manyyears previous, nearly in the same locality. The Rev. RobertTrail, in his statistical account of Ballintoy ( Mason's Par.Survey), says, " within these few days a gold coin of Valentinian was brought to me in perfect preservation, and is nowin my custody. It is about the size of half a guinea, and onthe head side is the following inscription D. N. VALENTINIANUS, P. F. AUG. On the reverse RESTITUTOR REIPUBLICÆ.As Valentinian succeeded Jovian in 364, and died in 375,this money must have been struck during that period, buthow it came into this parish I cannot conjecture. " -(II.p. 155) .A single coin might be accidentally dropped and lost bysome collector or virtuoso, on his tour to the Giant's Causeway; but we cannot account in this way for a large collectionof coins of ancient date. They must have been placedwhere they were found, by some careful hand, probably intimes of turbulence and danger, as in a place of safety,whence they might be removed at a more favourable season.Afew years ago, G. Putland, Esq. , of Bray, had occasionto build piers for a gate contiguous to the sea-beach, on thenorth side of Bray Head. His workmen, on digging for afoundation, were surprised to meet with the skeletons of several human bodies, which, on farther examination, theyfound to be placed, not confusedly heaped together, as theslain on a battle field , but in graves placed regularly sideby side, and separated each from its neighbour, by thinpartitions of flag or of stone. On the exposure to the air,187the bones crumbled to atoms; the teeth alone were moredurable, and in tolerable preservation . * The most remarkable circ*mstance connected with these skeletons was a number of Roman copper coins, one or two of which lay on orbeside the breast of each. Of these coins , which were aboutthe size of our penny pieces, some bore the image and superscription of Adrian, and others those of Trajan, in clear anddistinct relief. Several were greatly corroded, and renderedaltogether illegible . A few of the best of these coins werefor a short time in Dr. Drummond's possession. He shewedthem to the late lamented Dean of St. Patrick's, who saidthat he had seen a coin precisely similar, which was foundin the island of Lambay.As the Romans never formed any settlement in Ireland ,the question naturally arises, how came these coins to beplaced in this locality, and under such circ*mstances? Theready reply is, that the bodies here interred were probablythose of mariners, the crew of some Roman galley that hadbeen stranded and lost on the shores of Bray, and that someof the survivors who had escaped, performed the funeralrites . Among the Romans it was deemed an act of great impiety to leave a corpse unburied; and hence Horace introduces the shade of the drowned Archytas, imploring thepasser by to sprinkle a little dust on his body, which hadbeen cast on the shores of Tarentum. Palinurus, in Virgil,makes a similar request.The coins, it is presumed, were the fee designed for thegrim ferryman; a part ofthe funeral rites of the greatest importance, and by no means to be neglected , for the shades ofthose who had not the proper fee, as well as of those whose

• Sir William Hamilton, in a paper in the Archæologia (vol. iv. p.161 ) , observes

that the teeth of some skeletons of soldiers, found at Pompeii, were remarkablysound. " Perhaps," says he, " among the ancients, who did not use sugar, theymight not be so subject to decay as ours."VOL. II.188bodies remained unburied , were condemned to wander ahundred years on the banks of the Styx ,Thus may we account for the Roman coins found at Bray;but how shall we account for those dug up at Fermanagh, ordiscovered at Dungiven, Ballintoy, and the neighbourhood ofthe Giants' Causeway?Though the Romans never had any permanent station inIreland, they were well acquainted with its geographical position, its passages, and its harbours, as we learn from theunquestionable testimony of Tacitus; and though this andother testimonies were wanting, it might be fairly presumedthat the Roman fleets which encompassed Great Britain,sailed beyond the Orkneys, and boasted that they had arrived at the Ultima Thule, could not be ignorant of Irelandand its coasts, though not induced by the spirit of commerceor adventure. The mariners would sometimes be tempted toland, if not to repair their shattered vessels, to procure wood,water, and provisions.Tacitus informs us that Agricola obtained informationconcerning the state of Ireland , from one of its chiefs, who,for disaffection or rebellion, had been driven into exile, andsought refuge from the Roman commander. It is to be lamented that our native Irish historians, as far as the writerhas been able to ascertain, are completely dark on this subject. Though an eminent Irish scholar, profoundly versedin our ancient MSS. , can produce one passage--but it is theonly one he ever met with-which seems to countenancethe idea that the Romans had subjected any sept oftheIrish to their yoke. He states that in discussing the meansbywhich Conor Mac Nesa, King of Ulster, and cotemporarywith Christ, discovered the crucifixion of the Saviour, awriter, in an old Irish MS. , in the library of T.C.D. , saysthat " he learned it from the Druid Bachrach, or from Altusthe Consul, who came from Octavin to ask the tribute fromthe Gaels."189Roman coins might find their way to Ireland in the common intercourse of trade. They may have been brought bythe early Christian missionaries, or by men who fled hither,as to an asylum, from persecution . It is universally admitted, says Lanigan, that there were Christian congregations inIreland before the mission of Palladius in 431 , though it isimpossible to determine who first introduced Christianity.-It is reasonably conjectured , that during the persecution ofDiocletian and Maximian, the only one recorded as havingextended to Britain, some Christians , and particularly thoseof the clerical order, sought refuge in Ireland; and it is a fairpresumption that they would bring with them such articles aswere most precious and most easily carried, among whichcoins and jewels are the chief. There is yet another mode ofaccounting for these remains of antiquity, not less plausible.The early Irish, like the neighbouring nations, were fond ofmaking predatory excursions. They often landed on theshores of England and Wales, and carried off whatever spoilfell into their hands. They also assisted their friends, theAlbanian Scots, whose country they colonized under CarbreRiada, in their wars with the Romans, and may havesometimes returned enriched with treasure, obtained by thesword.Of the spoils, by which they were sometimes enriched, itmay suffice to mention an instance, extracted from O'Flaherty's Ogygia. Crimthan Nianair, the 111th Monarch ofIreland, towards the end of the first century, returnedfrom a " foreign expedition, in which he obtained a veryrich booty; among which was a golden chariot; a pair oftables, studded with 300 brilliant gems; a quilt, of various colours; a cloak, interwoven with threads of gold; asword, engraved with various figures of serpents , which wereof the purest gold; a shield , embossed with refulgent silverstuds; a spear, which always gave an incurable wound; asling, so unerring, that it never missed; two hounds coupledQ 2190with a chain, which, being made of silver, was worth 300 cows,with other valuable rarities. ”—Ogygia, II. pp. 182–183.The same author informs us that about the middle ofthethird century, Cormac, the 126th Monarch of Ireland,equipped a large fleet, which he sent to the North ofBritain, where he was committing depredations for three-p. 238.66years."99He also states, on the authority ofAmmianus Marcellinusand Claudian, that the Saxons, in conjunction with our countrymen the Scots and Picts, made frequent excursions toBritain a long time before they made settlements in thatcountry. Ammianus, he says, writes that " the Scots (i . e . theIrish) and Picts, not only invaded those places in Britain thatwere adjacent to the Roman boundaries, but that in the firstyear ofthe Emperor Valentinian, A.D. 364, a combined armyofthe Picts, Saxons, Scots, and Attacots, reduced the Britainsto the utmost distress." Hence, he concludes, there was acommon league between them, with intermarriages and commercial intercourse.According to Dr. Drummond, when we consider the various modes in which Roman coins may have found their wayinto Ireland, the wonder perhaps should be, not that so many,but that so few, have been discovered .66 The Rev. G. Sidney Smith, D. D., M. R. I. A., read anAccount of some Characters found on Stones on the top ofKnockmany Hill, county Tyrone.”On the top of Knockmany hill, in the parish of Clogher,and demesne of the Rev. Francis Gervais , there are someinteresting remains of ancient times. Besides two moats, oneinternal to the other, there is an ancient chamber or kystvaen, consisting of upright flag-stones, about six feet high.It includes a space fourteen feet long by seven wide. Its position with respect to the moats is represented in the groundplan, fig. 1. The stones marked by a darker shade areFig: 1S00Fig:25WENCFig: 3Allen'sLith. 15 Grafton 3Fig: 6Fig: 5ررد 4 3Fig: 4Proceedings R.I.A.Vol: 2.P.190

191standing, and those in dotted lines have been thrown down.On five of the stones characters are found, which seemed tobe well worth copying, which I have accordingly done, andrepresented them in the accompanying figures . The mostremarkable of these characters occur on the stone markedNo. 1 , in the ground plan. Those represented in fig. 2, areon the lower part of the stone, and those in fig. 3, on the upper; there may have been other intermediate characters, butthey are effaced . The spiral in fig. 2, is about nine inchesin diameter, and that in fig. 3, about twelve inches. Fig. 4represents the characters on stone No. 2, and fig. 6, thoseon No. 5, on the same scale as in figs . 2 and 3; and fig. 5represents the stones marked 3 and 4 , which are six feet high.It will be observed that in the spirals and other marks, thereis some resemblance to the New Grange characters, and infig. 4, we have a close approach to the Ogham. The copieswere made with great pains, and are I believe exact in thesmall details.On the difficult subject of these ancient characters littlecan be done until a greater mass of facts shall have been collected; and hitherto few have been observed in the Northof Ireland. Mr. Windele and other zealous antiquarians haveprosecuted the subject in Munster with great zeal and success.Mr. S. Ferguson exhibited some gold beads found in thecounty of Donegal.January 10.REV. HUMPHREY LLOYD, D. D., Vice-President, inthe Chair.William Andrews, Esq. , John Thomas Banks, Esq. , RobertBateson, Esq. , John Burrowes, Esq. , Rev. Samuel Butcher,F. T. C. D., Fleetwood Churchill, M. D., Alexander Clendin-192ning, Esq. , Rev. Reginald Courtenay, Durham Dunlop, Esq. ,Alexander Ferrier, Esq. , Wrigley Grimshaw, M. D., William Hogan, Esq. , William John Hughes, Esq. , and WilliamRoberts, Esq., F. T. C. D., were elected members of theAcademy.RESOLVED, --Onthe recommendation of Council , -" Thathenceforth, at every annual election of officers, the Presidentfor the expiring year be considered as eligible to any one ofthe Committees of Council. "Mr. Ball, referring to his paper read before the Academyin November, 1839, relative to a Loligo, to which he gavethe specific name of Eblanæ, exhibited the following Acetabuliferous Cephalopoda, with the view ofshowing the increasedknowledge of species of the Irish seas, and of placing on record the very interesting discovery of two of the genus Rossia,which he had reason to believe had not before been noticed .He then exhibited specimens of1. Sepia officinalis. Dublin bay.2. Sepia Rupellaria.? A dorsal plate, being one of threespecimens found by G. Hyndman, Esq. , at Magilligan . SeeFerussac and D'Orbigny's Cephalopoda, plate 3 of Sepia.3. Loligo vulgaris. Dublin, &c.4. Loligo sagittata. Leith . Obtained by W. Thompson,Esq. , of Belfast.5. Loligo sagittata, var.? This was in the former paper considered as a variety, but on comparison with the truesagittata, No. 3, it seems to be a distinct species. It wasobtained by G. Allman, Esq. , on the coast of Cork.6. Loligo subulata, var.? Was obtained by John Montgomery, Esq. , of Locust Lodge, on the coast ofthe County Down.7. Loligo subulata, var. No. 2. Somewhat shorter thanNo. 5. Youghal, 1832.8. Loligo media. Youghal, 1819.1939. Loligo media, var. It approaches the form of sagittata in the termination of its visceral sac.10. Loligo Eblanæ. Ofthe former paper. Obtained byT.W.Warren, Esq . , in 1836; and other specimens of greater beautyand larger size obtained in the bays ofBelfast and Dublin byW. Thompson, Esq. , and Mr. Ball. As it now appears thatthe animal possesses both eyelids and a lacrymal sinus, characters not ascribed to the genus Loligo, it may require tobe placed in another genus.11. Eledone ventricosa. Youghal, 1820, and Dublin. Avery fine specimen was found by Mrs. Lyle at Kingstown.12. Octopus vulgaris. Plymouth, 1841. Mr. Ball.13. Sepiola Rondeletii. Youghal, 1819. Dublin, 1829.Mr. Ball,14. Rossia Owenii. Was obtained in 1839 by Mr. Ball,from a fishwoman who had found it in a Dublin bay fishingboat. It is remarkable for the great size and distinctnessof its acetabula, which are placed on long peduncles, and maybe compared to the pearls in a diadem: they are ranged inthree rows, those of the centre row being not more than halfthe diamater of those on each side; on the first pair ofarmsthe acetabula are more numerous, more equal in size, andsmaller than on the others. The specific name has been givenin honour of R. Owen, Esq. , the founder ofthe genus Rossia.15. Rossia Jacobii. Was obtained from the same womanas the foregoing, in 1840, by A. Jacob, Esq. , M. D., whokindly sent it to Mr. Ball. It is much larger, but differsconsiderably in its proportions from Rossia Owenii; its acetabula are smaller; its arms proportionably shorter; themembrane round the mouth forms a hexagonal figure, fromeach angle of which a ridge runs, which is decurrent in sixcases; on the second , third, and fourth pair of arms, and inthe seventh the ridge passes upon the web between the firstpair of arms, where it bifurcates, and runs out on each side.Its specific name is given in honour of Dr. Jacob, from194whom Mr. Ball has in many instances received valuable aidin zoological pursuits . The fins of both these species of Rossiæ are like in form and position to those of Sepiola Rondeletii .16. Spirula australis. Shell found at Youghal, 1820 .Thefollowing are the Measurements ofthe Rossia in Inches:Rossia Owenii.RossiaJacobii.Length ofbody, · 1.7 · 2.1Breadth over fins,.Length of fin,·Extreme breadth,Breadth between eyes,Extreme breadth of head,• 2.0 • · 2.70.7 • 1.5• 0.45 • • 0.7· 0.9 · · 1.21.1 • 1.4Length of head,· • 0.5 • 0.7Length of tentaculæ,Portion of tentaculæ occupied by Acetabula, ..Length of first pair of arms, counting4.0 · • 5.70.9 1.5from top of head,2.1 · 2.2Ditto,second ditto, ditto, 2.4 . 2.3Ditto, third ditto, ditto, 2.7 • 2.6Ditto, fourth ditto, ditto, 2.3 • • 2.4Depth of fin between first pair of arms,0.2 • 0.4Ditto, first and second do. 0.3 • · 0.5Ditto, second and third do. 0.42 • • 0.6Ditto,third and fourth do. 0.4 . • 0.8Ditto, fourth do. 0.04 • • 0.03William Roberts, Esq. , F.T. C. D., read a paper on a classof spherical curves, the arcs of which represent the threespecies ofelliptic transcendents.Acone of the second order, whose vertex is upon thesurface of a sphere, and one of whose principal axes is adiameter, will intersect the sphere along a curve which ad-195mits of several varieties, according to the nature of the sections of the cone parallel to its principal planes, and theposition of its internal axis . This curve may be made tofurnish, by means of its arc, a geometrical representation ofthe three species of elliptic trancendents, including the twocases ofthe third .In the course ofthe investigations alluded to, Mr. Robertswas also led to consider two species of the curve called thespherical conic, which appear to possess many remarkableanalogies to the properties of the equilateral hyperbola.These cases occur when the axis minor is a quadrant, andwhen the semi- axes a and b are connected by the relationsin a tan b.The following extract of a letter from Andrew Durham, Esq., to the Marquess of Downshire, was read to theAcademy by Sir William Betham, with his Lordship's permission:" MY LORD," Belvedere, Lisburn," 29th December, 1841 ." As your Lordship and party were prevented from attending the interesting search at Drumboe Tower, I begto inform your Lordship that about seven feet below wherewe commenced excavating, we found a skeleton, in situ, lyingby compass N.W. by W., wanting both legs and feet fromthe knees, and also the right arm. The earth we removedwas of a blackish colour, as if composed ofdecomposed vegetable matter, full of stones, many of which, from the mortaron them, must have fallen from the top and the entrance,which is about five feet from the external level; and on theeastern side, it also abounded in bones of different animals,and a few bones seemingly of black cattle. Under this earthwe came to a surface of mortar; this induced us to proceedstill more cautiously; and immediately under this mortar we196first discovered the skull, in good preservation, together withthe teeth; we then laid bare the whole body, a work of nolittle difficulty, from the wetness and adhesiveness of the soil.We were much inclined to leave the body as we found it, butwere obliged to raise it to continue our search. We excavated to the very foundation ofthe Tower, without finding anything else, with the exception of many pieces of charcoal.The skull was lying on the right side, and the dorsal and cervical vertebræ were considerably decomposed ." The diameter of the Tower inside is nine feet. Theskeleton was not placed exactly in the centre, but the headwas so near the side that there would have been room sufficient for the body with its legs and feet, had it been placedin the centre. The mystery seems increased by the want ofthe arm. None of the bones found had been acted on by fire ." There was noflag-stone, nor floor either above or belowthe body. The layer of mortar seems intended as a substitute for a floor." There were several jawbones, apparently pigs', from thesize ofthe tusks; but no skulls, with the exception of one ofa bird."The external circumference of the Tower is fifty-onefeet; the wall being four feet thick." I believe I have mentioned every thing of importance;I leave others to draw conclusions. "Sir W. Betham stated that he considered this tower hadbeen opened before, and that the skeleton was then dislocated.The propensity of searching for treasure may have led to theviolation of this tomb, asit had to that ofothers, as Cashel, fromwhich the bones had all been removed; but at Ardmore andCloyne the skeletons were found really in situ; the floor of mortar, both above and below, being perfect. The Tower ofAbernethy in Scotland has also been examined with the same results as at Ardmore and Cloyne. The stones, with mortarattached to them, found in Drumboe, were certainly part of197the concrete course of mortar covering the earth in which thebody reposed , which was broken up by the violaters of thetomb.A notice ofthe occurrence of a Metallic Alloy in an unusual state of aggregation and molecular arrangement, wasread by Robert Mallet, Esq. , M. R. I. A.Amongst the several classes of substances which chemistryat present considers as simple, the metals stand preeminentlymarked by their almost invariable possession of a nearly fixedand striking group of sensible qualities, which together constitute the well known " metallic character. " Some ofthese ,such as lustre and fusibility, are common to every metallicbody; but by the occasional variation of nearly every othersensible quality of the metals, the law of continuity remainsunbroken, which unites them in different directions with theother classes of material bodies. Thus opacity, which is probably mechanically destroyed in gold leaf, is lost in selenium;and so, in this most prevalent of their properties, the metals,through tellurium, selenium and sulphur, become translucent,andmingle with the nonmetallic elements. Soalso their solidity,at common temperature, is lost in mercury; their great density, in sodium and potassium; their malleability, in bismuth,antimony, and arsenic; while in tellurium, the power to conduct electricity is nearly wanting; and , lastly, hydrogen, toall intents a metal in its chemical relations , yet possesses nota single physical quality in common with these, but exists asan invisible and scarcely ponderable gas.But although different metals thus vary in sensible qualities, those which collectively belong to the same individualmetal are as remarkable for their permanence.Unless selenium be admitted to be a metal, no approachto dimorphism has hitherto been recognized in any body ofthe class; the only case recorded , that by Dufresnoy, of theoccurrence of cast iron in cubes and rhomboids, not having198been given by him with certainty, nor since verified by otherobservers. Hence any instance of such a character, or tendencytowards it, is worthy of attentive consideration; andit was withthis view that the author brought before the Academy thefollowing notice of the occurrence of an alloy of copper, intwo states, having totally different sensible and physicalqualities, while identical in chemical constitution. The alloyin question, in its original or normal condition, was in fact aspecies of brass; and the particular specimen presented tothe Academy was a portion of one of the brass bearings, orbeds, in which the principal shaft of a large steam engine revolved.The bearing, or bed of a shaft ( as is generally known),consists of a hollow cylinder, generally of brass, divided intwo by a plane passing through the axis; its inner surface isfinely polished, and sustains the shaft, during its revolution,which is also polished; the cavity of the brass being completely filled by the shaft, which, in the present instance, wasof cast iron, and about nine inches in diameter.It frequently happens, notwithstanding the polish ofbothmetallic surfaces, and the application of oil, that the frictiondue to their rapid passage over each other, while exposed toundue or irregular pressure, produces a considerable rise oftemperature, and the brass becomes abraded . Its particleshave no coherence, and much resemble the " bronze powder"used by painters.In an instance, however, which some time since cameunder the author's notice, a different result took place. Theminute particles of abraded brass were by the motion oftheshaft, during a few hours, impacted into a cavity, at the junction of the two semicylinders of the bearing, where they became again a coherent mass, and when removed presented allthe external appearance of an ingot or piece of brass, whichhad been poured in a state of fusion into the cavity. Onmore minute examination, however, the mass was found to199differ much in properties from the original brass, out of whichit was formed.The mass or ingot of brass, thus formed by the union ofparticles at a temperature which had never reached that ofboiling water, and a fragment of which was presented, possessed on that side which had been in contact with the shaft,a bright polished metallic surface, like that of the originalmetal from which it had been formed: its other surfaces borethe impress of the cavity in which it was found. It was hard ,coherent, and could be filed or polished like ordinary brass.It was, however, perfectly brittle; and when broken, the fracture, in place of possessing asub-crystalline structure, and metallic lustre, like that of the normal brass or alloy, was nearlyblack, and ofa fine grained earthy character, and without anytrace of metallic lustre or appearance.Examined with a lens, some very minute pores or cavitiesare found throughout its substance, which is uniformly of avery dark brown or nearly black colour, and devoid of all metallic character, except when cut or filed-that is , in mineralogical language, its colour is earthy black, and its streakmetallic.The author remarked that the observed cases of aggregation in solid particles, without the intervention either ofa solvent or of fusion, are extremely rare, and as bearing upon thelittle understood subject of cohesive attraction, are of muchinterest.66The property ofwelding, which is possessed by all bodies,whether metallic or not, which pass through an intermediatestage of softness or pastyness previous to fusion, and is notfound in any substance which readily crystallizes, and hencepasses per saltum" from the solid to the liquid state byheat, forms a " frontier instance" of cohesive forces, beingenabled to act in the aggregation of bodies, by only anapproach to liquidity, or by a very small degree of intermobility.200Aggregation may also take place between portions of abody merely softened by a solvent, which is afterwards withdrawn, as in the familiar instance of Indian Rubber, softenedby naptha for the manufacture of waterproof cloths; wherethe former, after being moulded or united in any way required , is left in its pristine condition by the evaporation ofthe naptha from amongst its particles. But the cases ofa*ggregation of solids , without such elevation of temperature,or the presence of solvents, are so rare, that but two or threehave as yet been observed. Ofthese the most remarkableis that recorded by Pouillet, of the gradual, but complete,adhesion of surfaces of clean plate-glass, when left to repose on each other for a considerable time. It has also beenstated, that clean plates of lead or of tin, if pressed togetherby a considerable force when cold, require a proportionablygreat force to separate them. The case presented to theAcademy, therefore, is another added to these rare instancesof molecular aggregation in solids, independent of solutionor fusion: the author therefore thought it worth while toexamine with a little care the properties both of the originalbrass, and of the mass thus curiously formed from it, or, ashe thenceforth called them, of the normal and the anomalousalloy.The normal alloy is of a bright gold colour, and sub- crystalline in structure, and of great toughness; its cohesive force isequal to 21.8 tons per square inch, which is above the averagestrength of any of the alloys of copper and zinc, or copperand tin , as found by my experiments on the cohesive powerof these alloys, published in the Proceedings of the Academy,and elsewhere. The cohesive force of the anomalous alloyis only 1.43 tons per square inch, or only about one-fifteenththat ofthe former.The specific gravity of the normal alloy is = 8.600; thatofthe anomalous only = 7.581 .201On submitting both alloys to analysis, their constitutionproved identical; it is as follows:Copper .• 83.523Tin • 8.833Zinc · 7.510Lead 0.024.Loss 0.110100.000Uniting the small amount of lead with the tin, and dividingby the atomic weights , the nearest approach to atomic constitution is,CopperZinc26.3 atoms.2.3Tin = 1.5These alloys have therefore not a strictly definite constitution,but one more nearly so than is usually found in commerce.Both alloys are equally good conductors of electricity.The author examined their relative powers of conducting heatby the method which Despretz has employed with so muchaccuracy, and found that of the normal to that of the anomalous alloy as 36: 35, numbers which are so nearly equal asto render it likely the difference is only error of experiment.He also endeavoured to determine their relative specificheats, using the method of mixture, which was the only onewhich the small size of the metals permitted , and eliminatingthe errors incident to this mode by first plunging the alloyhot into cold water, and then cold into hot water. In thisway, ifw and tM and tm .S •the weight and temperature of the water,the weight and temperature of the metallic alloy,= the mean temperature of both ,= the specific heat of the alloy,there are two values, one where the metal is the hotter,202S =W(m -t)M (t' — m)

and another where the water is the hotter body,w (t-m)$ = M (m - t')the mean of which is the specific heat of the alloy prettyexactly. The result gave the specific heat of the normalalloy = .0879, water as unity, and that of the anomalousalloy .0848; both of which are below the specific heat assigned by Dalton to brass.The normal alloy is malleable, flexible, ductile, and laminable. Inthe anomalous alloy there is an absolute negationof all these properties.The normal alloy readily amalgamates with mercury, atcommon temperatures; the anomalous alloy will not amalgamate with mercury even at 400° Fahr.When the anomalous alloy is heated to incipient rednessin a glass tube, a minute trace of water, and of a burned organic substance, probably adherent oil, are discoverable; itsuffers no change, however, but a slight increase of density.The normal alloy suffers no change when so treated. Thenormal alloy, treated on charcoal with the blow- pipe, fusesat once into a bead. On treating the anomalous alloy so,the fragment swells rapidly to more than twice its originalbulk, on becoming bright red hot; it then glows, or becomesspontaneously incandescent, in the way that hydrated oxideof chrome and some others do, and instantly contracts to lessthan its original bulk, and becomes a fluid bead, which, oncooling, differs in no respect from the original alloy.The anomalous alloy, when pulverized in an agate mortar, forms a black powder, devoid of all appearance of ametal; its filings also are quite black; while those of thenormal alloy, produced by the same file, possess the usualmetallic lustre. These facts, in connexion with the black203colour and fine earthy appearance of the fracture, bring tomind the case recorded by Sir David Brewster, of a pieceof smoky quartz, the fracture of which was absolutelyblack, and yet was quite transparent to transmitted light,and whose blackness, he found, arose from the surfacesof fracture, consisting of a fine down of short and slender filaments of transparent and colourless quartz, the diameter of which was so small (not exceeding the one- thirdof the millionth part of an inch) , that they were incapableof reflecting a single ray of the strongest light. In describingthis, Sir David Brewster predicted , that " fractures ofquartzand other minerals would yet be found which should exhibita fine down of different colours depending on their size. ”It seems, therefore, extremely probable, that the cause ofthe near approach to blackness in the fracture and filings ofthis alloy, arises from the excessive minuteness of its particles , and thus fulfils the foregoing prediction; the brownishtinge being produced by the reflexion of a little red light. *The polish and power of reflecting light of the anomalousalloy are not quite so great as those of the normal, but arestill remarkable; and, as it seemed a matter of some interestto determine whether both reflected the same quantity or intensity oflight at equal angles, the author endeavoured toascertain this point as respects heat, by means of Melloni'spile for the galvanometrical determination of temperature,assuming, as suggested to him by Professor Mac Cullagh,that what would be true of heat in this respect, would also beso of light; but from the small size of the reflecting surfaceshe had at his command, he found it impossible to arrive at

• Since this paper was read, Professor Lloyd suggested to the author, the analogy between the appearance of the powder and filings of the anomalous alloy and

Platina Mohr, and those powders obtained by reduction of other metals by hydrogen. None of these, however, are coherent, which constitutes the peculiarity inthe present case.VOL. II. R204any trustworthy result. He is, however, inclined to believe,that both metals reflect most at a perpendicular incidence.From the foregoing detail of the properties, in severalrespects so different, of this substance in its normal and anomalous states, the author thinks he is warranted in pronouncing it the first observed instance of an approach todimorphism in a metallic alloy; and one, the mode of production and characteristics of which present several pointsofinterest.The conditions under which the alloy was aggregated ,involved extremely minute division of the metal , great pressure in forcing the divided particles into contact, and nearlythe exclusion of air. Considerable electrical disturbancemay have also co-operated; such , together with induced magnetism, being the constant accompaniments of motion inheavy machinery. By re-establishing these conditions, undersuitable arrangements, the author hopes to repeat the results thus accidentally first obtained , and so produce possiblydimorphous states of other metals or their definite combinations.There is but one body which occurred to the author,presenting an analogy to this anomalous alloy, namely, indigo;whose fracture, it is well known, is fine earthy, and of theusual blue colour, but becomes coppery, or assumes the metallic lustre on being rubbed or burnished.DONATIONS.Uber den Galvanismus gegen ortliche Krankheiten, vonDr. Gustav Crusell.Recueil des Acts de la Seance Publique de l'Académie Imperiale des Sciences de St.Petersbourg, tenue le 29 Decembre,1840.Memoires de l'Academie Imperiale des Sciences de St.Petersbourg. 6me Série. Sciences Politiques, &c. Tome IV.Livraison 6, and Tome V. Livraisons 1-4 .205Sciences Mathematiques, &c. Tome IV. Premiere partie, Livraisons 5ere et 6eme; Tome VI. Seconde partie,Livraisons 1-5.Proceedings ofthe Committee of Commerce and Agriculture of Royal Asiatic Society, 1841 .Journal ofthe Royal Asiatic Society. No. 12.Prælection on the Studies connected with the School ofEngineering in Trinity College, Dublin. By the Rev. Humphrey Lloyd, D. D. Presented by the Author.The Chronicle of William de Rishanger. By RichardO. Halliwell, Esq. , Hon. M. R. I. A., &c . Presented by theEditor.Ordnance Survey of Wexford, in eighty-six sheets. Presented bythe Lord Lieutenant.Sketch ofthe Loan Fund System in Ireland. By CharlesPiesse, Esq. Presented by the Author.Catalogue ofthe Miscellaneous Literature in the Libraryofthe Royal Society. ( 1841 ) .Proceedings ofthe Royal Society, 1841. Nos. 46–50.Supplemental Instructions for the use of Magnetical Observatories. 1841.Phil. Transactions for 1841. Parts 1 and 2.Edinburgh Astronomical Observations. Vol. IV: 1838.Memoires de l'Académie Royale des Sciences de l'Institutde France. Tome XII.Memoires présentés par divers savans a l'Academie desSciences Mathematiques et Physiques. Tome IV.The American Almanackfor 1842.

PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1842.January 24.No. 33.REV. HUMPHREY LLOYD, D. D., Vice- President, inthe Chair.RESOLVED, On the recommendation of Council, -Thatit shall be the duty ofthe Committee of Publication to reporton Papers intended for publication in the Transactions.RESOLVED, -On the recommendation of Council , -Thatthe Treasurer be authorized to sell stock of the Academy tothe amount of £300, for payment of the Printer's bill andother arrears.66 The Rev. Charles Graves, F. T. C. D., read a paper onthe Motion ofa Point upon the Surface of a Sphere."When the motion of a material point is limited to a givenplane, the circ*mstances of its motion are commonly investigated by means of the equations,xdt2 = d²x, Ydt² = day,x and y being rectangular coordinates in the given plane.Mr. Graves shows that, in like manner, the motion of a material point, constrained to move on the surface of a sphere,whose radius = 1 , may be discussed by means of the similarequations,VOL. II. S208(1)dx xdt2 = d

d (1 + x² + y² ) ( 1)

dyxdf = d G( +7) (2 )y²in which x and y are used to denote the rectangular spherical coordinates of the moving point (vid . page 127) , and x, y,the moments, in the planes of the x and y arcs of reference,ofthe resultant of the forces acting upon the point. The reaction ofthe surface being taken into account, this resultantis tangential to the sphere, and so may be conceived to actalong a great circle passing through the point.From equations ( 1 ) and ( 2) we derive a third,(xy —- xx) dt² = d ( ydx -xdy\ 1 + x² + y²which leads to important consequences.(3)It appears from the second formula in p. 129 that, if theequations ( 1 ) (2) and (3) be multiplied respectively by2dx1 + x² +y²2dy1 + x² + y²and 2 (ydx — xdy )1 + x² + y² 'they will give for the velocity, v, of the moving point,' x [ dx +y (ydx − xdy) ] +x [ dy + x (xdy —ydx)]2Sx [dx--1 + x² + y²v².(4)Now, ifthe resultant tangential force R act always alonga great circle which passes through the origin, that is, if weconsider the case analogous to that of a central force in thedynamics of the plane,X yX = R and Y R(x² + y²)*' (x² + y²)In this case, therefore, which for simplicity we may call thatof a central force, equation (3) gives2gdx — xdy = hdt,1 + x² + y²and equation (4) is reduced to(5)2092Sxd. + xdy = v². 1 + x² +y²2(6)It is easy to show that these two latter equations are equivalent to the two following,sin²pdw = hdt,25Rdp = v²,(7)(8)in which p is the vector arc drawn from the origin to themoving point, and w is the angle between it and the x arc ofreference. Let us now describe the circle of the spherewhich osculates the trajectory along which the point p moves,and let c be the arc of the great circle passing through Pand the origin, and intercepted within the osculating circle;then it may be shown thatv2 R = •tanc (9)Ifp denote the arc of the great circle drawn from the originperpendicular to the arc touching the trajectory at P, we maydeduce from (7) that2² =h2sin2 p• (10)By the help of equation ( 9) it may be proved that " Amaterial point may be made to describe a spherical conic if itbe urged by a force, acting along the arc of a great circledrawn from the focus to the point, and varying inversely asthe square of the sine of the vector arc p. ”99Also: " A material point may be made to describe aspherical conic by the agency of a force, acting along the arcof a great circle drawn from the centre to the point, and varying as tanp sec²p. "In the dynamics of a point constrained to move on thesurface ofa sphere, we have, for the discussion of the inverseproblem of central forces, the following equation,$ 2210R = 7² ( 1 + u²) (u + 1/2in which u is the cotangent of p.d2udw2The analogy between the formula given in this paper andthose usually employed in discussing the motion of a pointon a plane is very striking. The former too become identicalwith the latter when the portion of the sphere on which thetrajectory is described becomes infinitely small in comparisonwith the radius.The Rev. H. Lloyd V. P. read the following paper " on aNew Magnetical Instrument, for the Measurement of the Inclination, and its Changes. "In order to know all that relates to the earth's magneticforce, at a given place, observation must furnish the values ofthree elements. Those which naturally present themselvesfor immediate determination are, the intensity of the forceitself, and the two angles (the declination and inclination)which determine its direction. We may substitute for these,however, any other system of elements which are connectedwith them by known relations. Thus, we have hitherto preferred to observe the declination, and the two components(horizontal and vertical) of the intensity; and , in general,the main considerations which should guide us in our choiceare, the exactness of the observed results, and the facility oftheir determination.In this point of view, the declination and the horizontalcomponent of the intensity leave us nothing to desire, theirdetermination being now reduced to a degree of precision,hardly (if at all) inferior to that of astronomical measurements. The same thing, however, cannot be said respectingthe third element, as hitherto observed. In the DublinMagnetical Observatory, and in the Observatories since established by order ofthe Government and of the East IndiaCompany upon the same plan, the third element chosen for211observation has been the vertical component ofthe intensity,the instrument for the measurement of which has been already submitted to the notice of the Academy. The principle of this instrument, it will be remembered, is to balancethe vertical component of the magnetic force by a fixedweight, and to observe the changes ofthe position of equilibrium, under the action of the changing force . Unexceptionable as this principle is in theory, the accuracy of theresults has not been commensurate with that of the othertwo instruments. This inferiority is to be traced to thelarge influence which the unavoidable errors of workmanship must necessarily have on the position of equilibrium ofa magnet supported on a fixed axle. It has been shown thatthe effect of magnetizing a bar, under the most advantageouscirc*mstances of form, and at the part of the globe wherethe vertical component ofthe magnetic force is greatest, isthe same (as to its position of equilibrium) as if its centre ofgravity had been transferred about the 5th of an inch towards the north end; so that the moment of the force,exerted by the vertical component of the earth's magnetism, can never exceed this small quantity multiplied by theweight of the bar. Now, in order to render the results ofthis instrument comparable to those ofthe horizontal- forcemagnetometer, it should enable us to measure changes ofthe vertical force, amounting to the 100000dth part of thewhole; i. e. we have to measure effects, such as would beproduced by shifting the centre of gravity through the onemillionth ofaninch. It will be easily understood, from thisstatement, how great must be the effect of a minute disturbance ofthe relative parts of the instrument, or of inequalitiesin the bearing points of the axle; and experience has accordingly shown that it is altogether unavailable for the determination of changes of long period .The same difficulties, and from the same source, havebeen found to attach to the usual method of observing the212magnetic inclination, and its changes, however refined theconstruction of the instrument. The sources of error seem,in fact, to be inherent in every direct process of determiningthe third element; and it is only by an indirect method thatwe can hope to evade them. Ofthis character is the methodnow proposed.If a soft iron bar, perfectly devoid of magnetic polarity,be held in a vertical position, it immediately becomes a temporary magnet under the inducing action of the earth's magnetic force, the lower extremity becoming a north pole, andthe upper a south pole . Accordingly, if a freely- suspendedhorizontal magnet, whose dimensions are small in comparisonwith those ofthe bar, be situated near, in a plane passingthrough one of these poles, it will be deflected from themagnetic meridian. The deflecting force is the inducedforce ofthe bar, which may be regarded as proportional tothe energy of the inducing cause, i. e. to the vertical component ofthe earth's force; while the counteracting force isthe horizontal component of the same force, acting directlyon the magnet itself, to bring it back to the magnetic meridian. Thus the magnet will take up a position of equilibrium, under the action of these opposing forces; and thisposition will serve to determine the ratio which subsists between them. When the right line connecting the centre ofthe horizontal magnet, and the acting pole of the bar, isperpendicular to the magnetic meridian, the tangent of theangle of deflection will measure the ratio of the two forces,and will therefore be proportional to the tangent of the magnetic inclination. Accordingly, by observing the changes of

• Two such indirect methods of determining the inclination have been proposed in Germany, one by Professors Gauss and Weber, the other by Dr. Sartorius von Walterhausen. That now suggested bears a close analogy, in principle,

to the former of these: it differs from it, however, not only in the means employed, but also in the end in view, -the main object of the present methodbeing the determination of the inclination - changes.213position of the horizontal magnet, so circ*mstanced, we caninfer those of the inclination itself.But the iron bar may have (and generally will have) acertain portion of permanent magnetism, which will concurwith the induced magnetism in producing the deflection;and it becomes necessary to institute the observations insuch a manner, as to be able to eliminate the effects ofthis extraneous cause. For this purpose we have only toinvert the bar, so that the acting pole, which was uppermostin one part of the observation, shall be lowermost in theother. The induced polarity will, under these circ*mstances,be opposite in the two cases; and the acting force will in onecase be the sum of the induced and permanent forces, andin the other their difference.Let x and y denote the horizontal and vertical components of the earth's magnetic force, м the intensity ofthepermanent magnetism in the acting pole, and m the magneticmoment ofthe suspended magnet. The intensity ofthe induced magnetism is, by hypothesis, equal toky,k being an unknown constant; and when this is ofthe samename as the permanent magnetism, the intensity of the acting force, at the unit of distance, isky + M.Accordingly, the moment of this force to turn the suspendedmagnet is (ky + м) mr cos u, u being the angle of deflection,and r a constant depending on the distance; or , making, forabridgment, kr = p, мr = q,(px + q) m cos u.But this deflecting force is resisted by the earth's horizontalforce, the moment of which to turn the magnet isxm sin u;214and the magnet will rest when these moments are equal.Hence the equation of equilibrium ispy + q = x tan u. (1)By the same reasoning it will appear, that when the inducedand permanent magnetisms are of contrary names, there ispYqxtanu';(2)in which u' is the new angle of deflection when the bar isinverted. And adding these equations together, and observing that Y = x tan 0, 0 being the inclination, we have2p tan 0 tan u + tan u'. (3)This equation would furnish at once the inclination sought,provided we knew the value of the constant k. In order todetermine it, we have only to place the iron bar horizontally in the magnetic meridian, its acting pole remaining inthe same place as before, but pointing alternately to the northand south. The inducing force is, in this case, the horizontal component of the earth's magnetic force; and it willbe readily seen that the equations of equilibrium are similarto ( 1 ) and (2) , substituting x for y. If therefore v and vdenote the angles of deflection in these positions , we have2p = tan v +tan v′; (4)and dividing (3) by this,tan 0 =tan utan u'tantan (5)Thus, from the deflections produced in these four positionsof the bar, we obtain the inclination.In order to determine the changes of the inclination , it isnot necessary to observe the deflections in the horizontal position ofthe bar. Let equation ( 1 ) be differentiated , x, y,and u being all variable, and let the resulting equation bedivided by (3). We thus obtain the following equation , fromwhich p and q are both eliminated:215ΔΥ =Y2 Aucos'u (tan utanu')2 tan u Ax +tanu +tanu' ' xBut from the relation Y = x tan0, we haveΔΥ Ax = +A0Y X sin 0 cos 0and substituting,A0sin 20cos u'Au sin (uu) Ax +1 (6)cos u sin(u + u') sin (u +u') xThe second term ofthe right-hand member of this equationcontains a correction required for the simultaneous changesofthe horizontal intensity; but this correction will be generally small, and, when the bar has no permanent magnetism,will vanish altogether. In this latter case, in fact, it appearsfrom (1 ) and (2) that u' u; so that the preceding equationis reduced toA0=sin 20sin 2uAu. (7)We must remember that the angle u in the precedingformulæ, being the deviation of the suspended magnet fromthe position which it would assume under the action of theearth alone, its changes are the differences between the observed changes of position of the suspended magnet, and thecorresponding changes ofdeclination. Let a denote the deviation of the suspended magnet, measured from some fixedline, and a' the corresponding angle when the iron bar isremoved; thenи - а- a', Au Aa- Aa'.But Aa kn, Aa'k'n'; in which n denotes the number ofdivisions of the scale of the instrument corresponding to theangle Aa, n' the number corresponding to the angle ▲a', asshown by the declinometer, and k and k' the arc-values of asingle division in each instrument. HenceAu kn k'n' .-(8)216I now proceed to the construction of the apparatus employed in these measurements.length is three inches,A mirror is attached toThe magnet is cylindrical; itsand diameter one-fourth of an inch.the stirrup by which it is suspended , by means of which thevarying position of the magnet may be observed with atelescope at a distance, after the method of Gauss. Thismirror is of course vertical; and it has a motion round a vertical axis, by means of which it may be adjusted to any desired position of the observing telescope. The mirror iscircular, and is three-fourths of an inch in diameter. Themoveable part of the stirrup to which it is attached has theform ofa cross; and it is rendered vertical by means of threescrews, near the extremities of three of the arms of thecross, the heads of which project and hold it. The mirroris maintained in contact with these heads by springs at theback.The box is octagonal; the interval between the oppositesides is four inches, and that between the top and bottomtwo inches. The top and bottom, and the connecting pillars,are formed of gun-metal; the eight sides are closed bymoveable pieces, three of which are of glass, and the rest ofebony. To the top of the box is attached an upright tubeof glass, eight inches in length, which encloses the suspension thread. The suspension apparatus at the top ofthetube is ofthe usual construction; the circular piece to whichit is attached has a movement of rotation , and its outer surface is graduated to 5º, for the purpose of determining theeffect of torsion ofthe suspension thread .The base of the instrument is a circle of gun-metal, sixinches in diameter, graduated on the edge. The box isconnected with this circle by a short conical stem, formingthe axis of a second plate, which revolves upon the fixedone. This moveable plate carries two verniers, by whichthe angle of rotation may be read off to minutes. Two217tubular arms, slightly inclined to one another, are attachedto this plate; and their other extremities are connected by across-piece, which carries a short scale at a distance ofeighteen inches from the mirror. This part of the apparatusis employed in determining the total angles of deflection.The soft iron bar is a cylinder, twelve inches long, andthree-fourths of an inch in diameter. One of its extremitiesis enclosed in a hollow cylinder of brass, connected with ahorizontal pivot which revolves in a fixed socket. The axisof this pivot being in the line passing through the centre ofthe suspended magnet, and perpendicular to the magneticmeridian, it is obvious that the bar has a movement of rotation in the plane of the magnetic meridian itself. The distance ofthe axis of the bar from the centre of the magnet isabout five inches; and it is so placed that the induced poleis in the direction of the axis of the pivot, and thus remainsfixed during the movement of the bar.The changes of position of the suspended magnet areobserved at a distance by means of a fixed telescope andscale. The scale, whose divisions are reflected by the mirror, is attached above the telescope to the support near theeye-end.Dr. Fulton made some observations on Grecian and Roman Architecture.February 14.SIR WM. R. HAMILTON, LL.D., President, in the Chair.CaptainStirling, 73rd Regt. , Rev. Thomas Stack, F.T.C.D.,Joseph Nelson, Esq. , Q.C. , and Rev. Robert Chatto, wereelected members of the Academy.Dr. Anster read a paper, by the Rev. J. Wills , uponMr. Stewart's attempt to explain certain processes of the218Human Understanding, on the supposition that it acquires,by habit, an acceleration in the succession of ideas, sogreat as to escape the consciousness.After having observed that Mr. Stewart's error consisted,not in his reasoning, but in having failed to observe that hisfacts are themselves complex results which demand a minuteanalysis, and having also dwelt upon some elementary errorsto which he mainly attributed the entire of Mr. Stewart's theory, the author proceeded to a detailed investigation of theseveral examples brought forward in its support.He first stated the case of a player on the harpsichord ,whose rapidity of execution is adduced to illustrate the proposition that so many separate acts of will and attention, as itseems to involve, are so accelerated as to take place withoutany consciousness of their separate occurrence . On thishe observed, that, to a very great extent, the separate actsassumed could have no existence, by reason of the absolutecoincidence, in point of time, of the rapid and complex movement ofthe musician's hand; from which he inferred, thatsome other law must be sought for to explain the phenomena.To discover this law, the author proceeded to examine theprocess ofthe mind in the acquisition of the art by whichthe complex and simultaneous movements are effected . Theseare, he observed, first separately attended to and separatelyexecuted; but so long as this separateness continues, it isevident that the required result is not attained . Slowly,however, and by frequent repetition of the same set of ideaspresented in combination, this combination itself becomestheobject of perception; and from being separate ideas andmovements, they become simultaneous, and assume the newform ofa single complex conception, executed by a complexmovement. In confirmation of this inference, he observed,that the slightest attempt to attend to any of the componentparts would disconcert the best skill. He also observed,that Mr. Stewart had been in some degree misled by having219generally fixed his attention on examples in which the component ideas are successive in the order of occurrence. Heobserved upon a considerable class of cases which are decisive against Mr. Stewart, being composed of very complexacts, ofwhich the separate parts are never recognized, suchas the class of movements called " mechanical."The author next entered on a detailed view of Mr.Stewart's example of a person reading, and showed that thesame reasoning is applicable. He noticed the complication of trains of thought, which, according to Mr. Stewart'stheory, must be simultaneously proceeding; and also observed ,that his theory could not stop short at any point of these;and that wherever he might attempt to stop, an explanationshould be given, which ought to supersede his whole theory.He then pursued the inquiry as in the previous example, byinvestigating the mind's progress in learning to read, and deduced similar conclusions. These he also confirmed, bynoticing the various errors which occur in reading and printing; ofthese he showed, that they illustrate the effect of thecombinations or complex conceptions previously formed tosupply even the want of many of the component parts; sothat the letter is inferred from the general form of the syllable, and the syllable from that of the word, rather than thecontrary process. From this example he concluded, that themind, by repeated acts of attention, acquires a stock of syllabic and vocal associations, of which the act of reading is acombined result; that by a further extension , written sentences may become combined with a process of thought, andthat every reader possesses some range of thought thussymbolized by habit; and finally, that the general inferenceto be drawn from this and other similar examples is , that bymeans ofhabit, groups ofsigns, ofmovements, facts, thoughts,sensations or phenomena, may acquire varied relations to eachother; and that these being acquired , the combination alonebecomes the object of notice. He then pursued the applica-220tion ofthe same reasoning to some other examples, not noticed by Mr. Stewart, which he observed were better adaptedfor illustration; and then proceeded to notice briefly the application ofthe same principles to the other examples adducedby Mr. Stewart.He then reverted to an explanation of Mr. Stewart's andofother writers, concerning the perception of the distance ofvisible objects; and after noticing the fallacy which it involved, he showed it to be explicable by the same generalprocess as in the former cases.He next observed that the numerous errors arising fromthe same law of habit might be made use of to illustrate orprove the same conclusions; and explained , at some length,the illusion of faces and other visual phenomena framed bythe imagination.After several observations on the comparative difficultiesof Mr. Stewart's method and his own, the author noticed thedistinction between the previous cases, in which there is anapparent character of combination, and others in which adifficulty must seem to arise from continuity. He then wentat considerable length to applythe same reasoning to the caseof the orator, as adduced by Mr. Stewart, and more fully described by Lord Brougham. He lastly adverted to Mr.Stewart's explanation of dreams, and showed that it involvedsome important contradictions and inconsistencies; and that,contrary to Mr. Stewart's assertion, it implies a new law ofmind. He then showed that it could be explained by thesame method which he had already applied to the other examples. And after some explanations of the manner in whichthe law of suggestion operated in dreams, he observed, inconclusion, that Mr. Stewart had set out with a notion adaptedto lead him astray; which he thought to be a subject of regret, as the line of investigation which he had selected wouldotherwise have offered a clearer and better evidenced founda-221tion for metaphysical science than any which had been previously adopted.DONATIONS.Catalogue ofthe Works of Art in the Possession of SirPeter P. Rubens, at the Time of his Decease. Presented byDawson Turner, Esq.Ueber die Himjaritische Sprache und Schrift. Von Dr.W. Gesenius. Presented by the Author.A Descriptive Vocabulary of the Language of the Aborigines ofWestern Australia. By G. Fletcher Moore, Esq.Presented by the Author.Magnetische undMeteorologische Beobachtungen zuPrag.Vom 1 Juli 1839, bis 31 Juli 1840. By Karl Kreil. Presented by the Author.Proceedings ofthe American Philosophical Society. Vol.II. No. 19.A Record of the Case of Mary Jobson. By W. R.Clanny, M. D., &c. Presented by the Author.February 28.REV. HUMPHREY LLOYD, D. D., Vice- President,in the Chair.Dr. Evory Kennedy read a paper on the peculiar System of Generation, and Habits, observed by him to prevail incertain Acephalocysts, parasitical animals inhabiting thehuman body, and belonging to the class of hydatid entozoa.Having considered their animal nature, and their primaryformation, as involving the question of spontaneous generation, he described generally the methods of reproductionadopted in this class of animals, and adduced the explanations and opinions offered by the best authorities on the22266subject, but particularly those of Bremner, Lænnec, andOwen, by which acephalocystic reproduction is referred toimperfect ovation or generation . Dr. Kennedy went on toshow that the uterine hydatid or hydrometra hydatica ofWiesmantel, which should more correctly be termed theAcephalocystis Hysterobiavel uterina, " multiplies byfissiparousgeneration, and that the creatures still continue adherentto, or connected with each other by filiform bands or elongations ofthe strictured parts of their bodies. Dr. Kennedyexhibited several preparations and drawings in which thismode of reproduction by subdivision was perceptible in different stages of progress, and having alluded to an imperfectdivision, observed also to occur in infusorial animalcules, recommended that the system of reproduction which he described should be termed " fissiparo- coherent."Apaper "on the colouring Matters ofthe Persian Berries"was read by Dr. Kane.These berries, the fruit of the dyer's buckthorn, RhamnusTinctoria, are imported from the Levant, and from the southof France, for the use of dyers, to whom they furnish a yellow colour of great brilliancy, though not so permanent assome others. The appearance of the berries, as found incommerce, varies considerably; some samples , and those themost valuable, being larger, fuller, and of a light greenisholive colour, whilst others are smaller, as if shrivelled , anddark brown in tint. The former Dr. Kane considers to havethe appearance of being gathered before complete ripening,whilst the latter owe their altered character to being allowedto remain longer on the stem, or to having been incautiouslydried.The colouring matter in these two kinds is essentiallydifferent. The unripe berries yield but little colour to purewater, and when digested in ether give abundance of a rich223golden yellow substance, to which Dr. Kane has given thename ofchrysorhamnine. The dark coloured berries containlittle of the substance soluble in ether, but give out to boiling water an olive yellow material, to which, in its pure form,Dr. Kane gives the name of xanthorhamnine. This substance is produced , however, only by the decomposition ofthe former; thus, if the unripe berries be boiled for a fewminutes in water, they, when dried , yield to ether scarcelytraces of chrysorhamnine, this principle being, by contactof air and hot water, changed into xanthorhamnine.Omitting the details of methods of purification, and ofanalysis, the properties and composition of these bodies maybe expressed as follows:Chrysorhamnine is of a rich golden yellow colour, of acrystalline aspect, and may be obtained in brilliant stellatedtufts ofshort silky needles. It is but very sparingly solublein cold water, and when boiled with water the portion whichdissolves does not separate on cooling, but is found to bechanged into xanthorhamnine. It dissolves in alcohol, butis not obtained by its evaporation, without being much altered. In ether, however, it dissolves abundantly, and bythe spontaneous evaporation of its solution is deposited in apure form. It has no acid reaction, but dissolves in alkalinesolutions, in which, however, it appears also to be mostlyaltered.Dried at 212° Fahr. it consisted ofCarbonHydrogen·OxygenI. II.58.23 57.81• • 4.77 4,6437.00 37.55100.00 100.00These numbers give the formula C23 H11 O11, by which thereshould be"VOL. II.T224C23= 138 58.23H₁₁ HI= 11 4.6411 88 37.13237 100.00On adding an alcoholic solution of chrysorhamnine to asolution of acetate of lead , a rich yellow precipitate isformed, which, when dried at 212°, was found to be expressedby the formula C23 H11 On + 2 PbO, the numbers being asfollow:CarbonHydrogen• ·Oxygen .Theory.138.0Experiment.29.98 • • 29.62· • • 11.0 2.39 2.1988.0 19.11 • 19.59Oxide of lead . • 223.4 48.52 48.60460.4 100.00 100.00Alittle water appears to have been lost in the analysis ,which, however, does not affect the formula deduced.By the decomposition of a more basic acetate of lead, ayellow precipitate is obtained, which consisted of one equivalent of chrysorhamnine united to three equivalents ofoxideoflead.The chrysorhamnine may be easily observed in its natural state of deposition in the berry; it lines the interior ofthe capsule- cells, with a brilliant resinous-looking pale yellow, and semitransparent coating.Xanthorhamnine is formed by boiling chrysorhamnine inwater, in a capsule, so as to admit of free access of air. Itdissolves with an olive, yellow colour, and on evaporating todryness, remains as a dark, extractive looking mass, quite insoluble in ether, but abundantly soluble in alcohol and water.It may be procured also from the berries, without previousseparation ofthe chrysorhamnine, by similar treatment, butit is then rendered impure by a gummy substance being225mixed with it. It is very difficult to determine when thissubstance can be considered anhydrous. Prepared by evaporation over sulphuric acid in vacuo, it is quite dry, andmay be powdered, but if heated it liquefies below 212°, andcontinues giving out watery vapour until the temperature israised to 350°, beyond which the organic matter itself cannotbe heated without decomposition. On cooling it reassumesits perfectly dry aspect, and may be easily powdered.It was hence analyzed in all these stages of desiccation ,with the following results. It contained:Dried in vacuo.CarbonHydrogenOxygen34.74 C23Formula deduced.138 34.78• • 6.93 H27 = 27 6.8058.33 029 = 232 58.42100.00 397 100.00Dried at 212º. Formula deduced.Carbon . 49.97 51.20 C23 138 50.92•·Hydrogen . 5.18 5.28Oxygen 44.85 43.52100.00 100.00Dried in an oil bath at 320°.H13= 13 4.80015 = 120 44.28271 100.00Formula deduced.CarbonHydrogenOxygen· ••52.55 C23 = 138 52.67· 5.15 H12 =12 4.5842.30 O14 = 112 42.75100.00 262 100.00By adding a solution of xanthorhamnine to solutions ofacetate of lead, two combinations may be formed, one byneutral acetate of lead, the other by using the tribasic salt.But it is difficult to obtain either unmixed with some tracesof the other, and thence the analysis of both vary a little.from the true atomic constitution . Thus the tribasic saltgives T2226CarbonDried at 212º.26.58Hydrogen 2.86 •Formula deduced.C23 = 138.0 26.93H15 =15.0 2.93Oxygen • 25.97 017 = 136.0 26.54Oxide of lead 45.36 44.59 2. PbO = 223.4 43.60100.00 512.4 100.00The tribasic salt givesDried at 212º, Formula deduced.Carbon • • 21.89 22.07 C23 = 138.0 21.20Hydrogen • 3.06 2.82 H₁ = 18.0 2.76Oxygen • 23.75 23.73 020= 160.0 24.57Oxide of lead 52.30 51.38 3. PbO 335.1 51.47100.00 100.00 651.1 100.00If we consider the xanthorhamnine, as dried in the oilbath, to be then anhydrous, the bodies analyzed becomeXanthorhamnine, dry = C23 H12 O14do.do.dried at 212°. C23 H12 O14 + Aq.dried in vacuo = C23 H12 O14 +15 Aq.1st lead salt, C23 H12 O14 + 2. PbO +3 Aq.2nd lead salt, C23 H12 O14 + 3 PbO +6 Aq.The xanthorhamnine is thus formed by the addition ofone equivalent of water and two of oxygen to the chrysorhamnine, as C23 H11 O11 + HO + O2 = C23 H12 014. Andif we were to consider the substance dried in the oil-bath at320° still to retain an atom of water, it should be simplyoxidated chrysorhamnine, being, when dry,C23 H11 O11 + 20.The Rev. H. Lloyd, V. P. , read a supplement to a formercommunication " on a New Magnetical Instrument, for themeasurement of the Inclination and its Changes. '227Having, on a former occasion , explained the principle ofthis instrument, and given the details of its construction , it remains only that I should now describe the observations madefor the purpose oftesting its performance. I shall pass overfor the present those which relate to the absolute inclination,because they have yielded results which can be regarded onlyas approximations to the truth, and I have not succeeded asyet in tracing the errors to their source. It is manifest, however, that an instrument may be a good differential instrument, while it is incapable of yielding absolute results; andthere are special reasons why this should be the case withthe apparatus now under consideration. Accordingly itsfailure in the latter respect, even though established , wouldfurnish no ground for despairing of its success in the former.It is obvious that the apparatus is wholly free from thesources of error already noticed, belonging to magnetical instruments moving on a fixed axle; and the only doubt of itsperformance must relate to the changes of induced magnetism in the iron bar. Thus it might be questioned , beforetrial, whether such a bar receives in all cases an amount offree magnetism proportional to the inducing force; —whether, again, the minutest changes in the latter are accompanied by corresponding changes in the former; —and whether,lastly, the changes thus produced are instantaneous, or, atleast, demand no appreciable time for their development.In the first experiments which I made, for the purpose ofdetermining these questions, the induced magnetism of theiron bar was altered by means of a permanent magnet, placedin the same right line with the bar, and at a known distancefrom it. The effect produced upon the position of the suspended magnet being observed, the distance was altered bya known amount, and a new observation taken; and so on,at many different distances. Then, the law of action of theinducing magnet being known, we may calculate the changesof deflection of the suspended magnet, on the supposition228that the changes ofthe induced force of the bar are proportional to those of the inducing action, and then compare themwith the changes of deflection observed. The calculated andobserved results of many series of observations, taken in thismanner, were found to accord as nearly as the accuracy ofthe observations themselves allowed.In making this comparison, however, it is necessary totake into account the effect of the direct action of the fixedmagnet upon the suspended one. The axis of the formermagnet being not far from the vertical passing through thecentre of the latter, its action upon it and upon the iron barfollow, nearly, the same law; so that its direct effects uponthe position of the suspended magnet are, very nearly, proportional to those which it produces through the mediumof the induced force of the bar. On this principle the observed results may be cleared, approximately, of those partsof the changes which are foreign to the question . Still itmust be admitted that such a complication of the resultstends to weaken their evidence; and it was therefore desirable to obtain further proof, in a manner less exceptionable.The object being to alter the inducing action accordingto a known law, and to observe the changes of the inducedforce, as shown by the position of the suspended magnet, itis manifest that it may be attained by simply varying theangle which the iron bar makes with the direction of theearth's magnetic force, the distance of its pole from the suspended magnet remaining unchanged. In fact, it will beseen, by pursuing the same reasoning as before , that if Rdenote the total force ofthe earth, and the angle whichthe bar makes with its direction, the equation of equilibriumof the suspended magnet isPR Cos + 9 = x tanu;the line connecting the pole of the bar with the centre ofthe229suspended magnet being, as before , perpendicular to themagnetic meridian. Hence, if the bar be devoid of permanent magnetism (or q = 0) , and if the forces R and x remainunchanged during the experiments, we havea being a constant.tan u = a cost,In order to observe whether the deflections of the suspended magnet obeyed this law, a small divided circle wasattached to the piece upon which the iron bar moved, in sucha manner that the axis ofthe pivot passed through its centre.The circle being fixed , and the bar connected with themoveable arm carrying the vernier, we have the means ofdetermining the angle through which it is moved. Theplane of the motion coinciding with the magnetic meridian,the inclination of the bar to the vertical was altered by 5°between the successive observations of the position ofthesuspended magnet. The following Tables contain the results oftwo such series of observations . The first column ofeach gives the inclination of the bar to the vertical; the second, its inclination (4) to the direction of the magneticforce, i. e. the former angle increased by the complement ofthe magnetic inclination ( 19° 10′) . The third column contains the observed readings of the scale, corresponding tothe positions of the suspended magnet; the fourth, the differences between each of these readings and the readingbelonging to the vertical position ofthe bar, converted intoangular measure; the fifth, the actual deflections; the sixth,the calculated deflections, as deduced by the formula givenabove; and the seventh, the differences.In order to derive the numbers of the fifth column fromthose ofthe fourth, it is necessary to know the deflection corresponding to the vertical position of the bar. This angleis determined by placing the bar vertically, with its actingpole above and below successively, and noting the readings.of the horizontal circle , when the same division ofthe move-230able scale, reflected by the mirror, was brought to coincidewith the fixed wire of the telescope. The differences between each of these readings, and the similar reading whenthe bar is removed, are double the deflections correspondingto the two positions of the bar; and, when they are nearlyequal, the mean of these deflections may be taken as that dueto the induced force.FIRST OBSERVATION.Acting end of bar a south pole, readingnorth pole,Bar removed,14° 8', deflection82 51 ,4817° 0'"" = 17 227, mean = 17 11Inclination to vertical.4.Reading Angular น น Difference.+14° 30' 33° 40'+10 0 29 10 13.25 0 24 10 23.10 0 19 10 31.45 0 14 10- 10 0 9 10.13 30 5 40of Scale. Differences. Observed. Calculated.2.2 -1 °56′.2 15° 14'- 8 15° 14'-5 +03-1 12.4 15 58.6 15 57.2+ 1.433.0 16 38.0 16 37.8 + 0.20.0 17 11.037-524-3 17 35.3 1742.845-4 17 56-4 1745.8 57.3 18 8.3 1836-754-7- 1.4+1.72.75.6SECOND OBSERVATION.Acting end of bar a south pole, reading = 14° 23′, deflection = 16° 36'"" north pole,Bar removed,82 15, "" = 17 20• 47 35, mean = 16 58Inclination to vertical.4.Reading Angular of Scale. Differences. Observed. Calculated.26 น Difference.+ 15° 0' 34° 10'+10 0 29 102.614.4+ 5 0 24 10 24.80 0 19 105 0 14 1033.220 1/8 14° 56/.2 14° 57'81 14.8 15 43.2 15 45.033.4 16 24.6 16 25.20.0 16 58-0- 1'6 -- 1.8- 0.640.0 + 27.1 17 25.1 17 23-3 + 1 · 8In the preceding observations a telescope oflow powerwas employed, and the arc-value of a single division of the231scale (which was at the distance of eighteen inches from themirror) was 3'. 98. The differences of the observed andcalculated results, therefore, do not in general exceed theamount which may be fairly ascribed to errors of observation; and the accordance is sufficient to establish the fact,that the changes of the induced force of the bar are, withinthe observed limits, proportional to those of the inducingaction . It is important to observe also that the changes ofthe induced force, produced artificially in these experiments,are much greater than any which are likely to arise from thevariations of the vertical component of the earth's magneticforce, and therefore that the experiments may be regardedas severe tests of the performance ofthe instrument.The preceding observations further showed, that thechanges in the inducing force were instantly followed by theireffects upon the suspended magnet; so that the changes ofinduced force required no appreciable time for their development. It remained only to ascertain, in a somewhat fullermanner, how far the bar was susceptible of minute magneticchanges, from very small variations ofthe acting force. Forthis purpose, a series of readings of the scale was taken, theinclination of the bar to the vertical being altered by half adegree between the consecutive readings. The mean difference of the successive readings was found to agree, veryexactly, with the calculated difference; while the partial differences deviated from the mean by an amount not exceedingthe limits of error of observation. It may be presumed therefore, that the changes of the induced force in the iron barare continuous; and, accordingly, that the sensibility of theinstrument is only limited by the optical power, which is applied to observe the changes of position of the suspendedmagnet. * In the experiments above described, the arc-value

• Against this conclusion is the fact, that considerable changes in the induced

force of the bar seem to be attended with some permanent changes of polarity;and it may be presumed that the same thing will take place, in a proportionate232of the divisions ofthe scale was 3'.98; with the modificationssince introduced into the reading part of the apparatus, thescale divisions have nearly the same value as in the instrumentfor the measurement of the declination, so that the readingsmay be made with certainty to less thanthe tenth of a minute.The present value of the inclination in Dublin is about70° 50'; and the mean deflection produced by the iron barin its actual position being about 19° , it follows from (7) thatthe changes of inclination are inferred with the same degreeof precision, very nearly, as the observed changes of angle.The last test to which the instrument was subjected, was,to employ it for some time in the regular observation of inclination changes, for which it is destined; and to ascertainhow far the mean results of the observations of successiveweeks agreed in exhibiting the law of the diurnal variation.The instrument was accordingly observed for five successiveweeks, every second hour during the day and night, and themeans calculated, omitting those days in which the serieswas broken by changes of adjustment during experiment.The curves now laid before the Academy represent the projected results of the observations of each of these weeks,together with that of the mean ofthe whole. An inspectionof them is sufficient to show that the curves of the separateweeks accord with one another, and with the mean, as nearlyas can be expected in the results of such limited series, thediscordances being only such as are due to the known irregularities in the direction of the earth's magnetic force.A communication from the President was read, containing some remarks supplementary to the account which hehad given at a former meeting, ofhis Researches respectingFluctuating Functions, (see Proceedings, June 22nd, 1840) .degree, with the minute changes induced by the variations of the earth's force.It remains for future examination to determine how far such permanent changes,if they occur, may impair the accuracy ofthe results.233The following general observations are extracted , on thenature and history of this branch of analysis:-Lagrange appears to have been the first who was led (inconnexion with the celebrated problem ofvibrating cords) toassign , as the result of a species of interpolation, an expression for an arbitrary function, continuous or discontinuous inform, between any finite limits, by a series of sines of multiples, in which the coefficients are definite integrals . Analogous expressions, for a particular class of rational and integral functions, were derived by Daniel Bernouilli, throughsuccessive integrations, from the results of certain trigonometric summations, which he had characterized in a formermemoir as being incongruously true. No further step of inportance towards the improvement ofthis theory seems tohave been made, till Fourier, in his researches on Heat, wasled to the discovery of his well known theorem, by which anyarbitrary function of any real variable is expressed, betweenfinite or infinite limits, by a double definite integral. Poissonand Cauchy have treated the same subject since, and enriched it with new views and applications; and through thelabours of these and , perhaps, of other writers, the theory ofthe development or transformation of arbitrary functions,through functions of determined forms, has become one ofthe most important and interesting departments of modernalgebra.It must, however, be owned that some obscurity seemsstill to hang over the subject, and that a further examinationof its principles may not be useless or unnecessary. Thevery existence of such transformations as in this theory aresought for and obtained , appears at first sight paradoxical;it is difficult at first to conceive the possibility of expressinga perfectly arbitrary function through any series of sines orcosines; the variable being thus made the subject of knownand determined operations, whereas it had offered itselforiginally as the subject of operations unknown and undeter-231mined. And even after this first feeling of paradox is removed, or relieved , by the consideration that the number ofthe operations of known form is infinite, and that the operation of arbitrary form reappears in another part of the expression, as performed on an auxiliary variablee; it stillrequires attentive consideration to see clearly how it is possible that none of the values of this new variable should haveany influence on the final result, except those which areextremely nearly equal to the variable originally proposed .This latter difficulty has not, perhaps, been removed to thecomplete satisfaction of those who desire to examine thequestion with all the diligence its importance deserves, byany ofthe published works upon the subject, A conviction,doubtless, may be attained , that the results are true, butsomething is, perhaps, felt to be still wanting for the fullrigour of mathematical demonstration. Such has, at least,been the impression left on the mind of the present writer,after an attentive study of the reasonings usually employed,respecting the transformations of arbitrary functions.Poisson, for example, in treating this subject, sets out,most commonly, with a series of cosines of multiple arcs; andbecause the sum is generally indeterminate, when continuedto infinity, he alters the series by multiplying each term bythe corresponding power of an auxiliary quantity which heassumes to be less than unity, in order that its powers maydiminish, and at last vanish; but, in order that the new seriesmay tend indefinitely to coincide with the old one, he conceives, after effecting its summation, that the auxiliary quantity tends to become unity. The limit thus obtained isgenerally zero, but becomes on the contrary infinite when thearc and its multiples vanish; from which it is inferred byPoisson, that if this arc be the difference oftwo variables, anoriginal and an auxiliary, and if the series be multiplied byany arbitrary function of the latter variable, and integratedwith respect thereto, the effect of all the values of that235variable will disappear from the result, except the effect ofthose which are extremely nearly equal to the variable originally proposed .Poisson has made, with consummate skill, a great numberof applications of this method; yet it appears to present, onclose consideration , some difficulties of the kind above alludedto. In fact, the introduction of the system of factors, whichtend to vanish before the integration , as their indices increase,but tend to unity, after the integration , for all finite values ofthose indices, seems somewhat to change the nature of thequestion, by the introduction of a foreign element. Nor is itperhaps manifest that the original series, of which the sum isindeterminate, may be replaced by the convergent series withdetermined sum, which results from multiplying its terms bythe powers of a factor infinitely little less than unity; whileit is held that to multiply by the powers of a factor infinitelylittle greater than unity would give an useless or even falseresult. Besides there is something unsatisfactory in employing an apparently arbitrary contrivance for annulling theeffect ofthose terms ofthe proposed series which are situatedat a great distance from the origin, but which do not themselves originally tend to vanish as they become more distanttherefrom. Nor is this difficulty entirely removed, whenintegration by parts is had recourse to, in order to show thatthe effect of these distant terms is insensible in the ultimateresult; because it then becomes necessary to differentiate thearbitrary function; but to treat its differential coefficient asalways finite is to diminish the generality of the inquiry.Many other processes and proofs are subject to similar ordifferent difficulties; but there is one method of demonstration employed by Fourier, in his separate Treatise on Heat,which has, in the opinion of the present writer, received lessnotice than it deserves, and of which it is proper here tospeak. The principle of the method here alluded to may becalled the Principle ofFluctuation, and is the same which236was enunciated under that title in the remarks prefixed tothis paper. In virtue of this principle (which may thus beconsidered as having been indicated by Fourier, althoughnot expressly stated by him) , if any function, such as thesine or cosine of an infinite multiple of an arc , changes signinfinitely often within a finite extent of the variable on whichit depends, and has for its mean value zero; and if this,which may be called a fluctuating function, be multiplied byany arbitrary but finite function of the same variable, andafterwards integrated between any finite limits; the integralofthe product will be zero, on account ofthe mutual destruction or neutralization of all its elements.It follows immediately from this principle, that if thefactor by which the fluctuating function is multiplied, insteadofremaining always finite, becomes infinite between the limitsof integration, for one or more particular values of the variable on which it depends; it is then only necessary to attendto values in the immediate neighbourhood ofthese, in orderto obtain the value of the integral. And in this way Fourierhas given what seems to be the most satisfactory publishedproof, and (so to speak) the most natural explanation of thetheorem called by his name; since it exhibits the actual process, one might almost say the interior mechanism, which, inthe expression assigned by him, destroys the effect of allthose values of the auxiliary variable which are not requiredfor the result. So clear, indeed , is this conception, that itadmits of being easily translated into geometrical constructions, which have accordingly been used by Fourier for thatpurpose.There are, however, some remaining difficulties connectedwith this mode ofdemonstration, which may perhaps accountfor the circ*mstance that it seems never to be mentioned ,nor alluded to, in any of the historical notices which Poissonhas given on the subject of these transformations. For example, although Fourier, in the proofjust referred to, ofthe237theorem called by his name, shows clearly that in integratingthe product of an arbitrary but finite function, and the sineor cosine of an infinite multiple, each successive positiveportion of the integral is destroyed by the negative portionwhich follows it, if infinitely small quantities be neglected,yet he omits to show that the infinitely small outstanding difference ofvalues ofthese positive and negative portions, corresponding to a single period of the trigonometric functionintroduced, is of the second order; and, therefore, a doubtmay arise whether the infinite number of such infinitely smallperiods, contained in any finite interval, may not produce, bytheir accumulation, a finite result. It it also desirable to beable to state the argument in the language of limits, ratherthan in that of infinitesimals; and to exhibit, by appropriatedefinitions and notations, what was evidently foreseen byFourier, that the result depends rather on the fluctuatingthan on the trigonometric character of the auxiliary functionemployed.The same view of the question had occurred to the present writer, before he was aware that indications of it were tobe found among the published works of Fourier; and he stillconceives that the details of the demonstration to which hewas thus led may be not devoid of interest and utility, astending to give greater rigour and clearness to the proofandthe conception of a widely applicable and highly remarkabletheorem.Yet, ifhe did not suppose that the present paper containssomething more than a mere expansion or improvement of aknown proof of a known result, the Author would scarcelyhave ventured to offer it to the Transactions* of the RoyalIrish Academy. It aims not merely to give a more perfectlysatisfactory demonstration of Fourier's celebrated theorem

• Sir William Hamilton's Essay on Fluctuating Functions, will be found in

the Second Part of volume xix. of the Transactions of the Academy.238than any which the writer has elsewhere seen, but also topresent that theorem, and many others analogous thereto,under a greatly generalized form, deduced from the principleoffluctuation. Functions more general than sines or cosines ,yet having some correspondent properties, are introducedthroughout; and constants, distinct from the ratio ofthe circumference to the diameter of a circle , present themselves inconnexion therewith. And thus, ifthe intention ofthe writerhave been in any degree accomplished, it will have beenshown, according to the opinion expressed in the remarksprefixed to this paper, that the development of the important principle above referred to gives not only a new clearness, but also ( in some respects) a new extension, to this department of science .DONATIONS.Memorie dell' Imperiale Regio Instituto del Regno Lombardo-Veneto. Vols. 1-5 .Memorie dell' Instituto Nazionale Italiano. Vol. 1 , 4 Parts,vol. 2, 2 Parts.Maxwell's Narrative ofthe Prince's Expedition. (1745).Published by the Maitland Club. Presented by John Smith,Esq. , Secretary M. C.Bibliotheca Scoto- Celtica. By John Reid, Esq. Presented by the Author.Hints for the better Construction of Dwellings for smallFarmers, &c. By W. J. Hughes, M. R. I. A.by the Author.PresentedPROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1842.March 16. (Stated Meeting) .No. 34.SIR WM. R. HAMILTON, LL.D. , President, in the Chair .On the recommendation of Council, Charles Wheatstone,Esq. , was elected an honorary member of the Academy.The Secretary of Council read the following Report,which was ordered to be entered on the Minutes:" The affairs of the Academy during the past year will require buta brief review, as the interval has not been very fertile in results. Thesecond part ofthe nineteenth volume of our Transactions has not yetbeen published; and the Essay on the Round Towers (which is tomake the twentieth volume) is still advancing slowly through thepress, its progress being necessarily retarded by the great number ofillustrations which are required from the nature of the work." The subscription which was opened last year, under the management of the Committee of Antiquities, for the purchase of the collection of the late Dean of St. Patrick's, has not hitherto answered theexpectations that were formed of it. Of the sum of one thousandpounds, which the Dean's representatives agreed to accept for thecollection, little more than one-half has been raised. Notwithstanding this circ*mstance, however, the Council are persuaded that publicfeeling is in favour of the project, and that a little more energy, onour part, is all that is required to ensure success. It would indeedbe a disgrace to us, if, for want of proper exertions, this fine collectionshould be lost to the country.VOL. II. U240"Meanwhile, the small cabinet in the possession of the Academyhas been augmented by some valuable articles, from the fund of twohundred pounds set apart for that purpose. Among these are agold torquis, weighing upwards of twelve ounces; and a gold collarof the most elegant form and workmanship, weighing four and a-halfThe latter beautiful specimen of ancient art was lately dugup in a bog, by a common labourer, and but for the existence of thefund above mentioned, which allowed it to be secured at once for theAcademy, it would probably have been condemned to the crucible;the usual fate of such old ornaments as possess a high intrinsicvalue.ounces." As this fund, however, is but small, and in the present state ofour finances cannot be expected to be permanent, while the resources of private subscription, to which we have so often had occasion to resort, must be considered as now almost exhausted, theCouncil have thought it advisable to try whether it might not be possible to obtain some public assistance towards carrying out an objectwhich is admitted to be one of great public interest. They havetherefore presented a memorial to the Lord Lieutenant, praying hisExcellency to recommend to her Majesty's Government the additionof £100 a year to our usual grant, for the sole purpose of purchasingantiquities; this additional sum to be strictly accounted for everyyear. Should the proposal be favourably received by the Government,the Academy will be in a position to accomplish its designs in this department, at a very trifling expense to the public.may" In order that a greater number ofthe members of the Academybe induced to take a lively interest in its affairs, by enjoying ashare of its honours, the Council have thought it expedient to recommend that there should in future be an annual change in the listof Vice- Presidents, the senior Vice- President going out of officeafter the stated meeting in March, and they hope that every futurePresident will consent to act upon this suggestion in the appointmentof Vice-Presidents. But as it is proposed, by this arrangement, thatno person should be appointed as Vice- President more than four timessuccessively, so it is not intended to recommend that any Vice- President should be displaced, who may have been appointed less thanfour times successively.66 Among the deaths that have occurred in our body, during the241past year, we have had to regret that of the Very Rev. RobertBurrowes, D. D., Dean of Cork, and formerly Fellow of Trinity College. Though not an original member, Dr. Burrowes was among thevery first members of the Academy. He filled the office of Secretaryfor several years, and contributed some very elegant papers, in thedepartment of Polite Literature, to the early volumes of our Transactions."Within the last few days we have had to lament the death ofanother distinguished member of the Academy and Council, the Rev.Cæsar Otway, the author of several well-known works illustrative ofthe history and antiquities of his native country, and abounding ingraphic sketches of Irish scenery, and vigorous delineations of Irishcharacter and manners." In the list of honorary members, we have lost an eminentBotanist, Aylmer Burke Lambert, Esq. He was the author of amagnificent work on Pines, in three volumes, the last of which, morerecently published than the rest, contains some fine contributionsfrom the Californian collections of our countryman and fellow- academician, Dr. Coulter." The other members deceased within the year are:Peter Burrowes, Esq. , Q. C.J. H. Blake, Esq. , Q. C.William Monsell, Esq.Robert Tighe, Esq.Isaac D'Olier, LL. D."And the new members elected within the year are:W. E. Hudson, Esq.G. Fitzgibbon, Esq.William Phibbs, Esq.Rev. James Reid.William Lee, Esq., F. T. C. D.Robert Jones, Esq.Thomas Wilson, Esq.Beriah Botfield, Esq.W. T. Mulvany, Esq.Oliver Sproule, Esq.James Thompson, Esq.James Patten, M. D.J. H. Jellett, Esq. , F. T. C. D.William Andrews, Esq.J. T. Banks, Esq.Robert Bateson, Esq.John Burrowes, Esq.Rev. Samuel Butcher, F. T. C. D.Fleetwood Churchill, M. D.Alexander Clendinning, Esq.Rev. Reg. Courtenay.Durham Dunlop, Esq. , Jun.Alexander Ferrier, Esq.Wrigley Grimshaw, M. D.William Hogan, Esq.W. J. Hughes, Esq.U 2242William Roberts, Esq. , F. T. C. D. Joseph Nelson, Esq.Captain A. C. Sterling.Rev. Robert Chatto."Rev. Thomas Stack, F. T. C. D.RESOLVED, That we have heard, with deep regret, ofthedeath of our fellow Academician, the Rev. Cæsar Otway, andthat, while we wish to record our sense ofthe value of his services to the Academy, and our opinion of his merits as anauthor, who, possessing in his own person many of the besttraits in the Irish character, has by his lively and interestingsketches powerfully assisted in drawing public attention tothe history, scenery, and antiquities ofhis native land; we desire also to convey to his afflicted family the assurances ofoursincere sympathy in their sorrow for one whose private virtues rendered him the delight of the domestic circle, as histalents and information made him valuable as a member ofourInstitution.-- RESOLVED, That the Academy have heard, with regret,that Dr. Aquilla Smith, having found his attendance on theCouncil inconsistent with his professional pursuits, has tendered the resignation of his place as a member of Council;and they desire to express their sense of the valuable assistance they received from him during the time they had hiscooperation in advancing their objects.The ballot for the Annual Election having closed, thescrutineers reported that the following gentlemen were electedOfficers and Council for the ensuing year:President-Sir William Rowan Hamilton, LL.D.Treasurer -James Pim, Jun. , Esq.Secretary to the Academy-Rev. Joseph H. Singer, D.D.Secretary to the Council-J. Mac Cullagh, Esq. LL.D.Secretary of Foreign Correspondence-Rev. HumphreyLloyd, D.D.Librarian- Rev. William H. Drummond, D.D.Clerk and Assistant Librarian-Edward Clibborn.243Committee ofScience.Rev. Franc Sadleir, D.D. , Provost of Trinity College;Rev. Humphrey Lloyd, D.D.; James Apjohn, M.D.; JamesMac Cullagh, LL.D.; Rev. William Digby Sadleir, A.M.;Robert Ball, Esq.; Robert Kane, M.D.Committee ofPolite Literature.His Grace the Archbishop of Dublin; Rev. Joseph Henderson Singer, D.D.; Samuel Litton , M.D.; Rev. WilliamHamilton Drummond, D.D.; Rev. Charles Richard Elrington, D.D.; Rev. Charles William Wall, D.D.; Rev. ThomasH. Porter, D.D.Committee ofAntiquities.George Petrie, Esq.; Rev. James Henthorn Todd, D.D.;Henry J. Monck Mason, LL.D.; Samuel Ferguson, Esq.;Joseph Huband Smith, Esq.; James Pim, Jun. Esq.; Captain Larcom, R.E.The President then appointed , under his hand and seal ,the following Vice-Presidents:His Grace the Archbishop of Dublin; the Rev. Humphrey Lloyd, D.D.; the Rev. James Henthorn Todd, D.D.;the Rev. Joseph Henderson Singer, D.D.The auditors appointed by Council to examine the Treasurer's accounts reported as follows:“ We have examined the above accounts, * with the vouchers produced, and have found it to be correct; and we find that there is abalance in bank, amounting to £ 169 17s. 1d. sterling."March 16, 1842."66 (Signed, )" THOMAS HUTTON," JOSEPH CARSON.

• Entered in Treasurer's book.

244" The Treasurer reports, that there is £1052 6s. 8d. in 3 perCent. Consols, and £ 1609 4s. 9d. , in 3 per Cent. Stock, the latterbeing the Cunningham Fund." March 16, 1842."66 (Signed, )" AQUILLA SMITH."April 11.SIR WM. R. HAMILTON, LL.D. , President, in the Chair.Rev. Richard Butler, Robert Law, M. D. , and JohnToleken, M. D. , F. T. C. D. , were elected members of theAcademy.Mr. Ferguson read a paper by the Rev. Arthur B.Rowan, A. M. , M. R. I. A., on the ancient Church of Kilmelchedor.This church stands in a small hamlet and parish of thesame name, in the barony of Corkaguiny, county of Kerry,at the foot of Brandon mountain, and near the harbour ofSmerwick. At the top of the neighbouring mountain is asmall ruined oratory, and a well of great reputed sanctity,which are dedicated to St. Brandon, or Brendan, the founderof the Diocesan Cathedral of Ardfert; and the neighbourhood is further remarkable for some of those small stoneroofed cells or chapelries which are supposed to belong toa very remote age, and of which one that has been describedand engraved by Smith, in his History ofKerry, still remains.in complete preservation. The church derives its name fromSt. Melchedor, who is mentioned in a catalogue of saints inthe book of Ballimote; also in a MS. calendar in the Libraryof the Academy, where, under the date May 14, he is commemorated as " Melchedar, son of Ronan, son of the Kingof Ulster, of Kilmeilche [ dor?] , on the sea shore , at Knock-245Brennaun in the west. " For this information the author acknowledges himself indebted to Mr. Owen Connellan. Hethen proceeds to the description of the church, of whichplans and drawings are given. " The building," he says," stands due east and west, and consists of two parts, thenave and choir, separated by a richly carved semicirculararchway. The former is twenty-six feet long, by sixteenfeet wide, and thirteen feet high to the springing of thestone roof. The choir is, as usual, much smaller, being butsixteen feet long, by twelve wide, and eleven feet high to theroof, which was also of stone. There are five windows, onein the eastern gable, and one at each side in the nave andchoir; all of them having the round arch of the same style ofarchitecture as the ornamented doorways. The entrance tothe church is at the western end, through a richly ornamented doorway ofthe Anglo-Norman, or, as it is more correctly called, the Lombardic style of architecture . Makingallowance for the greater size and profusion of ornament, Ifind in the arches ofthe western door and nave ofRochesterCathedral, the nearest model for the doorways of Kilmelchedor church. In Ireland, the account given by Grose, in hisAntiquities, of Cormac's Chapel or Crypt at Cashel, may,pro tanto, be copied as a description of Kilmelchedor. Thushe tells us, ' it is a stone- roofed chapel,' with ' a nave andchoir,' with columns supporting the grand arch leading intothe choir; the columns short and thick; the portal semicircular, with nail-head and chevron mouldings; the windowsalso round.' So far the descriptions of both buildings exactlyagree."6The roofof Kilmelchedor seems to have been constructedon the same principle as the roofs of the ancient and curiousstone hermitages in its neighbourhood; one stone overlapping the other, with sufficient bearing to sustain the weightas the work advanced. But the chief peculiarity of thischurch is the elaborate ornament of the interior nave,246which is of a kind to attract attention even if found in oneof our most richly adorned churches, but much more soin a building in this remote situation . At the height of aboutfour feet from the floor, the nave shows, on each side throughits whole length, a series of square pannelled compartments,separated by short massive pilasters projecting from thewall. These compartments, twelve in number, are in perfect preservation, and appear to have been originally executed in polished stone . The nave windows occupy a compartment at each side, and are surmounted by plain roundarches.Within the choir, and springing directly from each sideof the doorway, there are small arched apertures, the use ofwhich the author is at a loss to conjecture. The semicircular head of the western doorway is filled with a singlestone, on the inner side of which is a projecting effigy, nowtoo much defaced to admit more than a conjecture as to whatit represented. In the church-yard stands a rude giganticcross, formed of a single stone; another, less rude, lies halfprostrate, and has been built into the wall ofa tomb. Oghamstones are found at several places in the neighbourhood;there is one, much effaced , in the churchyard.66Having noticed the vulgar tradition that the church.was built long ago by the Spaniards," the author offers someconjectures as to the probable date of its erection , which heconcludes to have been in the eighth or ninth century, “ whenthe Danes had intercourse with this and with other parts ofIreland;" but he supposes that it was ornamented and finishedin its present style at a subsequent period .The following notice of an ancient Boat, found nearDrogheda, was read by W. 1. Hughes, Esq.During the progress of the works carried on by the Corporation of Drogheda for the improvement ofthe port andharbour, it was found necessary to deepen the bed ofthe River247Boyne below the bridge, towards the sea, which left thatpart of the river above the bridge, towards Oldbridge, quitedry. At this part (in the Summer of 1837) , the boat, thesubject ofthe present notice, was found by some workmenwho were engaged taking gravel from the river, close by theobelisk erected to commemorate the battle fought betweenJames the Second and William the Third, about two milesfrom the town of Drogheda.Its extreme length is eighteen feet nine inches, andbreadth two feet eight inches, tapering to a breadth of fourteen inches at the back, and to nine inches in the front, beingflattened at either end; no oars seem to have been used inpropelling it, there being no marks on the sides , or places fordowells used in modern boats to secure the oars, but at eitherend a groove is perceptible where oars were placed to steeror scull with . Paddles may have been used in the samemanner as the Indians manage their canoes. Some ofthepaddles have been found, but they are of a very rough kind ,having the appearance of the branch of a tree, feathered atone end, without any attempt at shape."Along with this cott was found what I shall call ananchor; it is four feet in length, and three feet across, havingtwo arms, to one of which a rope was attached to secure theboat.The Royal Dublin Society have one of those ancient cottsin their possession , which differs from that now described inshape and size; the cott found at Drogheda being flattenedat both ends, whilst that belonging to the Dublin Society hasone end flat and the other pointed , being of the shape of amodern boat. Its length is twenty-one feet twoinches, breadthone foot, and depth ten inches; being scarcely sufficientfor a person to sit in. There is no keel to either oftheboats.Another was found lately in a bog, on the estate of SirCharles Kennedy, in the county of Waterford; it is only248eight feet six inches long, and two feet ten inches broad, andis round at the bottom, having a keel.Ware, in his work on the Antiquities of Ireland, statesit as his opinion, that the Phoenicians were the original colonisers ofthis country, and that they used boats made of osiersor wicker work, and covered with skins, in which they navigated the bays and the mouths of the rivers. The ancientIrish, he says , made use of another kind of boat in therivers and lakes, formed out of an oak wrought hollow,which is called by the Irish coiti, and by the English cott, avessel well known to antiquity under other names. Plinycalls boats hollowed out of a single beam, Monoxylæ, from aGreek word of that import, and describes them to be--lintres ex uno ligno excavatæ, i. e . boats formed out of onepiece of timber wrought hollow. And in another placePliny relates that the German pirates sailed in boats hollowed out of single trees, each of which they made so largeas to contain thirty men.April 25.SIR WM. R. HAMILTON, LL.D. , President, in the Chair.The Rev. Dr. Kennedy Bailie commenced the reading ofa paper containing an Account of his Researches in certainparts of Asia Minor.The Rev. Dr. Robinson gave an account of the castingof the great six - foot Speculum by the Earl of Rosse.The publication of this account is deferred , for the present, by Dr. Robinson. On a future occasion he expects tolay before the Academy a statement of the performance ofthe telescope when it shall be turned , for the first time, tothe heavens. The history of the casting of the specu-249lum, ofthe performance of the telescope, and of the machinery by which it is moved, will then appear in the Proceedings.May 9.SIR WM. R. HAMILTON, LL.D. , President, in the Chair.William Blacker, Esq. and the Rev. James Booth wereelected members of the Academy.James Mac Cullagh, Esq. was elected Secretary of theAcademy, in the room of the Rev. Dr. Singer, resigned;and Dr. Kane was elected Secretary of Council.A paper, by the Rev. Dr. Hincks, " On the True Dateof the Rosetta Stone," was read.The date usually assigned to this monument, on the authority ofDr. Young, is the 27th March, 196 B. C. , accordingto the proleptic Julian reckoning; the true date, as determined by Dr. Hincks, is the 27th March, 197 B. C. Takingthe former date for granted, M. Letronne has drawn from ita great many inferences, which the error of a single year entirely vitiates. These inferences relate to the history ofPtolemy Epiphanes, and to the mode of computing the yearsof his reign and of the reigns of other Egyptian kings; asalso to the various priesthoods of royal personages that arementioned on the Ptolemaic monuments. The conclusionsof M. Letronne, and those which are to be deduced fromthe corrected date, are exhibited by the author in parallelcolumns.The President made some remarks on the day of theVernal Equinox at the time of the Council of Nice.It has been stated by some eminent writers on astronomy,for example by Brinkley and Biot, and seems to be generally supposed, that the vernal equinox in the year 325, a. d.250fell on the 21st of March. But Sir W. Hamilton finds thatVince's Solar Tables (or Delambre's, from which those areformed) conduct to about 24 hours before the Greenwichmean noon ofthe 20th of March, as the true date of theequinox in that year; which thus appears to have been assigned to a wrong day, by some erroneous computation orreport, perhaps as long ago as the time of the phenomenonin question.As this result is curious, Sir W. Hamilton conceives thatit may not be uninteresting to confirm it by a very simpleprocess of calculation , derived from the Gregorian Calendar.According to that calendar, 400 years contain 146097 days,being a number less by 3 than that of the days in four Juliancenturies; and if the farther refinement be adopted, whichsome have suggested , of suppressing the intercalary day ineach of the years, 4000, 8000, &c. , then, in the calendarthus improved, 4000 civil years will contain 1460969 solardays. Assuming then, as a sufficiently near approximation,that such is the real length of 4000 tropical years; multiplying by 3, and dividing by 8 , we find that 1500 tropical yearsare equivalent to 547863 days and a fraction; which fractionof a day, according to this simple arithmetic, would be equivalent to 9 hours. But 1500 Julian years contain 547875days, that is , 12 more than the number last determined; andthese 12 days are precisely the difference of new and oldstyles in the present century. If, then, we neglect the fraction, the new-style date of an equinox in any year of thenineteenth century ought to be the same with the old- styledate ofthe same equinox in the corresponding year of thefourth century; and in particular the vernal equinox of 325ought to have fallen on the 20th of March, because that of1825 fell on the day so named: while the fraction of a dayabove referred to, though not entirely to be relied on, renders this result a little more exact, by throwing back theequinox from the evening to a time more near to noon.251The following communication from the Rev. ThomasKnox was read:" River Glebe, Toomavara,66 April 27, 1842." An application of the Daguerreotype process to astronomical purposes occurred to me last autumn. It is wellknown that an inscription on a building which it would require a telescope to read, from its smallness or distance, can(if a view ofthat building be taken in the camera on one ofDaguerre's plates) be read by a microscope, though invisibleon the plate to the naked eye; also, that the internal structure of some insects can be as well studied by examining theimage of the object on the plate by a microscope (that imagehaving been formed from the oxyhydrogen microscope) ."From these known facts it is extremely probable thatwere an image of a double star, or of one of the nebulæ, takenon a Daguerre plate in the focus of a telescope of moderatepower, but which of itself could not divide the star or resolvethe nebula; that by then examining the plate by a strongmicroscope, the state of that star, &c. might be ascertained,as well as if it had in the first place been examined by atelescope of very high power." That the light of the fixed stars possesses chemicalrays, and would therefore affect Daguerre's plates, there canbe little doubt; and I feel certain in my own mind that theimage thus formed would reveal to the microscope as muchas a telescope of equal power could in the first instance haveascertained." I am aware that theorising this way is very unprofitable, but I do not possess instrumental means for trying theexperiment myself, my equatorial not having any clock motion adapted to it. On the accuracy and steadiness of theclock movement all would depend; any small telescope, orperhaps even a single lens, equatorially mounted, would do252the rest. The plates need not exceed in size the pencil ofrays, and may be very small." Ifthis succeed, we might gain great advantages by thusmapping the stars and nebulæ, and examining their state atour leisure, in our study, and being able to take advantageofwhat every practical astronomer knows to occur so seldomin our climate, namely, a state of the atmosphere favourablefor delicate observation."To try it, some easily divided star, such as Ursæ,might be first used, and, if the plate registered it as a doublestar, we might then proceed to other more difficult objects."DONATIONS.ALetter on the State ofSchools ofChemistry in the UnitedKingdom. By Wm. Gregory, M. D. , M. R. I. A., &c . &c.Presented by the Author.A volume of Tracts relating to the Historical Society ofDublin. Presented by G. A. Kennedy, M. D. , M. R. I. A.&c. &c.Journal ofthe Franklin Institute. Third Series. Vol. II.Eleventh Report of the British Association for 1841 .(Plymouth). Presented by the Association.Account of the Magnetical Observatory of Dublin. Bythe Rev. H. Lloyd, D. D., &c. Presented by the Author.AView ofthe Coinage of the Heptarchy. By John Lindsay, Esq. Presented by the Author.Mémoires de la Societe Géologique de France. Tome IV.Second Part.Transactions ofthe Royal Society ofCopenhagen. Vol . VI.(1841) .On the Use and Study ofHistory. ByW. Torrens M'Cullagh, LL. B. Presented by the Author.253May 23.SIR WM. R. HAMILTON, LL.D., President, in the Chair.The Rev. Dr. Kennedy Bailie, late F. T. C. D. , concludeda paper which he had commenced on the last meeting butone of the Academy, the subject of which was a generalstatement of his researches in certain parts of Asia Minor,relative to Inscriptions of the Græco- Roman era. The following is an outline of his communication.He commenced with some brief notices of what has beendone by scholars in this department of classical literature,and with remarking on its importance, as illustrative of thelanguage, the history, and the institutions of the people whohave bequeathed these monuments to after-ages. In thissection, the labours of Chandler, Poco*cke, Spon, Clarke, andProfessor Böeckh, were particularly commemorated.Next followed an account of the rules by which he wasguided, in forming his collection of inscriptions, during atour which he had recently made in the countries borderingon the Mediterranean.The third section embraced notices of the inscriptionswhich he copied in six of the Apocalyptic sites , namely,Ephesus, Philadelphia, Sardes, Thyatira, Pergamus, andSmyrna, and of a few others which he found in some neighbouring localities, viz. two sepulchral, from the sites oftheancient Cotyaion, and three from the Turkish town of Kîrkagatch, situated on the road from Thyatira to Pergamus.The Ephesian monuments related chiefly to circ*mstancesconnected with the Artemisiac festivals. They were three innumber; one, a psephisma, or decree of the senate andpeople of Ephesus; the two remaining, honorary tituli .Ofthe four inscriptions found at Philadelphia, the mostremarkable was a fragment of a titulus , which, in all probability, had been inscribed on the pedestal of a statue of the254eunuch Eutropius, after the downfall of the power of thatfavourite of Arcadius.In support ofthis opinion , Dr. Kennedy Bailie entered atsome length into that part of the history of the period whichconcerns the expedition against Trigibild the Ostrogoth ,under the auspices of Eutropius, which terminated in the discomfiture and death of the general whom he had selected.This inscription was found in an extremely mutilatedstate; and an attempt has been made by the author of thepaper to restore it, on the basis of the historical notices derivable from Claudian's two books against Eutropius.It was metrical: the lines alternately hexameter and pentameter.The inscriptions found at Thyatira were nine in number,of which four at least were entaphial. The others werechiefly honorary tituli, and of these, the most perfect whichDr.Kennedy Bailie found, was one which had been inscribedon the pedestal of a statue erected in memory ofthe skill andprowess ofa distinguished Thyatirene athlete, Menander theson of Paullus, by the youths of the first Heraclean Gymnasia.The most perfect amongst the sepulchral epigraphs wasfound on a soros which had been the property of a distinguished citizen of Thyatira, named Fabius Zosimus. In thisare recited, at full length, the intentions of the owner, thelegal sanction under which they were to be carried intoeffect, the names of the Proconsul and Registrar, as also thedate.It contains , moreover, some interesting notices relating tothe astyography of the ancient site amongst the ruins ofwhich it was found.Ofthe Sardian monuments, the most remarkable was onewhich appeared to have been destined to commemorate themunificence of Tiberius, Trajan, and, most probably, of Hadrian also, to the citizens of Sardes.255This record was found by the author in a most mutilatedstate; but sufficient of it fortunately remained, to enable himto connect its notices with the accounts given by Tacitus,Spartianus, and Dio, of the liberality of those emperors tothe distressed States ofthe Proconsular Asia, which had beendevastated by a succession of earthquakes in the region ofthe Katakekaumene.The most remarkable of the Pergamenian incriptionswere those in honour of Hadrian, both after his assumptionofthe purple, and during the life-time of Trajan. One ofthese may be regarded as peculiarly valuable, the great probability being, that it still exists amongst the inedited monuments of the Græco- Roman era, and that it bears moststrongly on the historical doubt originated by the abovementioned Dio, on the subject of Hadrian's adoption.Two other inscriptions, which were copied at Pergamos,appear evidently to belong to the period of the Lower Empire. They have, however, been allowed a place in thiscollection, as tending to illustrate the taste and style of theage in such matters. Both are honorary, and one entaphial.The Smyrnæan Tituli are five in number, viz. a fragmentof a decree, or treaty; a notice of the officers of the customsof the port ofthe ancient city; a votive epigraph, on a stele;a fragment of an inscription from the frieze of a temple;lastly, an epitaph.On these the author of the essay dwelt at considerablelength, more especially on the third, in which he pointed outa circ*mstance which appeared to have escaped the noticeof former writers: amongst these, of Mr. Arundell, whosework on the Apocalyptic Churches appeared in 1828. Thisremark concerned the metre, and led to a conversation witha gentleman present, who expressed an interest in Mr.Arundell's discoveries, and a wish to be informed on the subject ofthe accuracy of that traveller's statements.VOL. II. X256Dr. Kennedy Bailie's reply was: that his sole concern , atpresent, was the literature of inscriptions; that therefore hefelt not at liberty to venture any observation on either thestyle or the accuracy of the reverend gentleman's volumes,excepting so far as related to that subject; and that he wasbound in candour to confess , that the form in which his collection of inscriptions has been offered to the public is notone on which any reader could rely as a scholar- like representation of the original monuments.The inscriptions of the Turkish town of Kîrgagatch andCotyaion, next occupied the author's attention . The firstof these, three in number, comprised an honorary titulus , infavour of Hadrian, inscribed on a block of marble, which wasmost probably brought from Stratonicea. Secondly, a decree ofthe senate and people of that city in honour of Diodorus Philometor, son of Nicander, in consideration of hispublic services. Thirdly, a dedication of a church, in theage of the Lower Empire, or what appears to have beensuch, for the characters had been very much effaced .Ofthese the author read a detailed account, and statedhis reasons for supposing that the more ancient tituli hadbeen brought from Stratonicea in Caria, thus establishingsome connexion between that site and the Turkish town.This is the more remarkable, inasmuch as there exist noarchitectural remains in Kîrkagatch to lead to the suppositionthat it occupied any known ancient site.Two inscriptions from Kûtaïah (Cotyaion) concluded theseries, both of which were copied from grave- stones in theArmenian cemetery. They were sepulchral tituli, and thestones themselves , on which they were engraved, most probably fragments of Sarkophagi.The Secretary read a letter from Dr. Hunter, presentingto the Academy three mathematical works, by the NuwabShums-ool-oomrah of Hyderabad.25766 SIR," Dublin, Royal Barracks,66 May 23, 1842." I beg to present to the Library of the RoyalIrish Academy the three accompanying works on scientificsubjects, printed in the Persian language and character, andthe composition of a native prince.66 They were brought home by me three years ago, onmy return from India, where I was serving with my regiment,and were given me by the Prince for the purpose of beingpresented to some scientific Institution." Theyare the composition of Nuwab Shums-ool- oomrahof Hyderabad, in the Nizam's Country; a prince who hasdistinguished himself much by his scientific acquirements,his original genius, and general love of literature. He hasgreat curiosity about every European invention, and hishouse is set round with every sort of mechanical contrivance.These works were printed by himself in his lithographicprinting press. The large work is on geometry and trigonometry; the two smaller are on spherical trigonometry andlogarithms." I remain, Sir, &c."6" THOMAS HUNTER, M.D.,'Assistant- Surgeon, 12th Royal Lancers."Tothe Secretary ofthe66 Royal Irish Academy.”DONATIONS.Three Lithographed Manuscripts in Persian, on Geometry, Trigonometry, and Logarithms. By the Prince Shumsool- oomrah, of Hyderabad. Presented by Thomas Hunter,M. D., &c.Ordnance Survey ofKilkenny, in 49 Sheets. Presentedby His Excellency the Lord Lieutenant.258Statistical Returns of the Dublin Metropolitan Policefor1841. Presented by the Commissioners.Nouveau Catalogue des principales Apparitions d'EtoilesFilantes. Par M. Quetelet. Presented by the Author.Annuaire de l'Academie Royale de Bruxelles ( 1842) .Bulletins de l'Academie Royale de Bruxelles ( 1841 ) .The Manuscript Rarities ofthe University ofCambridge.ByJames Orchard Halliwell, Esq. Presented by the Author.Notes on the United States of North America in 1838–9–40. By George Combe, Esq. , Hon. M.R. I. A. Presented bythe Author.PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1842. No. 35.June 13.REV. HUMPHREY LLOYD, D. D., Vice- President, inthe Chair.Maria Edgeworth was elected (by acclamation) an Honorary Member of the Academy.Arthur B. Cane, Esq. , B. J. Chapman, Esq., Francis M.Jennings, Esq. , and Sir Thomas Staples, Bart., were electedOrdinary Members.Mr. J. Huband Smith read a paper descriptive of therecent discovery of a vast number of Cinerary Urns at theHill of Rath, within a few miles of Drogheda, on the road toCollon.At the foot of the hill a quarry had been opened to procure stones for the repair of the road. In the beginning ofspring the tenant in the occupation of the farm proceededto level this quarry, by carrying down the earth from thebrow of the hill; and in the progress of his work he discovered from 150 to 200 urns of unbaked clay, of various sizes,almost all placed in an inverted position , and covering, eachof them, a considerable quantity of human bones.As it seemed probable that a more careful examinationofthe portion of this interesting rath or tumulus which yetremained undisturbed might be productive of some discoveryVOL. II.Y260calculated to throw light upon the still unsettled question ofthe date ofthis mode of interment, as well as "the authorsof these sepulchral memorials," Mr. Smith was induced toundertake it, and accordingly proceeded to the spot for thatpurpose on the 30th of November last.The rath appears to have occupied the declivity of ahill, sloping gently to the west, and was originally enclosedby a breastwork of earth, of inconsiderable elevation, alltrace of which had nearly disappeared, but which, accordingto report, may have once enclosed a space of five or sixacres. The soil upon the surface having been found to consist of rich clay, had been from time to time spread over thepoorer land adjoining. It was not, however, till the processof levelling was begun that urns were discovered; they werethen found at a depth of from four to five feet beneath theoriginal surface, resting upon the till, or gravelly subsoil.Mr. Smith proceeded to a part of the hill pointed out tohim as not having been yet disturbed , and, with the assistanceof a few labourers, very soon had the satisfaction of layingbare four or five , or more urns. They were placed apparently without any regularity, about two or three feet asunder, and having been imbedded in yellow clay, without anyflags or other stones to protect them, had in most cases beenpressed in, and broken to pieces, by the superincumbentearth. One, however, which remained whole, Mr. Smith,by the utmost care in freeing it from the moist clay whichsurrounded it, and by allowing it to dry for two or threehours before he ventured to move it, was enabled to carryaway entire, and he now presented it, with its contents, to theAcademy.These urns varied in size, and were in general from abouteight to fifteen inches in height. Closely adjoining one ofthe larger ones, in fact crushed against it, lay two smaller,measuring probably but two or three inches each in diameter;these latter ones did not appear to have held bones. In261another instance a group of three or more urns, of a largersize, appeared pressed together. On removing the brokenpieces ofeach urn the bones appeared in a little conical heapwithin, in very small fragments, the larger ones having fallento the sides, mixed at bottom with black unctuous earth, andoccasionally small morsels of charred wood. In the verylarge and fine urn which had been found previous to Mr.Smith's visit to the tumulus, and which he now presented tothe Academy in the name of Mr. Kelly of Drogheda, bywhom it had been disinterred, some very interesting mattershad been found mixed up with a very considerable quantityof human remains which it contained. These consisted of aflint arrow head, a curious curved needle of bone, one endof which was flattened and perforated , and some small stonetools, one of which seemed likely to have been used inmaking the indentations or rudely sculptured patterns bywhich this urn, in common with all the others, was ornamented; and lastly, a small, thin scale ofcopper, pierced witha small hole. No other metallic remains of any kind were discovered, nor upon the closest inquiry does there seem anyground for supposing that any ornaments, either of silver orgold, such as have been so frequently obtained in barrowsand other sepulchral tumuli, both here and in England, werefound in this rath. This last mentioned urn, which was thelargest discovered here, measures seventeen inches in height,and the same in extreme breadth; and would probably contain about eight gallons of liquid.The most remarkable differences between this tumulusand most other repositories of the ashes of our pagan predecessors, both in this country and in England, appear to bethe vast number of urns which were found here, in one vastcemetery, and the total absence of any kist of flags, or othercavity formed to receive and protect the urns from the pressure ofthe earth either laterally or from above.Y 2262A paper entitled, " An Inquiry as to the Coefficient ofLabouringForce in Overshot Water-Wheels, whose diameteris equal to, or exceeds the total descent due to the fall; andof Water-Wheels moving in Circular Channels , " was readby Robert Mallet, Esq. , Mem. Ins. C. E., M. R. I. A.This paper is partly mathematical and partly experimental . The investigation which it describes, the results ofwhich are given in ten tables, had in view principally to obtain definite experimental answers to the following questions:1st. With a given height of fall and head of water, or inother words, with a given descent and depth of water in thepentrough, will any diameter of wheel greater than that equalto the fall give an increase of labouring force (i . e. a bettereffect than the latter) , or will a loss of labouring force resultfrom such increase of diameter?2nd. When the head ofwater is necessarily variable, under what conditions will an advantage be obtained by theuse of the larger wheel, and what will be the maximum advantage?3rd. Is any increase oflabouring force obtained by causingthe loaded arc of an overshot wheel to revolve in a closelyfitting circular race or conduit, and if so, what is the amountof advantage, and what the conditions of maximum effect?The author briefly reviews the history of our knowledgeof this branch ofhydrodynamics, the experimental researchesof Da Borda, Smeaton, &c. , and the more recent improvements in the theory of water-wheels, due to the analyticinvestigations of German and French engineers, and theadmirably conducted experiments of Poncelet, Morin, andthe Franklin Institute.Smeaton, in his paper on water-wheels, read to the RoyalSociety in May, 1759, and Dr. Robison of Edinburgh, in histreatise on water-power, lay down as a fixed principle, that noadvantage can be obtained by making the diameter of an over-263shot wheel greater than that ofthe total descent, minus so muchas is necessary to give the water a proper velocity on reachingthe wheel. The author, however, contends that the reasoningby which the latter writer upholds this is inconclusive, —thatthere are some circ*mstances which he points out necessarilyin favour of the larger wheel, and that conditions may occurin practice in which it is desirable to use the larger wheel,even at some sacrifice of power; and that hence it is of importance to ascertain its value in use, as compared withSmeaton's size for maximum effect.The author states the general proposition, " that the labouring force (travail of French authors, or mechanical powerof Smeaton) of any machine, transferring the motive powerof water, is equal to that of the whole moving power employed, minus one- half of the vis viva lost by the water onentering the machine, and minus one-half of the vis viva dueto the velocity of the water on quitting it." He then obtainsgeneral equations expressing the relations between the fall ,the velocity, the weight of fluid, the power, &c. in overshotwater-wheels, at whatever point the water may first reachthe wheel, and whether the latter move naked, or in a circular channel or course. From these he deduces, that1st. Ifthe portion of the total descent passed through bythe water, before reaching the wheel, be given, the velocity ofthe circumference should be one- half that due to this height.2nd. If the velocity of the circumference be given, thewater must descend through such a fraction of the whole fall,before reaching the wheel, as will generate this velocity.3rd. The maximum of labouring force is greater as thevelocity of the wheel is less , and its limit theoretically approaches that due to the whole fall; general equations arethen given, expressing the amount of labouring force in allthe conditions considered by the author, and their maxima.One of the principal advantages of using an overshotwheel greater in diameter than the height of the fall, is the264capability thus given of making any additional head of wateroccurring at intervals, by freshes or any other cause, available, by letting the water on the wheel at higher and higherlevels.The first course of experiments is devoted to the determination of the comparative value of two water-wheels, theone whose diameter is equal to the whole fall; the other tothe head and fall, or to the total descent. By the head, theauthor always means the efficient head, or that due to theactual velocity of efflux at the sluice or shuttle, as determinedby Smeaton's experimental method, -this was equal to sixinches in all cases.The apparatus employed in these researches consisted oftwo accurately made models of these wheels, with curvedbuckets, made of tin plate, the arms, &c . of brass, and theaxes of cast iron, working on brass . Special contrivanceswere adopted to measure the weight of water passed througheach wheel in each experiment, which was in every case1000 lbs. avoirdupoise; and others, to preserve the head ofwater quite constant, -to determine the number of revolutions made per minute, and thence the speed of the wheels.One wheel was 25.5 inches diameter, the other 33 inchesdiameter. The value of the labouring force was determineddirectly by the elevation of known weights to a recordedheight by a silken cord over a pulley; the altitude was readoff, on a fixed rule placed vertically against a lofty chimney.The relative power of the wheels was determined by thespeed ofrotation of a regulating fly or vane.All the principal results given in the ten tables are theaverage offive good experiments. From the accurate workmanship and large size of these models, the peculiar contrivances for ensuring accuracy of observation, and the caretaken in the experiments, the author reposes considerableconfidence in his results as practical data.The velocity, in reference to maximum effect, is determined ,265and found to be lower than that deduced by Smeaton fromhis experiments, which the author presumes arises from thebetter construction of apparatus, and better form of bucketused in the present case.The author then ascertains, by another train of experiments on both wheels, the value of the circular conduit orrace, and finds, in round numbers, that there is an economyof labouring force, amounting to from eight to eleven per cent.of the power of the fall, obtained by its use. This conduitacts by retaining the water in the buckets at the lower portion of the loaded arc. The velocity of a water-wheel working thus, he finds may vary through a greater range withouta material loss of power than when working naked, and thata steady motion is also continued to a much lower velocity.The author arrives at the following practical conclusions:1st. When the depth of water in the reservoir is invariable, the diameter of the water-wheel should never begreater than the entire height of the fall , less so much of itas may be requisite to give the water a proper velocity onentering the buckets.2nd. When the depth of water in the reservoir variesconsiderably and unavoidably in depth, an advantage maybe obtained by applying a larger wheel dependent upon theextent offluctuation and the ratio in time that the water is atit* highest and lowest levels during a given prolonged period;if this be a ratio of equality in time there will be no advantage, and hence in practice the cases will be rare where anyadvantage will be obtained .3rd. If the level of the water in the reservoir never fallbelow the mean depth of the reservoir, when at the highestand lowest, and the average depth be between an eighth anda tenth of the height of the fall, then the average labouringforce ofthe large wheel will be greater than that of thesmall one, and it will of course increase this advantage atperiods of increased depth of reservoir.266Hence the author affirms that Dr. Robison's conclusionsmust henceforth receive a limitation.Having shown that a positive advantage is obtained bythe use ofthe circular conduit, amounting to about elevenper cent. of the total power, and that this value increaseswith an increase in the velocity of the wheel up to six feetper second, or more in large wheels, the author contends,that it is practicable to increase the efficiency of the bestovershot wheels as now usually made, at least ten per cent. bythis application. The only objections ever urged against theconduit were ofa merely practical character, and the authorshows that improved workmanship, and the modern use ofcast iron, of which the conduit may be constructed , andprovided with adjustments, render these no longer tenable.Drawings of the apparatus used in these researches, andthe tabulated results, were exhibited to the Academy.Professor Lloyd read a paper " on the Phenomena ofThinPlates in Polarized Light."The author stated , that his attention had been drawn tothis subject by a letter which he had received from Sir DavidBrewster, describing a large class of hitherto unobservedphenomena. Sir David Brewster having expressed his desire, in this letter, to know whether the wave-theory couldfurnish an explanation of the facts which he had observed ,Professor Lloyd was thus led to undertake the investigationwhich formed the subject ofthe present communication. *Mr. Airy had long since inferred , from a consideration ofthe form of Fresnel's expression for the intensity of reflectedlight, that when light, polarized perpendicularly to the plane

• The present paper was read in the Mathematical Section of the British

Association, last year; and a summary of the results was published in the Athenæum, ofAugust, 1841. The author deferred submitting it to the Academy, in thehope of being able to add an experimental confirmation of some of the conclusionsnot noticed by Sir D. Brewster. He has, however, been compelled, by the pressureof other duties, to postpone still further this branch of the investigation.267of incidence, was incident upon a thin plate bounded bymedia of unequal refractive powers, a remarkable change inthe reflected light should take place, when the angle of incidence was intermediate to the polarizing angles of the twosurfaces ofthe plate. This theoretical anticipation was fullyverified by experiment. When a lens oflow refracting powerwas laid upon a plate of high refracting power, the ringswhich were formed appeared with a black centre, when theangle of incidence was less than the polarizing angle ofthe lowrefracting substance, or greaterthan the polarizing angle ofthehigh refracting substance; while, when the incidence was intermediate to these two angles , the rings were white- centred,and the whole system was complementary to what it had beenbefore. At the polarizing angle itself the rings disappeared,there being no light reflected from one ofthe surfaces of theplate, and therefore no interference.The examination of this subject has since been resumed by Sir David Brewster; and he has repeated the experiments of Mr. Airy in a more general form , the incidentlight being polarized in any plane. He has thus been led tomany new results. The rings are found to disappear undercirc*mstances in which light is reflected from both surfacesof the plate; and there are many remarkable peculiarities inthe transition ofthe rings into the complementary system. *It was to the theoretical explanation ofthese phenomenathat Professor Lloyd now invited the attention of the Academy. In the conduct of the investigation he has generalizedthe methods followed by M. Poisson and Mr. Airy on thesame subject. The incident vibration being resolved intotwo, one in the plane of incidence, and the other in the perpendicular plane, each portion will give rise to an infiniteseries of reflected vibrations , into which it is subdivided atthe bounding surfaces of the plate. The expression of theresultant intensity, for each portion, being then deduced, the

• The researches of Sir David Brewster are now published in the Philosophical

Transactions for 1841.268actual intensity of the reflected beam is the sum of these intensities. Its value is found to be expressed by the formulaI = cos²yu2 +2 uu' cosa + u²²1+2uu'cosa +u²u'² + sin²y w2 +2ww' cosa + w/21 +2ww'cos a +w²w/2¹in which u and u' denote the ratios ofthe reflected to the incident vibration at the two surfaces of the plate, when thelight is polarized in the plane of incidence; w and w' thecorresponding quantities for light polarized in the perpendicular plane; and a the difference of phase of the successiveportions of the reflected beam. The values of u, u' , w' , w, are,sin(0-0') sin(0'′-0″) tan(0-0') tan(0′-0″)sin(0 +0')' sin( 0' + 0″)' tan(0+0')' tan(0' +0')where denotes the angle of incidence on the first surface ofthe plate; the corresponding angle of refraction, or theangle of incidence on the second surface; and 0" the angleof refraction at the second. The value of a isu= u'= w= w'=α =4πT cos0';λT being the thickness of the plate, and λ the length of thewave.When the obliquity of the incident pencil is not verygreat, the squares and higher powers of u, u', w, w', may beneglected in comparison with unity, and the expression ofthe intensity has the approximate value ,1 = cos²y(u² + 2uu'cosa + u'²) +' sin²y (w² + 2ww'cos a +w²²)This quantity will be independent of the phase a, and therefore the intensity will be constant, and the rings disappear,whenuu' cos² y + ww'sin²y = 0;that is, when the azimuth of the plane of polarization has thevalue given by the formula,tan² y =--- un'ww =cos (0—0') cos ( 0′ — 0″)cos (0 + 0') cos (0′ + 0 ')'In this formula cos ( 0-0) and cos (0' -0") are always positive;269and accordingly the resulting value of tany will be real, andtherefore the disappearance of the rings possible, only whencos (0 +0′) and cos ( 0′ + 0″) are of opposite signs; i . e. whenthe angles of incidence on the two surfaces are, in the onecase greater, and in the other less, than the polarizing angle.The media at the two sides of the plate, therefore, musthave different refractive powers.Again, the phases of the two portions of the reflectedbeam, and which are polarized respectively in the plane ofincidence and in the perpendicular plane, are given by theformulas,tan a' =tana" =u' ( 1- u²) sin au( 1 +u'² ) + u' ( 1 +u²) cos a'w' (1 -w²) sin aw( 1 + w'²) + w' ( 1 +w²) cos a'The phases, a' and a", are consequently in general different,and therefore the resulting light will be, in general, elliptically polarized. The author entered into some developmentsconnected with this part of the subject, which does not appear to have been noticed by Sir D. Brewster in the courseof his experimental inquiries; and he concluded by statingthe important bearings which it may possibly have upon thephenomena of elliptical polarization by metals.Professor Lloyd having, in the preceding communication,thrown out the idea that the elliptical polarization of metalsmight possibly be identified with that which is producedby a thin film on the surface of a reflecting body, Professor Mac Cullagh took occasion to observe that an analogous, but far more general, hypothesis had occurred tohimself some years ago, among the various conjectures bywhich he had sought to account for the remarkable difference between the action of metals and that of transparent media in reflecting light. In his theory of crystallinereflexion he had found it allowable to suppose that thechange in the elasticity of the ether, in passing out of270one medium into the other, takes place abruptly at theircommon surface; and he had thought it not unlikely that thesupposition of agradual change of elasticity , taking place within a very small space at one or both sides of the surface of ametal, might afford an explanation of the peculiar phenomenaof metallic reflexion. Such a supposition would be mathematically equivalent to the hypothesis that an immense number of films , of which the refractive powers vary betweengiven limits according to some law, compose a very thinstratum at the surface of a polished metal; and it wouldbe in accordance with the inference drawn by ProfessorMac Cullagh from certain formulas (Transactions R. I. A. ,vol. xviii. p. 70) that the law of equivalent vibrations is notobserved in metals; an inference which, indeed , originallysuggested to him the hypothesis in question . He had notyet compared the hypothesis with his formulas, but it waseasy to see that it would explain the non- existence of anangle of complete polarization for metals, as well as the general fact of elliptical polarization; and perhaps the metallicbrilliancy, difference of colour, &c. might be occasioned bythe great number of reflexions in the variable stratum atthe surface, and the endless variety of interferences produced by them.The above was only one of the conjectures which hadbeen formerly made by Professor Mac Cullagh in relation tothis subject, and it was mentioned on this occasion chiefly onaccount ofits analogy with the view taken by Professor Lloyd.Another and very different hypothesis, which was the firstthat had occurred to him, as being immediately suggested bythe imaginary form which he had assumed for the velocityofpropagation in a metal, will be found stated in the ComptesRendus ofthe French Academy, tom. viii. , p. 962, in a letterto M. Arago, dated May 11 , 1839. It consisted in supposingthe amplitude of the vibration within the metal to be proportional to a certain exponential ofwhich the value is there given,accompanied with the remark that this expression for the vibra-271tion, ifintroduced into the differential equations (at that timeunknown) which subsist at the confines of two media, wouldprobably explain the peculiar phenomena of metallic reflexion, such as change of phase, &c. Very soon after thatdate the equations were discovered which hold good at thecommon surface of two transparent media (see ProceedingsR. I. A. vol.i. , p.378); and it is certainly not a little singular thatthese equations, with the help of the aforesaid expression forthe vibration, not only explain the change of phase, but leadto the precise formulas which had been previously given forthe case of metallic reflexion (Transactions R. I. A. vol. xviii.p. 71) . The application of the equations, however, to thiscase, cannot be regarded as legitimate without further proof;and the hypothesis is attended by another difficulty, the nature of which may be seen in the letter alluded to.Onthe whole, ProfessorMac Cullagh did not consider himself warranted, as yet, in choosing between his two hypotheses, nor even in concluding that one or other of them mustbe the right one. Before constructing any refined theory, hethought it necessary that the formulas to which he had referred, and which, ifthey are correct, must be the foundationof the theory, should be tested by experiments more accurate than any that had yet been made, and this was a task towhich he hoped he should soon have leisure to devote himself.Professor Lloyd explained , that the hypothesis which hehad suggested had not been offered by him as an exactphysical representation of the optical constitution of metals;but rather as one which lent itself, with tolerable facility, tomathematical expression, and the results of which mightpossibly, by a suitable determination of the constants oftheformulas, be found to coincide with the phenomena, andtherefore with the results of a more rigid theory.RESOLVED, That, in future, when the office of Secretaryof the Academy is vacant, the vacancy shall be filled up byexpress election.272June 27.REV. J. H. TODD, D. D. , Vice- President, in the Chair.H. J. Monck Mason, Esq. , LL.D., read an account ofa visit which he had paid to the Tomb of the Volumnii atPerugia.Mr. Mason then presented a gold fibula found in Ireland ,as a contribution to the Museum of Antiquities, now in process of formation by the Academy.The thanks ofthe Academy were voted to Mr. Mason forthe donation .66 A paper was read by Dr. Macartney on the minuteStructure of the Brain in the Chimpanzee and the humanIdiot, compared with that of the perfect Brain of Man, withsome reflections on the Cerebral Functions."The author commenced by stating, that he had discovered the brain of all animals to be composed ofa plexiformarrangement of white (or, as he termed them, sentient) filaments, the most delicate of which he found to pervade all thecoloured substances ofthe brain. He attributed the highersensorial powers of the cerebral organ to the disposition andintercommunication of these filaments, more especially wherethey exist in the coloured substances. The mode he employs for rendering the finer filaments evident is to moistenthe different substances during the dissection with a solutionof alum in water, which, causing a slight coagulation , makesthe filaments opaque and visible. The author accounted forthe fact that the existence of the most delicate plexuses hadhitherto escaped observation, from the circ*mstance thatother anatomists had not used any fluid to coagulate them.He considers the shape and magnitude of the different partsof the brain as merely subservient to the proper arrangement and number of the plexuses of the sentient substance.273The principal object of the paper was to point out thefirst gradations from the perfect structure of the brain inman, and for this purpose the author related the dissectionofthe brain ofthe chimpanzee (simia troglodytes, Lin. ) and oftwo human idiots, from which he was led to conclude that theprimary deviations in the anatomy of the brain were to befound in the essential structure of the locus niger, ofthe corpusfimbriatum, and of the corpora olivaria, —in the existenceof the white stria in the fourth ventricle, of the corpora candicantia, and of calcareous granules in the pineal gland,—inthe degree of intermixture of the white filaments of the arborvitæ, the distinction of the anterior crura of the fornix, andlastly the decussations of the pyramids. By the dissectionsit was evident that the brain ofthe chimpanzee possessed asuperior structure to that of the natural human idiot.As the author had previously ascertained that all theplexuses in the brain are conjoined, and all the cerebral andspinal nerves are incorporated with the parts from whichthey are said to arise, he was led to infer that the functionsofthe brain are not confined to particular parts of the surface,but that all the parts exercise a mutual influence on eachother, that its powers and operation are systematic and harmonious, instead of the effect of different parts of the brainacting independently and often in opposition to each other.He stated a number of facts contradicting the opinion of thecerebellum being designed to produce the sexual instinct, astaught by Gall and his followers. He ascribed the origin ofallinstincts to the organs to the operations of which the instinctsare subservient. He argued that if instinctive impulses wereto originate in the brain, they would interfere with all itshigher functions. The author further considered the perfect continuity and incorporation of the nerves with centralparts ofthe system, as sufficient to account for the functionsof sensation and voluntary motion, without the interpositionof nervous fluid.274Dr. Macartney exhibited a drawing of the base of thebrain of an idiot, in which there was a singular deficiency ofthe cerebellum; and also a cast of the brain of the chimpanzee, and one of the human brain. These two, makingallowance for the size, almost perfectly agreed with regard toexternal appearances.J. Huband Smith, Esq. , by command of His Excellencythe Lord Lieutenant, presented to the Academy an ancientgold semilunar ornament of considerable value, found in thecounty of Roscommon.The thanks of the Academy were voted to His Excellency for this donation.A considerable number of ancient bronze articles, consisting of portions of chain armour, a spear head , a lanceblade, with some coins, found near Headfort, County Galway, were presented to the Museum on the part of RichardJ. Mansergh St. George, Esq.Mr. St. George received the thanks of the Academy.The collection of Antiquities of the late Dean of St. Patrick's was presented to the Academy in the name of theSubscribers.- RESOLVED, That the List of Subscribers be printed asan Appendix to the Proceedings. *

• See Appendix, No. I.

275August 4.REV. C. W. WALL, D. D., in the Chair.The President made a communication respecting a method which had been lately proposed by Professor Badanoof Genoa, for the solution of algebraical equations of thefifth and higher degrees. *Lagrange has shown that the functiontɔ = (x² +wx" + w² x" + w³x¹V +w¹x")5receives only twenty-four different values, for all possiblechanges of arrangement of the five quantities, x', . . . x , ifw be an imaginary root of unity, so thatw¹ + w³ + w² + w + 1 = 0.Professor Badano has proposed to express these twentyfour values by certain combinations of quadratic and cubicradicals, suggested by the theory of biquadratic equations ,and having the following for their type:-- † = H₁ + √ H₂ + √/H3 + √ H₁ + √/H5− √/ H6+ √ { H, +√ H8 + ✔H9 + √ H10 + √/H11 −√ H12 }+√ { H13 +√ H14 + 0H15 +√ H16 + 0² /H17 - √ H18 }+√ { H19 + √ H20 + 02H21 +√ H22 + H23 - √ H24};being here an imaginary cube root of unity. He contendsthat the twenty-four quantities, H₁ , ... H24, are all symmetric functions of the five quantities x' , ... x; and that theyare connected among themselves by the sixteen relationsH3H5, H4H6, H7 H13H199 H8 H14 H20, H9 H15 H21,H10 H16H22, H11 H17 =H23, H12 =H18H24, H9 H11 , H10 =H12.

• Nuove Ricerche sulla Risoluzione Generale delle Equazioni Algebriche del

P. GEROLAMO BADANO, Carmelitano scalzo, Professore di Matematica nella R.Universita di Genova. Genova, Tipografia Ponthenier, 1840. See also an " Appendice" to the same work.VOL. II. Z276Sir W. Hamilton examines, in great detail, the composition ofthe two conjugate quantities H4, H6, which are each of thethirtieth dimension relatively to the five original quantitiesx', ... x; and arrives at the conclusion that neither H₁ norHe is a symmetric function of those five quantities x' , . . . x " ,though each is symmetric relatively to four of them. Hefinds also that these two quantities H4 and H are not generally equal to each other, but differ by the sign of an imaginary radical, namely,(0-0²) (w - w² - w³ + w¹) = √ —15,when they are fully developed, in consistency with ProfessorBadano's definitions. Analogous results are obtained forthe two quantities H3, H5; and these general results are verified by applying them to a particular system of numericalvalues of the five quantities x', . . .x". It is shown also thatthe three quantities H7, H13, H19, are neither independent ofthe arrangement of those five quantities x, nor (generally)equal to each other. And thus, although H, is symmetric,and H₂ vanishes, Sir W. H. conceives it to be proved thatProfessor Badano's expressions, for the twenty-four valuesof Lagrange's function ť , give no assistance towards thesolution of the general equation of the fifth degree, andtherefore that the same method could not be expected toresolve equations still more elevated, even if we were not inpossession of an à priori proof that no root of any generalequation above the fourth degree can be expressed as a function ofits coefficients, by any finite combination of radicalsand rational functions.DONATIONS.Three Silver Coins, found at Rockingham, the seat ofViscount Lorton. Presented by C. T. Webber, Esq.Copper Medal, " The glorious attempt of LXIV. to pre-277serve the Constitution." MDCCXLIX. Dublin. Presentedby Miss A. Clibborn.Thepast and present Statistical State ofIreland exhibitedin a Series of Tables. By Cæsar Moreu, Esq. , F. R. S. Presented by James Hardiman, Esq.Proceedings ofthe Royal Society ofEdinburgh, Nos. 19,20, for 1841-2.Transactions of the Royal Society ofEdinburgh. Vol.XV. Part 2 (pp. 265-334).Memoirs of the Literary and Philosophical Society ofManchester. Vol. VI. New Series.Statistical Returns ofthe Dublin Metropolitan Police forthe year 1841. Presented by the Commissioners.Lecture on the Application of Science to Agriculture. ByCharles Daubeny, M. D. Presented by the Author.Proceedings ofthe American Philosophical Society. FromNovember, 1841 , to April, 1842.The New County Book of Tipperary. By Jeffries Kingsley, M. R. I. A. Presented by the Author.Proceedings ofthe Geological Society ofLondon. Vol. III.Part II. 1841-42. Nos. 77 to 83.Fourth Annual Report ofthe Commissioners ofthe CentralLoan Fund Board ofIreland. (Act 1 & 2 Vict. c. 78.) Presented by Mr. Piessé.Transactions ofthe American Philosophical Society heldat Philadelphia.Flora Batava, door Jan Kops. Nos. 123 and 124.Niewe Verhandelingen Van het Bataafsch Genootschap derProefondervindelijke Wijsbegeerte te Rotterdam. AchtsteDeel. Tweede Stuk.Copy of an Inscription found in Babylon by HarfordJones, Esq. Presented by Professor H. H. Wilson.Abhandlungen der Philosophisch- Philolog. Classe derKoniglich Bayerischen Akademie der Wissenschaften, Drit-278ten Bandes Zweite Abtheilung, in der Reihe der denkschriftender XVIII. Band.Philosophical Transactions ofthe Royal Society ofLondon forthe Year 1842. Part I.Abhandlungen der Mathematisch- Physikalischen Classe derKaniglich Bayerischen Akademie der Wissens- chaften, Dritten Bandes Zweite Abtheilung, in der reihe der denkschriftender XVI. Band.Ueber das Magnetische Observatorium der Königl. Sternwarte bei München. Von Dr. J. Lamont. Presented by theAuthor.A Piece of Leather, found in taking up Part of the oldCity ofDublin Wall, adjoining the old Tower in the lowerCastle Yard, by Mr. Johnson, and which is supposed to havelain there since the Year 1202. Presented by W. Farren, Esq,Memoires de l'Institut de France. Academie des SciencesMorales et Politiques. Savans Etrangers, Tome I.Academie des Sciences Morales et Politiques. Tome III.Memoires presentés par divers Savans à l'AcademieRoyaledes Sciences de l'Institut de France. Sciences Mathematiques et Physiques. Tome VII.Memoires de l'Institut de France, Academie Royale desSciences. Tome XVIII.Notices et Extraits des Manuscrits. Tome XIV. 2ndPartie.Archæologia. Vol. XXIX.Journal of the Statistical Society ofLondon. Vol. V.Part 2. July to September, 1842.Archives du Musée d'Histoire Naturelle. Tome I. Liv.1, 2, 3, 4; and Tome II. Liv. 1 and 2.The South Australian Almanack for 1842. By James F.Bennett. Presented by George Davies, Esq. , T. C. D.Proceedings of the Zoological Society of London. PartIX. 1841.PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1842.November 14 .No. 36.SIR WM. R. HAMILTON, LL.D., President, in the Chair.The Secretary read a paper by Sir David Brewster, " onthe Compensations of Polarized Light, with a description ofa Polarimeter for measuring Degrees of Polarization."The author first directed attention to the difference ofopinion between him and most other philosophers, as to theconstitution of partially polarized light; it being generallysupposed that such light is a mixture of common light andperfectly polarized light, whilst he considers that the entirequantity of light undergoes a physical change by approximating more or less to the condition of light completely polarized. Upon this view he had long since explained the lawsof polarization discovered by himself, but he had beenanxious to obtain experimental evidence capable ofdecidingbetween the two ideas, and in this he considers that he isnow successful.By means of experiments, -described in the paper, --theauthor points out that when two portions of light oppositelypolarized compensate each other, the proportions and conditions necessary are not those which could result from mixtures of common light with fully polarized light, and henceinfers that the pencils must be wholly in different physicalconditions. These experiments led him to the invention ofVOL. II . 2 A280an instrument termed the Compensating Rhomb, by means ofwhich he considers decisive evidence of the correctness ofhis views has been obtained .In order to determine if this principle be general, and toascertain the laws of the compensation of polarized light,Sir David Brewster constructed an instrument for measuringthe degrees of polarization. This he calls a Polarimeter. Itconsists of two parts , one of which is intended to produce aray of compensation, having a physical character susceptibleof numerical expression, and the other to produce polarizedbands, or rectilinear isochromatic lines, the extinction ofwhich indicates that the compensation is effected . The details of the construction of the instrument are fully given inthe memoir, and numerous experiments made with it, andconfirmatory of the author's views, are described.In conclusion, Sir D. Brewster points out as the generalresults of his inquiries, as follows:" 1. The first, and most important result of this inquiryis, that it affords a newand independent demonstration of thelaws of the polarization of light by reflexion and refraction,given in my papers of 1830. As this result has been alreadyreferred to, I shall merely mention the following generalproposition." When a ray of common light is incident at any angleupon the polished surface of a transparent body, the wholeofthe reflected pencil suffers a physical change, bringing itmore or less into a state of complete polarization; in virtueof which change, its planes of polarization are more or lessturned into the plane of reflexion, while the whole of the refracted pencil has suffered a similar, but opposite change, invirtue of which, its planes of polarization are turned more orless into a plane perpendicular to the plane of reflexion ."2. Asthe light of the sky and the clouds is more or lesspolarized, the employment of the light which they reflectmay, in delicate experiments, be a serious source of error, if281we are not aware of its properties. By the principle of compensation, however, we may convert this partially polarizedlight into common light, and thus make experiments with asgreat accuracy in the day- time, as we can do with the directlight of a flame. If the light from a particular part of thesky be admitted into a dark room, or otherwise employed , wehave only to compensate its polarization either by reflexionor refraction, and employ, as unpolarized or common light,that part of the light which corresponds with the neutralline." 3. The laws ofthe compensation of polarized light enableus to investigate the polarizing structure of the atmosphere,and to ascertain the nature and extent of the two oppositepolarizing influences, which I have found to exist in it, andby the compensation of which the neutral points are produced. But, as I shall soon submit to the Society the resultsof my observations on this subject, I shall not add any thingfurther at present.4. In every case where reflected or refracted light reachesthe eye of the observer, whether it comes from bodies nearus, or from the primary or secondary planets of our system,the doctrine of compensation enables us to obtain importantinformation respecting the phenomena presented by lightthus polarized. The nature of the reflecting or refractingsurface, the angles of reflexion or refraction , and the natureof the source of illumination, may, in certain cases , be approximately ascertained."5. Whenthe light ofthe sun, or any self-luminous body,is reflected from the surface of standing water, such as thesea or a lake, it is polarized according to laws which are wellknown; but when the partially polarized light of the sky(light polarized in every possible plane, passing through thesun and the observer) is reflected, a variety of curious compensations take place, which, when the position of the observer is fixed, vary with the season of the year, and the hour2 A2282of the day. In some cases, there is a perfect compensation,the partially polarized light of the sky being restored tocommon light by the reflection of the water. In other casesthe light of the sky has its polarization increased by reflexion from the water in the same plane in which it wasitself polarized; and in other cases, the compensation iseffected only in particular planes. At sunset, for example,the light reflected from the sea at a great obliquity in twovertical planes inclined 45° to a vertical plane passing throughthe sun and the observer, is compensated in these two planes,or the plane of its polarization is inclined about 45° to thereflecting surface. The same observations apply to the lightof the two rainbows when reflected from the surface ofwater." 6. When the light of the sky, or of the rainbow, is reflected from surfaces not horizontal, such as the roofs ofhouses, sheets of falling water, or surfaces of smoke and vapour, the compensations are more varied, and a perfectneutralization of the light by the second reflexion is morefrequently obtained."Professor Lloyd mentioned some circ*mstances whichappeared to be opposed to Sir David Brewster's views.Professor Kane commenced the reading of a paper " ontheTannin of Catechu, and the chemical Substances derivedfrom it."The abstract of this paper will be printed when the conclusion has been read.DONATIONS.Transactions of the Zoological Society of London. Vol.III. Part 1. 1842.Reports of the Auditors and Council of the ZoologicalSociety of London, April 29th, 1842, and List ofMembers.283Proceedings ofthe Royal Society. Nos. 52, 53.Supplementary Appendix to the Report of the Poor LawCommissioners of the Medical Charities in Ireland, with Indexes. 1841. Presented by the Commissioners.Apamphlet entitled, " Is Selenium a true Element?" Presented by Septimus Piesse.November 30. (Stated Meeting. )SIR WM. R. HAMILTON, LL.D. , President, in the Chair.John Anster, LL.D., was elected a member ofthe Committee of Polite Literature, in the room of the Rev. Dr.Porter, who had resigned.RESOLVED, On the recommendation of Council, -ThatMr. E. Curry be employed to make a Catalogue of the IrishMSS. in the Library of the Academy, for the sum of £ 100.The Secretary read a letter from George Birch, Esq. ,presenting to the Academy an ancient tombstone, from theAbbey of Monahinchy, with an inscription in the Irish character.RESOLVED, That the thanks of the Academy be givento Mr. Birch for his donation.Rev. Dr. Todd, V.P., gave the following account of theProceedings of the Committee for the purchase of the lateDean of St. Patrick's collection of Irish Antiquities, whichhad been recently presented to the Academy."It has been thought fitting that some record should appear inthe Proceedings of the Academy of the successful efforts that havebeen made under the direction of the Committee of Antiquities, forraising the subscription, which has preserved from dispersion, and284placed in the safe keeping ofthis Society the invaluable Collectionof Irish antiquities belonging to our late lamented Vice- President,the Dean of St. Patrick's." It was well known to all his intimate friends that one of theprincipal motives that influenced him in the formation of his Museum, next to the zeal for the preservation and study of antiquitieswhich characterized him, was a wish to have his collection preserved for public use, under the care of the Royal Irish Academy."As soon as it was ascertained, therefore, that he had died intestate, and consequently without makinganyprovision for carrying thesehis often expressed wishes into effect, many of his personal friends,knowing how deeply he would have deprecated the dispersion of hisCollection, felt anxious, were it only as a testimony of respect to hismemory, that the Irish part at least of the Museum should be obtained for the Academy; and in this they were warmly seconded byall who were aware of the value of the Collection, and who felt thegreat importance of a National Museum of Antiquities to the studyof our ancient history."Accordingly, at the Stated Meeting of the Academy in November, 1840, soon after the lamented death of the Dean, the subject was brought forward, and the Committee of Antiquities wererequested to take immediate steps towards opening a subscriptionfor the purchase of the Irish part of the collection ."The Committee met immediately after, and their first act wasto publish in the principal newspapers of Dublin a short address ,for the purpose of ascertaining the state of public feeling on thesubject. A circular was also prepared, and sent to the principalnobility and gentry of Ireland , to all in short, as far as they couldbe ascertained, who were thought likely to take an interest in thedesign." This was all that could be done at that time. The absence ofMrs. Dawson on the Continent, and the consequent difficulty of ascertaining the wishes of the Dean's family, rendered it impossibleto discover what sum they were likely to accept for that portion ofthe Museum which the Committee were commissioned to purchase,or indeed whether they would consent at all to separate the Irishpart of the Collection from the rest.285" From this unavoidable delay, the zeal of many appeared tocool, and the subscription for a time proceeded but slowly; but atlength, on the 27th of March, 1841 , the Committee took the boldstep ofauthorizing Mr. Petrie and Dr. Aquilla Smith to offer £ 1000for the Collection ." I should have mentioned that this sum was decided upon afteran exact valuation of the whole. The coins were valued by Dr.Aquilla Smith, and the other antiquities, at Mrs. Dawson's specialrequest, byMr. Petrie; and the sum at which these gentlemen fixedthe value of the Collection was £1060. The Committee were ofopinion, therefore, that in offering the sum of £1000, they weredealing fairly with the public fund entrusted to them; while bystriking off about six per cent. from the amount of the valuation,they were only allowing for the necessary expenses which wouldhave attended the sale of the Museum had it been submitted to apublic auction." It was not, however, until the 26th of June following that afinal answer was obtained from the Dean's family to the proposal ofthe Committee. On that day Dr. Smith reported that Mrs. Dawsonhad consented to accept the offered sum, and also that she was willing to allow three months from that date for its collection." New efforts were then made by the Committee: circulars wereagain sent out, and an address to the public was inserted in thenewspapers; a deputation was appointed to wait on His Excellencythe Lord Lieutenant, who contributed £20 to the fund; and inshort every exertion was made to rouse the friends of Ireland to theimportance of the great national object that was in view." The success that has crowned these efforts is mainly owing tothe zealous manner in which the exertions of the Committee wereseconded by some other members of the Academy, who aided themby their advice and counsel, and also by their invaluable and indefatigable labours. Of these it is impossible to avoid naming Mr.Carr and Mr. Hutton, as the individuals to whose cooperation theCommittee were most deeply indebted for the success of their undertaking; and although it is obviously improper to allude to anyindividual of those who were members of the Committee itself, yetfeel sure I shall be pardoned in departing from strict propriety so286far as to say, that to the exertions ofDr. Aquilla Smith and Mr. Petrie,their intimate knowledge of the contents and value of the Collection,and their good offices with the family of the Dean, the Academyand the country are mainly indebted for the possession of the treasures which have been added to our Museum."Still, however, the subscriptions for some time came in soslowly, that it became necessary to solicit more time for collectingthe money than was originally agreed upon; and this request wasacceded to by Mrs. Dawson, with a liberality for which she deservesthe gratitude and the thanks of the Academy." At length on the 9th of April of the present year, the first instalment of £500 was paid to Mrs. Dawson, and the Collection wassoon after removed to the Academy House, under the superintendence of Dr. Aquilla Smith."A guarantee for the payment of the remaining half of thepurchase money having been given to Mrs. Dawson by certain subscribers to the fund, the Antiquities were at first placed under thecustody of those gentlemen; who bound themselves to hand overthe Collection to the Committee as soon as the debt for which theyhad made themselves responsible was discharged." On the 31st May the whole remainder of the purchase moneywas paid to Mrs. Dawson, and the gentlemen who had so liberallycome forward to guarantee its discharge were released from theirobligation. It was found also, that after the payment of all theincidental expenses, a balance remained at that time in favour ofthefund to the amount of £24 17s. 6d. This balance was subsequentlyincreased by some subscriptions that afterwards came in , and thewhole overplus has been applied , under the direction of the Committee, to the purchase of some valuable antiquities, which have beenadded to the Collection." In recording this last stage of the proceedings of the Committee it is necessary to remark, that but for the public spirit of theindividuals who came forward to give their personal security toMrs. Dawson for the payment of the purchase money, all wouldhave been lost, and the Museum would necessarily have been sentfor public sale to London. For although at that time the stipulatedsum had been very nearly promised, yet many of those who had put287down their names had not paid their subscriptions , and the time necessary for collecting the money would have exceeded the limit towhich the Committee had bound themselves to Mrs. Dawson; andthus she would have been left at liberty to take other means fordisposing of the Museum. It is necessary, therefore, that the Academy should know that the gentlemen who came forward to rescuethe Committee from a dilemma which would have made vain alltheir previous exertions, and to whom we are therefore so particularly indebted for the great step that has been made towards theformation of a National Museum, are George Carr, Esq. , Dr. AquillaSmith, Professor Mac Cullagh, Thomas Hutton, Esq. , and RobertCallwell, Esq." The thanks of the Academy are also due to Mr. Clibborn forhis invaluable services throughout the whole of these transactions,and particularly in the last stage of them, when it became necessaryto make exertions to call in the subscriptions that had been promised, and to take steps , after the Museum had come into our possession, for the arrangement and safe keeping of its contents. Tohim also we are indebted for the ingenious plan for a new BoardRoom, which has received the approval of the Council, and is submitted to your consideration this evening: a plan which will enableus to convert the room in which we are now assembled into a Museum, where the treasures of which we are now the guardians, maybe displayed in a manner useful to the public, and their permanentsecurity duly provided for."The special thanks of the Academy are also due to Messrs.Boyle, Low, Pim, and Co. , who kindly permitted subscriptions tobe paid at their house, without any charge whatsoever to the fund;and who also offered to advance to the Committee any sum that mightbe required as a temporary accommodation, during the necessarydelay that attended the collection of the subscriptions. This liberaloffer the Committee were compelled to avail themselves of, bydrawing upon Messrs. Boyle and Co. for a sum of £53 15s. 5d. onthe 1st of June last, a sum which was not entirely repaid for upwards of two months afterwards." It is proper to mention here, that His Excellency Earl DeGrey, in addition to his subscription to the fund for the purchase of288the Dawson Collection, has also been pleased to present to theAcademy a valuable Aision of gold, which was recently found inthe county of Roscommon, and of which His Excellency became thepurchaser, for the express purpose of placing it in our Museum. Mr.H. J. Monck Mason also, in addition to his subscription, presented avery beautiful gold Fibula, of considerable weight and value." It should be distinctly understood, that the subscriptions received have enabled the Committee to pay all the expenses attendantupon these transactions, without any charge whatsoever to the fundsof the Academy."The Academy, as a body, have had nothing whatsoever to dowith the purchase of the Museum, and there will be found amongthe subscribers very many names of gentlemen who are not members of, or in any way connected with our Society. The Museum ,therefore, strictly speaking, is the property of the subscribers, andis by them presented to the Academy, to be kept by us in trust, forthe benefit of the public. The Academy, as a Corporation, havecontributed nothing to the purchase, except so far as their consenting to take the charge of so valuable a gift, and to provide a roomfor its exhibition, may be considered, as it doubtless is , a most important contribution to the great end which the subscribers havehad in view."The accounts of the Committee have been audited by Messrs.Callwell and Hutton; they are in the hands of Mr. Clibborn, andare open, of course, to the inspection of any of the contributors." It may be well now to say a few words on the value and contents of the Museum of which we are thus become the guardians."The Museum contains no less than ninety - seven ornaments ofsolid gold, whose total weight amounts to 98 oz. 14 dwt. It possesses also 252 articles of pure silver , and 1674 bronzes and otherantiques, composed of pottery, amber, glass, and the baser metals." This enumeration does not include the coins and medals, whichare of singular interest and value, and of which a catalogue, in thehandwriting of Dean Dawson, is now on the table." To specify the various articles of value and interest more particularly, so far at least as to give any detailed account of them ,would be too great a trespass on your time, even if I could feel my-289self fully competent to the task; but it is impossible to close thisReport without endeavouring to give you some rough and generalview at least of the treasure which we have now obtained."Among the gold ornaments are twenty- seven fibulæ, one ofthem of considerable size; three perfect torques, and fragments ofsome others; two gorgets; two singular hollow balls or beads ofgold, which were found with eleven others in the County of Roscommon, and which the Dean saved from the crucible of the goldsmith; a most interesting collection of ancient finger rings, andsixteen specimens of the small solid rings of gold, which are believed to have been the current money of the ancient inhabitants ofIreland." The collection of silver finger rings and of ancient seals, is ofgreat interest and value. Among them will be found the matricesof the seals of the O'Neills and other Irish chiefs , with several ecclesiastical seals of various periods ." There is a remarkable collection of the ancient Irish bells ,whose uses and history our friend Mr. Petrie has so ably discussed;some of these are the large bells, which once, perhaps, were suspended in the Round Towers; others are the small altar bells, manyof them exhibiting proofs of great antiquity. One ofthe large bellscontains an Irish inscription, which proves it to be as old as theninth century."The collection of military weapons and other antiques connected with the warfare of our ancestors is of great extent andvalue. It contains a great variety of specimens, in excellent preservation, of the flint arrow heads and spear heads, which are supposedto have been the most ancient weapons in use in Ireland; a largenumber ofthe peculiar weapon, in stone and bronze, called celts , ofall the sizes and forms in which they are found; and a magnificentcollection of swords and spear heads, from many of the remarkablefields of battle recorded in the history of Ireland." It would be drawing too much on your patience to entermore particularly into a description of particular objects of interestin this Collection; at some future time it might perhaps be an entertaining, as well as an instructive task (if some of our antiquarieswould undertake it) , to exhibit to the Academy, from time to time,290the more remarkable and important articles of our Museum, withremarks on their history, and use. But a more fitting occasion forthis will perhaps be found, when THE DAWSON COLLECTION is properly arranged and displayed, as I hope it soon will be, in a roomfitted for its reception." I must say a few words of the coins and medals before I canconclude this Report.66 They may be divided into three classes:" 1. The Danish Irish coins ofthe ninth and tenth centuries."This series comprehends the coins of Domnald and some ofthe sovereigns unknown; a coin of Ivar, A. D. 872, and a largecollection of the Dublin coins of Sitric, A. D. 980 and 989. Alsothe Dublin coins of Æthelred, and some of great singularity andrarity, which bear the impress of the Dublin mint, and which theDean, on grounds however admitted by himself to be doubtful, wasat one time disposed to refer to the reign of Æthelstan."2. The coins struck in and for Ireland by British sovereigns."Among these are a magnificent series of the coins of John,minted in Dublin, Waterford, and Limerick, between the years 1177and 1199; and a singularly perfect series ofthe coins struck in Ireland from the reign of John to that of George IV. , containing manyvarieties of great rarity and value." 3. A series ofmedals struck in Ireland."The most complete that has ever been collected. This seriesis particularly interesting to the Academy, because the late Dean, avery short time before his decease, contributed to our Transactionsa valuable paper on the subject of Irish Medals, in which the mostremarkable of these very medals are noticed and described." On the whole, I would congratulate the Academy, and not theAcademy only, but the country, on the possession ofthis importantand invaluable Collection. As one of those who enjoyed the privilege of an intimate acquaintance with its late lamented owner, Icannot help expressing the gratification which I feel in the reflectionthat this, the national part of his Museum, is saved from dispersion,secured to Ireland, and presented to the Academy, for which hehad destined it. I feel a melancholy satisfaction, in which his291friends will sympathize with me, in having (in however humble adegree) taken a part in bringing about the fulfilment of the wishI have often heard him utter, that his Museum might be here; andin the assurance that here his name will live as a benefactor to hiscountry, and an example to our gentry, by whom the study andpreservation of our antiquities have been (I must say) disgracefullyneglected."But on public grounds, most of all, I would congratulate theAcademy on having now laid the foundation of a National Museum,which will doubtless be the means of preserving many articles ofvalue and interest from destruction-of bringing together the manycurious relics of the past, which are now in the hands of privatefamilies or individuals , and perhaps also of awakening the attentionof the Government of the country, to the importance (too long forgotten or overlooked) of forming, upon a liberal and extensive basis,a really National Museum ofthe Antiquities of Ireland. "RESOLVED, That this Report be entered on the Minutes,and published in the Proceedings.RESOLVED, That the special thanks of the Academy begiven to those subscribers to the Dawson Fund who are notmembers ofthe Academy. *RESOLVED, -On the recommendation of Council, ―Thatthe plan of the new Board Room proposed by Mr. Murrayand Mr. Owen, be approved of by the Academy.December 12.SIR WM. R. HAMILTON, LL.D. , President, in the Chair.Rev. Dr.Todd, V. P. on the part ofthe Knight of Glin, presented to the Academy a gold coin, with an Arabic inscription, found in the wall of a house in the townland ofKilleny,near Glin.

• See List of Subscribers in Appendix No. I.

292The thanks ofthe Academy were presented to the Knightof Glin for his donation.Dr. Apjohn read a paper by Dr. Andrews, " on the Heatdeveloped during the Formation of the Metallic Compoundsof Chlorine, Bromine, and Iodine."The author confines his attention in the present paperto the combinations of zinc and iron, which metals, he shows,will not combine at ordinary temperatures with chlorine,bromine, or iodine, unless water is also present. The reactions which take place when an excess of iron in a state offine subdivision is agitated with any of the three elementsjust mentioned, are rather complicated , —a sesqui-compound(Fe, Cl3, Fe, Br3, Fe, I3) being first formed, which afterwardscombines with an additional atom of iron , and becomes converted into a proto- compound (Fe, Cl3, &c. ) The heat developed during this process consequently arises from threedistinct causes: -first, the union of Fe, with Cl¸; secondly,the solution ofthe compound so formed in water; and thirdly,its conversion into Fe, Cl, by its combination with Fe. Theheat arising from the two latter causes being determined byseparate experiments, and taken from that obtained duringthe original reaction, the remainder will be evidently the heatdue to the union of Fe, and Cl3; and by a similar method,the heat developed during the union of Fe, with Br¸, and ofFe2 with I3 , may also be determined. Referred to the number of degrees of Fahrenheit's scale, through which one grainofwater would be heated by the combination of one grain ofiron in each case, the heat evolved during the formation ofFe2 + Cl, is 3246°; during that of Fe2 + Br3, 2302°; and ofFe2 + I3, 834°. The reaction which occurs when zinc istreated in a similar manner is much simpler, and the heatdeveloped, referred to the zinc as unit, is 2766° for Zn + Cl;2284° for Zn + Br; and 1474° for Zn + I.The author also proves, by direct experiments, that when293solutions of the sesqui- chloride, sesqui-bromide, or sesquiiodide of iron are converted into the corresponding protocompounds of iron , by combining with iron , the heat in allcases is the same for the same quantity of iron dissolved .The method by which these numerical results were obtained, and the apparatus employed , are minutely describedin the original communication.Dr. Kane inquired how far he considered the final resultsobtained by Dr. Andrews to affect the ideas of thermo- chemical combination, founded on the experiments of Despretzand Dulong?Dr. Apjohn stated that the results of Dr. Andrews werequite opposed to their experiments, as he found the quantities of heat not to bear any relation to the atomic weight ofthe combining bodies.The Secretary read a paper by the Rev. Edward Hincks"on the Chronology of the Eighteenth Dynasty of Manetho."The object of this paper is to determine the period atwhich the eighteenth dynasty of Manetho flourished , by therecorded dates , in months of the wandering year, of facts,which must, from their nature, have occurred at known seasons of the solar year. Three such dates are brought forward: two of them relating to the time ofthe commencementof campaigns; and the third, to that of the inundation: andthey all concur in depressing the epochs of the eighteenthdynasty about 350 years below those, which the Champollions and Rosellini have adopted. An approximation tothe dates of the accession of many monarchs ofthe dynasty isattempted. For example, the year B. C. 1278 is fixed uponas very nearly, if not exactly, that of the accession of Amenothph III.Mr. Mallet having become acquainted with the recentimprovements effected by Mr. Bessemer in the art of glass-291making, for optical and other purposes, gave a short accountof them to the Academy.The improvements consist chiefly in—1st. The use of platina bottoms to earthen melting pots,and heating these in improved furnaces from below, so as toproduce circulation in the fluid glass.2nd. In preserving the liquid glass from all contamination from without by " tears," &c. and from the dome ofthe furnace, as well as from deoxidation of the lead salts bycontact of carbon.3rd. In an improved mode of cutting off, by a platinablade, the upper portion of the fluid glass, without disturbance ofthe remainder; thus separating the whole of theimpure dross at top, which was heretofore stirred down intothe mass just previous to casting.4th. In a beautiful and effective mode of removing theair bubbles, or " seeds," as they are called , from the liquidglass, by placing the ignited glass pot of liquid metal withinan exhausted receiver, so contrived that it can be rapidlyplaced within, and withdrawn from the vacuum vessel.Mr. Mallet was not aware that as yet any specimen ofglass prepared by these improved processes had been wroughtfor any optical purpose, the inventor's efforts having been asyet principally directed to the manufacture of plate glass;but he considered that the practical nature of these improvements, and their capability of being applied upon a largescale, gave good hope of their extension to the making ofoptical glasses also .Rev. Dr. Robinson made some remarks with reference toMr. Faraday's experiments on the manufacture of glass foroptical purposes, and described the processes adopted atMunich in selecting the portions ofglass of which lenses areformed.PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1843. No. 37.January 9.SIR WM. R. HAMILTON, LL.D. , President, in the Chair.Stewart Blacker, Esq. , Thomas Cather, Esq. , William V.Drury, M. D. , William Gore, M. D. , Thomas Hodder, Esq.R. N., Rev. John Homan, Henry Hutton, Esq. , Robert LeslieOgilby, Esq. , the Hon. Frederick Ponsonby, and George Salmon, Esq. , F.T.C.D., were elected members ofthe Academy.Rev. H. Lloyd, V. P. , read a paper " on the Determination of the Intensity of the Earth's Magnetic Force in absolute Measure. "Themeans ofdetermining the intensity ofthe earth's magnetic force in absolute measure consist, it is well known, inobserving the time of vibration of a freely- suspended horizontal magnet, under the influence of the earth alone, andthen employing the same magnet to act upon another, whichis also freely-suspended, and noting the effects of its actioncombined with that of the earth. From the former of theseobservations we deduce the product of the horizontal component ofthe earth's magnetic force into the moment of freemagnetism ofthe first magnet,-from the latter, the ratio ofthe same quantities; and, the product and the ratio beingthus known, the two factors are absolutely determined. Theformer part of this process involving no difficulty which mayVOL. II. 2 B296not be overcome by due care in observing, we shall confineour attention, in the present communication, to the latter.Two methods have been proposed for this second observation, one by Poisson, and the other by Gauss. The method of Poisson consisted in observing the time of vibrationof the second magnet, under the combined action of the firstand of the earth, the acting magnet having its axis in themagnetic meridian passing through the centre of the suspended magnet. In the method of Gauss, which is nowuniversally adopted, we observe the position ofequilibriumof the second magnet, resulting from the action of the sameforces. The acting magnet being placed transversely withrespect to the suspended one, the latter is deflected from themeridian, and the amount of this deflection serves to determine the ratio of the deflecting force to the earth's force.The position chosen by Gauss for the deflecting magnet isthat in which its axis is in the right line passing through thecentre ofthe suspended magnet, and perpendicular to themagnetic meridian, in which case the tangent of the angle ofdeflection is equal to the ratio of the two forces. From thisratio it remains to deduce that of the magnetic moment ofthe deflecting bar to the earth's force.The difficulty of this process arises from the form oftheexpression of the force of the deflecting bar. This forcebeing expressed by a series descending according to thenegative odd powers of the distance, with unknown coefficients, it is evident that observation must furnish asmany equations of condition, corresponding to differentdistances, as there are terms of sensible magnitude in theseries; and from these equations the unknown quantities areto be deduced by elimination . Now, the greater the number ofunknown quantities thus eliminated , the greater willbe the influence of the errors of observation on the final result; and if, on the other hand, the distance between themagnets be taken so great, that all the terms of the series297after the first may be insensible, the angle of deflection becomes very small, and the errors in its observed value bear alarge proportion to the whole.It fortunately happens, that at moderate distances (distances not less than four times the length of the magnets) allthe terms beyond the second may be neglected. The expression for the tangent of the angle of deflection is thusreduced to two terms, one of which contains the inverse cubeof the distance, and the other the inverse fifth power; thatis, if u denote the angle of deflection, and D the distance,tanu = +Qin which and q' are unknown coefficients, the former ofwhich is double of the ratio sought. Accordingly, the method recommended by Gauss consists in observing the anglesof deflection, u and u', at two different distances, D and D',and inferring the coefficient Q by elimination between thetwo resulting equations of condition.It is evident, however, that if the coefficient of the inverse fifth power of the distance be evanescent,-or, moregenerally, if the ratio of the two coefficients be known àpriori, -the quantity sought may be obtained , without elimination, from the results of observation at one distance only.For if o' ha, h being a known quantity, the preceding expression becomestan u =음(1+ )

and accordingly the value of a is obtained , from the result ofobservation at a single distance, by the formulaQD3tanu1 +hD−2And, not only is the labour of observation thus diminished,but (which is of more importance) the accuracy of the re2 B 2298sult is increased. In order to show this, the author entered into an examination of the amount of the probableerror in the two methods, from which it appeared that theprobable error of Q, arising from an error in the observeddeflection, will be less than in the usual method in the ratioof 1 to 5.563 , even when the latter is employed in the manner most conducive to accuracy. In fact, the ratio of theprobable error to the entire quantity is found to be expressed, in the two cases, by the formulæAu AQ q= "=И10 +1 Δq²-1Иwhere q denotes the ratio of the two distances; and the leastvalue of the factor Vq + 1 is 5.563, and corresponds to theratio q = 1.32.102q² – 1In order to know the ratio h, it is necessary to determine the moment of the force exerted by the deflectingmagnet upon the suspended magnet, extending the approximation to the terms involving the fifth power of the distance.The axis of the deflecting magnet being supposed to lie inthe right line joining the centres of the two magnets, andthe axis of the suspended magnet forming the angle ↓ withthat line, this moment is found to be2MM'ᎠᏰ.M3sinų { 1+ (23M + 3 ( 5 cos²4 −1 ) M³);in which м and м' , м, and м'39,, denote certain integrals depending on the distribution of free magnetism, in the deflecting and suspended magnets, whose values areMSmrdr, M3 = S+mr³dr,-1m being the quantity of free magnetism in any transversesection ofthe magnet, r its distance from the centre, andhalf the length of the bar. The form ofthis result exhibits299the advantage ofthe method of deflection recently proposedby Professor Lamont, in which 90°, or the deflecting barperpendicular to the suspended bar.In the ordinary method, ↓ = 90° - u; and, the momentofthe force exerted bythe earth being XM' sinu, where x denotes the horizontal component of the earth's magnetic force,the equation of equilibrium istanu =2M 1X D3 + (2 M3-3M3 +15 sin' uMM3M'1The angle of deflection, u, being small, the term involvingthe square of its sine may be neglected, in comparison withthe others; and the equation assumes the form already adverted to, namely,tanu =h11/13 (1+1/125in which we have made, for abridgment,2M M3 M'3 = Q, 2 3 = h.X M MIn order to apply this result, we must know, at least approximately, the law of magnetic distribution , or the functionof r by which m is represented. Almost the only knowledgewhich we possess on this subject is that derived from theresearches of Coulomb. From these researches M. Biot hasinferred, that the quantity of free magnetism, in each pointof a bar magnetized by the method of double touch, may berepresented by the formulam = s (u²μ--r - μ²+");μμ being a quantity independent of the length of the magnet,and A a function of µ and l. M. Biot has further shown, thatwhen the length of the magnet is small, the relation betweenm and r is approximately expressed by the simple formularm = m²;;300the curve of intensities becoming, in that case, very nearly aright line passing through the centre of the magnet.Employing then this approximate formula, we haveM = m'l²; M3 = } m'l¹.M3 The ratio of these quantities is 3 = §², a value indepen- Mdent of m'; and substituting in the expression of h abovegiven, and designating the half lengths ofthe deflecting andof the suspended magnets by l and l, respectively,h = } (21² — 312);an expression whose value may be exactly known, independently of experiment. This value vanishes, when l² = § 12, or7 = 1.224 l';and in this case, therefore, the quantity sought is given bythe simple formulaQ = D³ tan u.The author concluded his paper with an account of aseries of deflection experiments , instituted for the purposeof confirming these results. The magnets employed werecylindrical, their lengths being 3 inches and 33 inches, andtheir diameter 3-10ths of an inch. The observations weremade with every precaution necessary to insure exactness,and at times when the fluctuations in the direction and intensity ofthe magnetic force were very small; and their results verify the conclusions above obtained, as applied to thecase of small magnets.Dr. Apjohn next read the following letter, which he hadreceived from Captain Boileau, superintendent of the Magnetic Observatory at Simla, in India." MY DEAR SIR," Simla, March, 7 , 1842."I have the pleasure of forwarding to you, through theGovernment of India, a complete set of hygrometric tables,301computed by my assistant, from your last formula, to whichI have added a vapour table, computed by Biot's formula,from Dalton's experiments, which is the same that Pouillethas used in the last edition of his Traité de Physique, thatI have seen. Every one of the numerical values in thistable (No. 3) has been computed directly from the formulato seven places of decimals, five of which only have beenretained. In like manner, in part 1 , each of the numericalvalues for depressions to one-tenth of a degree Fahrenheit,has been directly computed for twenty and for thirtyinches ofpressure, and the intermediate values obtained by addition.All the work has been checked by differences, and examinedby three separate computors.66 Accompanying, are also sent the separate observationsof the wet and dry bulb thermometers, of Daniell's hygrometer, and of the standard barometer, with notice of theweather for the twelve term days of 1841 , which have beentaken specially for your own use, and which you will, I think,find to confirm the views you had already taken upon thesubject. There is one point which strikes at first sight, viz.,that with very few exceptions , the dew-point, by the hygrometer, is too high. It is a difficult instrument to use. Itrequires the observer to approach near to it; and, even withthe utmost care, it is difficult to prevent an effect sensible attimes to a prejudicial extent, upon the hygrometric conditionof the surrounding air. None of these difficulties occur withthe wet and dry thermometers, which have one still greateradvantage, viz ., the ease with which the wet ball can, underalmost any circ*mstances, be moistened.66 During several months, we observed the hygrometerhourly on term days, but finding that this gave much trouble,and was likely to prejudice the readings of the magnetometer, I discontinued the practice, and had since but one observation every two hours.During this year, I regret to say, that a failure in ether302has prevented any readings on either January or Februaryterm days, and of a supply of five pints just had up underorder of Government, nearly three and a-half pints haveevaporated on the journey. So much for an Indian climate,and bottles not hermetically sealed . You will oblige me byacknowledging the receipt of this packet, either through ourmutual friend Professor Lloyd, or through the Military Secretary at the East India House, Philip Melvill, Esq.; andifyou wish me to alter the system adopted, you have only tosay so, and I will endeavour to meet your views. I hope tocontinue the regular series from this month again withoutinterruption."Believe me to remain, with kind regards," My dear Sir,"Yours very truly," S. BOILEAU." P. S.-You can make any use of the accompanying document you may please to do. "Dr.Apjohnthen observed , that availing himself ofthe permission given him by Captain Boileau , he would make a fewremarks upon the hygrometric observations made on the magnetic term days for 1841. These observations were highly interesting to meteorologists, having been made by an officer ofgreat scientific attainments, of extensive experience as anobserver, and with the aid of first-rate instruments: but his(Dr. Apjohn's) reason for considering them particularly important was, that they furnished the means of estimating therelative merits of the two hygrometric processes at presentin use, viz. , that according to which, the dewpoint is directlygot by the aid of Mr. Daniell's instrument, and that whichconducts to the same conclusion through the application ofthe well known formula,f" = f – , 01147 ( t− t ) ×-p-f'30

• In this expression is the force of vapour at dew-point, f' the force of

303to the temperatures indicated by a wet and dry thermometer.The observations for the April term day, were thoseto which it was his intention to advert, as they exhibitedhigher values for t-t', than those made in any other month.Now upon looking through these which amount to 24, thefirst fact which at once presents itself is, that in every instance but two, the observed dew- points are higher than obtained by the formula, and in some instances, by as many asnine degrees Fahrenheit. One or other series, therefore,must be erroneous. That the observed dew- points are inaccurate, Dr. Apjohn inferred, on the ground of their being inconsistent with each other; for he held it as quite certain, whether the hygrometric expression be correct or not, that whenin the case of any two distinct observations, t and t' have thesame values, that upon both such occasions the air includesthe same amount of moisture, or has the same dew-point.Tried by such a criterion , the results obtained with Daniell'sinstrument are defective, as is well illustrated by the following extract from the April observations .t ť' t" ob. t"calc.10 $ 70 51 43.51171.2 51 3434.733.3} 9.5 1.4763 47 311762 47 36.631.6232.8}6.6 1.22$ 55 42.5 30.524 55 42.2 33 2828.972.5 0.9From what has been just said, it is obvious, that observations 10 and 11 should give nearly the same dew- point. Thisis true of the dew points got by the formula, but not at allof the direct determinations by the hygrometer, as thosevapour at t' , the temperature by the wet thermometer, and t the temperature ofthe air.304differ 90.5. In 7 and 17, the dew- points are necessarily nearlythe same. The results got by the formula differ by only1º.2, while the instrumental ones differ by 6°.6. Again,2 and 24 should give g.p. the same dew-point. This is true ofthe formula, but not at all of the hygrometer, as the temperatures it yields differ by 2° .5. The preceding instances,the number of which might be greatly augmented, were, Dr.Apjohn conceived, quite sufficient to show, that even in thehands ofCaptain Boileau, Daniell's instrument has not givencorrect conclusions; and that, therefore, generally it cannotbe relied upon for determining, accurately, the hygrometricrelations of the atmosphere.With respect to the column of results obtained by Captain Boileau, from the wet bulb process, Dr. Apjohn couldnot entertain the slightest doubt of their exactness, havingfound that his formula stood the severest experimental teststo which he could subject it. These experiments, however,(see Transactions Royal Irish Academy, vol. vi . ) were, headmitted, all made under pressures, at or about 30: andhence it always appeared to him desirable, that they shouldbe repeated at such diminished pressures, as are met withat elevated points on the earth's surface. In this point ofview, the Simla observations appeared at first highly important, the pressure there being but little over 23; but as noreliance can be placed on the dew-points directly got, theycannot be used to test the accuracy of the hygrometric expression.Dr. Apjohn then expressed a hope, that no one whoheard him would misunderstand him to assert, that the dewpoint could not be accurately got by Daniell's instrument.He knew it could, and he had explained elsewhere how touse it, so as to arrive at a correct result. What he had,however, asserted before, and would again repeat, was, first,that it was an instrument very difficult to observe accuratelywith; and second, that when Mr. Daniell's rule is attended305to, namely, to take as dew-point, the mean ofthe temperaturesindicated by the inner thermometer at the instant ofthe deposition of the dew, and at that of its disappearance, theresult is necessarily higher than the truth.Dr. Apjohn concluded, by drawing attention to the greatvalue of the other tables alluded to in Captain Boileau'sletter, the construction of which, must have been a work ofimmense labour. Two of these greatly simplify the calculations necessary in applying the hygrometric formula, as thearithmetical operations are thereby reduced to mere additionand subtraction.The third table gives the force of vapour to tenths of adegree Fahrenheit, throughout the entire range includedbetween -3° and + 146, Fahrenheit, calculated de novo bythe well known method of Biot, from the experiments ofDalton and Ure. It does not materially differ, except in itsgreater extent and minuteness, from the table ofthe tension ofaqueous vapour which Dr. Apjohn has hitherto used, andthe superior accuracy of which, as compared with the tableof Kaemtz, and that not long since published by the Meteorological Committee of the Royal Society, has been renderedhighly probable by Professor Lloyd.Professor Mac Cullagh read a paper on the Catalogue ofEgyptian Kings, which is usually known by the name oftheLaterculum of Eratosthenes.This Catalogue, which the distinguished mathematicianand philosopher whose name it bears drew up by command of Ptolemy Euergetes, contains a long series of kingswho reigned at Thebes in Upper Egypt; and has been preserved to us in the Chronographia of Georgius Syncellus, aGreek monk of the eighth century. It is a document whichhas been made much use of by chronologers; by some ofwhom, as by Sir John Marsham for example, who calls it"venerandissimum antiquitatis monumentum," it has beenreckoned of the very highest authority; but it is extremely306corrupt in the latter part, owing to the carelessness withwhich it was transcribed either by Syncellus himself or hisimmediate copyists. The writers on Egyptian antiquitieshave in consequence been much perplexed in settling thechronology of the reigns in which the errors exist, and theattempts that have been made to remove the confusion haveonly served to increase it. It was the object of the authorto restore the document to its original state, and he showedthat this might be effected, with complete certainty, by a proper attention to the manuscripts of Syncellus. Ofthese onlytwo are known; one has been used by Father Goar, the firsteditor of the Chronographia (Paris, 1652); the other, whichis a much better one, has been collated by Dindorf, the second and latest editor. Dindorf's edition was published atBonn, in the year 1829, as part of the Corpus Scriptorum Historia Byzantine, and on its first appearance Mr.Mac Cullagh had satisfied himself as to the original readingsof the Catalogue, and had seen howto account for the errorswhich, probably from Syncellus's own negligence, had creptinto it; but he did not publish his conclusions at the time,thinking that similar considerations could not fail to occur tosome of the numerous writers who were then giving theirespecial attention to such subjects. This, however, has notbeen the case. Chronologers have continued to follow in thefootsteps of Goar, a man of little learning, and of no criticalsagacity, who corrected the Catalogue most injudiciously,and whose corrections, strange to say, are left without anyremark by Dindorf. Thus Mr. Cory, in his Ancient Fragments, a work much referred to, merely transcribes Goar'slist; and Mr. Cullimore, in attempting to reconcile ancientauthors with each other and with the monuments, has adoptedan hypothesis respecting the identity oftwo sovereigns, whichis not tenable when the true version of the Catalogue isknown. Even in Goar's edition, however, there was quiteenough to have led a person of ordinary judgment to the307correct readings of the Catalogue, though perhaps they couldnot be said to be absolutely certain without the additionallight obtained from that of Dindorf.The Catalogue in question professes to contain the namesof thirty-eight sovereigns, with the years of their reigns; thewhole succession occupying, as is stated, a period of 1076years; but it is only in the last eight reigns that the errorsand inconsistencies occur. The thirty- second prince is calledStamenemes B, that is, Stamenemes the Second, thoughthere is, at present, no other of that name in the list; andthe beginning of his reign-as appears from the years oftheworld, which Syncellus has annexed according to the Constantinopolitan reckoning-follows the termination of thepreceding one by an interval of twenty- six years. Jackson ,in his Chronological Antiquities, is positive that this prince iscalled the Second by a mistake, and adds the years that arewanting to the reign of his predecessor, as Goar had previously done. In the first part of this view all authors, without exception, are agreed, though they do not explain how amistake, so very odd, could have originated; but the learnedMarsham, —who, having adopted the short chronology of theHebrew Bible, is so hard pressed to find room for the Egyptian dynasties that he is obliged to begin the reign ofMenes the very year after the Deluge,—is glad to omit thetwenty-six years altogether, thus reducing the sum of all thereigns to 1050 years, contrary to what is expressly stated bySyncellus. The natural inference fromthe state of the MSS.is, however, simply this: that the thirty- second king wasStamenemes I., that he reigned twenty-six years, and wassucceeded by Stamenemes II. We may easily conceive thatthe eye of the transcriber, deceived by the identity of names,passed over the first, and rested on the second, thus occasioning the error. Indeed there can now be no doubt that thiswas the fact; because, in the MS. marked (B) by Dindorf,the next king is numbered as the thirty-fourth, the next but308one as the thirty-fifth, and so on; which shows that a namehad dropped out, and this name could be no other than thatof Stamenemes I., who must have filled the vacant interval,and must consequently have reigned the number ofyears thathas been assigned to him.As neither Goar nor any other writer perceived this omission, the successor of Stamenemes II. has always been reckoned as the thirty-third in the list, and the next following asthe thirty-fourth, &c . But as one error begets another, theomission was compensated by the insertion of an anonymousking, who is placed thirty-sixth in the list, with a reign offourteen years; the insertion being necessary to completethe number (thirty-eight) which the Catalogue ought to contain. And, by a further error, these fourteen years are takenout of the reign of the thirty- seventh sovereign, who oughtto have nineteen years instead of the five that have beenhitherto assigned to him. This last error was occasioned byan ignorant correction of a mistake which is found in boththe MSS. , and which therefore probably arose from the carelessness of Syncellus himself. The thirty-seventh king andhis predecessor are stated to have begun to reign in thesame year of the world , and to have reigned the same number ofyears (five) . Now from what goes before it is plainthat both these numbers belong to the thirty- sixth king; andfrom the year of the world in which the thirty- eighth andlast king began to reign, it is clear that the thirty-seventhreigned nineteen years. The mistake in the MSS. is onewhich might easily be made by a thoughtless writer; forthe Catalogue is given in detached portions—a few reigns ata time-separated by a great quantity of other matter, andthe name of the thirty-sixth king ends one of these portions,while that ofthe thirty- seventh begins another; so that, nothaving both before his eyes at the same moment, a person socareless as Syncellus might, without being conscious of it,attach the same reign and date to the two names, by tran-309scribing twice over the same line of numbers in the Cataloguewhich he was copying; the whole of which Catalogue, in alllikelihood , he had previously drawn up in a tabular form, withthe years of the world annexed according to his own chronology, that it might be ready, as any portion of it was wanted,for immediate transference to his pages. Such seems to be thenatural account of the matter; but, as usual, it does not occurto Goar, who takes the opportunity, which the confusionaffords him, of foisting in his supplementary king betweenthe two last mentioned, giving each of these five years, as inthe MS. , by which means he obtains room for him, while onthe other hand he alters the year of the world attached tothe thirty-seventh king , so as to make it suit his hypothesis.The following is a view of the last eight reigns, as theyappear to have stood in the original document, comparedwith the erroneous list of Goar. The years of the worldare omitted, as being of no importance, except so far as theyare useful in the preceding argument.I. GOAR'S LIST. II. CORRECTED LIST.Years. Years.31. Peteathyres reigned 4232. Stamenemes 2331. Peteathyres reigned 1632. Stamenemes I. 26 "9 وو33. Sistosichermes 55 33. Stamenemes II. 23 29 9934. Maris 43 34. Sistosichermes 55 99 9935. Siphoas ,, 5 35. Maris 99 4336. Anonymous 99 14 36. Siphoas 5 ""37. Phruoro 5 37. Phruoro 19 ""9963 38. Amuthartaus 99 63 38. Amuthartaus 99The interval of time which has been shown to belong tothe first Stamenemes, and which was added by Goar to thereign of Peteathyres, is differently disposed of by Mr. Cullimore, in a chronological table which he has given in thesecond volume of the Transactions ofthe Royal Society ofLiterature. His object being to compare the lists of Eratos-310thenes, Manetho, &c. , with the supposed hieroglyphicalseries , he makes Saophis, the fifteenth in Eratosthenes' Catalogue, the same as a king whose name is read PhrathekOsirtesen; but the forty- third year of the latter is mentionedon the monuments, whereas Saophis has only twenty-nineyears in the Catalogue. To escape from this difficulty,therefore, Mr. Cullimore adds the unappropriated interval tothe reign of Saophis, thus giving him fifty-five years insteadof twenty-nine. But it now appears that such a suppositionis altogether inadmissible, and consequently the two personages in question cannot be identified; a circ*mstancewhich proves that there is some fault in Mr. Cullimore'sassumptions, and that his other conclusions, at least in thispart of his table, cannot be relied on.The corrections here given do not interfere with the inferences drawn by Professor Mac Cullagh from the Catalogue of Eratosthenes in a former paper on Egyptian Chronology (Proceedings of the Royal Irish Academy, vol. i. p. 66) ,because the portion of the Catalogue with which he was thereconcerned terminates with the reign of Queen Nitocris, thetwenty-second in the list. The corrections, indeed, thoughnot hitherto published , were made long before the date(April, 1837) of that paper, but not before he had adoptedthe hypothesis therein proposed , as an answer to the oldand ever-recurring question-Who were the Egyptian sovereigns that were contemporary with Moses? For it was inconsequence of this hypothesis, which had suggested itselfto him at a very early period, that he was led to examine theCatalogue minutely, in order to discover whether his chronology was affected by its errors.Having been led to refer to his hypothesis, Mr. Mac Cullagh took occasion to observe that, in the interval which hadelapsed since it was published, he had not met with anyfacts that were opposed to it: on the contrary, the morehe considered it, the more he was inclined to believe in its311reality; though it was entirely different from every other thathad been proposed, either by modern chronologers or by theearly Fathers of the Church, in their manifold attempts toconnect the narrative of Moses with the remaining fragmentsof Egyptian history. The hypothesis, indeed, is the onlyone which, while it gives a probable date for the Exodus,also satisfies what Mr. Mac Cullagh conceives to be the necessary conditions of the question; namely, a very long reign-ofat least eighty years-during which the Israelites werepersecuted, succeeded by a very short one-apparently notmore than a year during which their deliverance waswrought; and it is interesting in itself, on account of theremarkable connexion which it establishes between sacredand profane history, and the highly dramatic character oftheevents which are thus, for the first time, brought into view.Mr. Petrie exhibited a drawing, on a large scale, of anancient inscribed grave stone at Clonmacnoise, which he considered as interesting, not only as a characteristic exampleof the usual sepulchral memorials ofthe Irish, from the sixthto the twelfth century, --and of which Mr. Petrie has collected upwards of three hundred examples, but also as amonumental record of a person very eminently distinguishedfor his learning in Ireland in the ninth century.This stone, which is about four feet in length, and threein breadth, though never squared or dressed, exhibits a veryrichly carved cross, and the following simple inscription:C.SVIGINE. M maizae HVMⱭi•SUIBHNE, THE SON OF MAILÆHUMAI.Ofthe celebrity, in his day, of the person who is thusrecorded, the Irish Annals, as well as those of England andWales, bear abundant evidence.In the Chronicon Scotorum his death is thus recordedVOL. II. 2 c312at the yearnois, deg.890: Suibne mic Maoilhuma, ancorita Cluana macThus also in the Annals of Ulster at the same year, ormore correctly 891: Suibne mac maele humai, Ancorita, etscriba optimus Cluana mac nois, dormiuit.To the latter entry, Doctor O'Conor, in his Rerum Hib.Scriptores, appends the following note:6" Suibneum hunc Annales Anglosaxonici Suifnethum appellant.-Vide Chron. Saxon. ad ann. 891 , Tres Scoti deHibernia, ad Ælfredum regem Anglorum venerunt, Dubslanus, Maccebethus, et Mælinmunus, Swifneth etiam , præcipuusdoctor qui inter Scotos fuit, decessit, '-concordat FabiusÆthelwerdus, qui tertium appellat—' Magilmumenum artibusfrondentem, littera doctum, magistrum insignem Scotorum.'-Chron. l. 4, c. 3. Eadem habet Wigorniensis ad ann. 892, etMathæus Florilegus, ad ann. 891. Huc etiam referenda suntquæ habet Caradocus ad ann. 889, Suibnion Cubin Doctorum Scotiæ maximus obiit. ' "6Sir James Ware, in his Irish Writers, tells us, that " hisworks, and the titles of them, are lost. "Mr. Griffith presented , on the part of the Shannon Commissioners, a collection of antiquities discovered in the Shannon, and gave the following account of the locality and othercirc*mstances attending the discovery.The object ofmy present communication is to notice thediscovery of certain ancient arms in an excavation made inthe bed of the river Shannon at the ford of Keelogue, fourmiles below Banagher, in the King's County.The ford at Keelogue, and that of Meelick, which is immediately below it, is the first point of the river Shannonwhich was anciently passable except by boat, above the fallsat Killaloe, a distance of thirty British, or nearly twenty-fiveIrish miles; and consequently, previously to the constructionof roads, and the erection of bridges at Portumna and Ba-313nagher, this ford must have been the main pass between thenorthern portion of the county of Clare, and the southernportion ofthe county of Galway, with the counties of Tipperary, King's County, &c . &c. Hence it is probable that ata former period the ford at Keelogue, which is the shallowest on the river, and much better than that of Banagher,was the principal point of communication between the districts above enumerated; and even in modern times, in common with the passes by the bridges of Banagher, ShannonBridge, and Athlone, the defence of the pass at Keelogueand Meelick was considered ofsufficient importance to inducethe British Government to erect two towers, mounted withcannon, on the King's County side, to guard the passes ofthe river from the west.The fall of the river Shannon at Keelogue and Meelickamounts to ten feet; and to render the river navigable, thecommissioners appointed to direct the improvements of thenavigation of the Shannon, have agreed with contractors forthe construction of a lock of very large dimensions , a stoneweir to regulate the discharge and the level of the water,and for the deepening of the river at Keelogue ford, by excavating the bed to the depth of six feet below the presentbottom, so as to give a depth of full seven feet six inches fornavigation when the works shall have been completed .Towards deepening this ford the contractors dammed offa portion ofthe river 100 feet in width , and 700 feet in length,and have commenced an excavation of nearly six feet indepth; the material to be excavated consisted at the top oftwo feet ofgravel, loose stone, and sand, and at the bottomoffour feet of a mass, composed of clay and rolled limestone,which in some parts was found to be so solid and compact,that it became necessary to blast it with gunpowder, inpreference to excavating, according to the ordinary system ,through detrital matter.This compound of clay and rolled limestone, and lime-314stone gravel, is similar to that which forms the bed of theShannon at all the other fords over which bridges havebeen erected, as at Banagher, Shannon Bridge, Athlone, &c. ,and these gravel banks in most cases are in connexion with,and in fact form a part of those low, but steep, ridges orhills, composed of clay and rolled limestone, which occur soabundantly in the King's, Queen's County, and the countiesofWestmeath and Longford, on the east side of the river, andin the counties of Clare, Galway, and Roscommon, on thewest.These gravel ridges, or eskers, as they are generally called,usually affect an east and west, or north-west and south- eastdirection, and consequently cross the river Shannon, whosedirection between Athlone and Killaloe is north-east, southwest, nearly at right angles; hence the fords, which, particularly at Athlone, Shannon Bridge, &c. , are merely gaps cutthrough the eskers by the action of the water, run directlyacross the river, and present shallow, having deep ponds ofwater on either side, so that when the falls are not considerable, as at the fords of Banagher, Shannon Bridge, &c. ,the excavation of the bed of the river at the ford will bringthe water on both sides to a level, and there will still remainample depth above for the purposes of navigation.But to return to Keelogue, I have already mentionedthat the upper part ofthe excavation consisted of two feetof loose stones, gravel, and sand, and the lower part of fourfeet of a very compact mass, composed of indurated clay androlled limestone. In excavating in the loose material ofwhich the upper two feet was composed, the labourers foundin the shallowest part of the ford , a considerable number ofancient arms, consisting of bronze swords, spears, &c. , inexcellent preservation, which are similar to those which havebeen frequently discovered in other parts of Ireland; and towards the lower part of the upper two feet they discovered agreat number of stone hatchets, also similar in many respectsto those which have been so frequently met with in different315parts of this country. In regard to the stone hatchets , Iwould merely observe, that the greater number, which areblack, are composed of the siliceous rock called LydeanStone, which occurs in thin beds, interstratified with thedark gray, impure limestone called Calp, which is abundant in the neighbourhood of Keelogue and Banagher; butthe others, some of which present a bluish gray, and some ayellowish colour, are composed of a subcrystalline, and apparently igneous porphyritic rock, none of which occurs inthe neighbourhood, or possibly in the south of Ireland ,Hence it is probable that the latter, which are much moreperfectly executed than the black, or those composed ofLydean Stone, were brought from a distance, and probablyfrom a foreign country.The important and interesting subject for considerationin the antiquities before us is, that they are evidently therelics of very different, and probably distant periods . Owingto the rapidity of the current at Keelogue ford, it is extraordinary that any comparatively recent deposit should havebeen formed, and at all events the annual increase must havebeen inconsiderable; hence, though not more than one footof silty matter may be found between the stone weapons ofa very remote age, and the swords and spears of anotherperiod still remote from us, yet under the circ*mstances described centuries may have intervened between the periodsof mortal strife which must have taken place in the riverprobably between the Leinster men and Connaught men ofold, disputing the passage of the river at two distinct and nodoubt very distant periods.I am not sufficiently versed in the ancient Irish history tosay whether any records are in existence of a battle havingbeen fought at the fords of Meelick and Keelogue; but ifany such exist I have no doubt that many members of theAcademy, and lovers of ancient lore, will be enabled to enlighten us on the subject. I have only further to mention ,316that I have been deputed by my brother Commissioners forthe improvement ofthe Shannon Navigation to present theseancient relics to the Royal Irish Academy, for the purposeof being added to their already important and valuable collection of Irish antiquities.DONATIONS.Supplementary Appendix to the Report of the Poor LawCommissioners of the Medical Charities in Ireland, with Indexes. 1841. Presented by the Commissioners.Apamphlet entitled, " Is Selenium a true Element?" Presented by Septimus Piesse.Transactions of the Zoological Society of London. Vol.III. Part 1. 1842.Reports ofthe Auditors and Council of the ZoologicalSociety of London, April 29th, 1842, and List of Members.Su la Falsita dell' Origine Scandinava di Jacopo Grabergdi Hemso.Sunto della Letteratura Svezzese.Degli Ultimi Progressi della Geografia (two copies).Saggio Istorico su Gli Scaldi o Antichi Poeti Scandinavi.Occhiata Sullo stato della Geografia nei Tempi Antichi eModerni.Specchio Geografico, e Statistico dell' Impero di Marocco.Presented by the Author.A copy ofthe Ordnance Survey of the County of Waterford, in forty-two sheets, including the Title and Index. Presented by His Excellency the Lord Lieutenant.Extraits du Tome XV. et XVI. des Memoires de l'AcademieRoyal de Bruxelles, with Notes. Presented by the Academy.Examinations at the University of London for M.D.,B. M., B. L., M. A., and B. A., (six pamphlets). Presentedby the University.Memoiresde l'Institut Royal de France. Tome Quinzieme.Presented by the Institute.317Specimen de l'Imprimerie de Bachelier. Presented bythe Author.Memoirs ofthe Royal Astronomical Society. Vol. XIV.Presented by the Society.Memoire sur la Chaleur des Gas Permanens. Par JeanPlana. Presented by the Author.Proceedings of the Royal Society, &c. 30th Nov. 1842.Presented by the Society.Revista de Espana y del Estrangero. B. Fezuier Gonzalo Moror. Tomo I. Presented by the Author.Geological Report of Londonderry. By Captain Portlock, M.R.I.A. , &c. Presented by the Master General andBoard of Ordnance.Archives du Muséum d'Histoire Naturelle de Paris. TomeIII. Liv. 1 and 2. Presented by the Museum.Address to the Geological Society of London. By Roderick Impey Murchison, F.R.S. , &c. Presented by the Author.Report ofthe Twelfth Meeting ofthe British Association,held at Manchester in 1842. Presented by the Association.Statutes relating to the Admiralty, to the eighth Year ofGeorge III. Presented by Captain Portlock.Ancient Irish Pavement Tiles, with Introductory Remarks.By Thomas Oldham, Esq. Presented by the Author.Proceedings ofthe Glasgow Philosophical Society, 1841 ,1842. Presented by the Society.Memoires publies par la Société Hollandaise des Sciences.Second Serie. Tome II. Presented by the Society.Proceedings of the American Philosophical Society. Vol.II. Nos. 24 and 25.Transactions ofthe American Philosophical Society. Vol.VIII. New series. Parts 2 and 3. Presented by the Society.Fifth Annual Report of the Loan Fund Board ofIreland.1843. Presented by the Commissioners.Communication to the Right Hon. Sir Robert Peel, Bart.318By Jeffries Kingsley, Esq. , M.R.I.A. Presented by theAuthor.Bulletin des Séances de la Société Vaudoise des SciencesNaturelles. Nos. 1-4. Presented by the Society.Sur les Figures Roriques et les Bandes Colorées produitespar l'Electricité. Par M. P. Riess. Presented by the Author.Expériences sur la non caloricité propre de l'Electricité.Sur les relations qui lient la lumiere a l'Electricité.Sur les travaux récents qui ont eu pour objet l'etude de lavitesse de propagation de l'Electricité. Par M. le Prof. ElieWartmann. Presented by the Author.Journal of the Franklin Institute. Vols. III. and IV.Third Series. Presented by the Institute.Proceedings of the Zoological Society of London. Part10. 1843. Presented by the Society.

ANATOMY OF PALUDICELLA ARTICULATA.Fig 4.Fig. 3.hkk.kCbhaFig.2.kFig. 1.kkkPROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1842.January 23.No. 38.REV. JAMES H. TODD, D. D. , Vice- President, in theChair.Mr. G. J. Allman, read the following paper on the Muscular System of certain fresh water ascidian Zoophytes, beingthe first of a series of memoirs which he proposed presenting to the Academy on the physiological and zoological history ofthe zoophytes of fresh water."The subject on which I have now the honour of addressing the Academy, belongs to a hitherto but little investigated department of zoology, the structure of the ascidianzoophytes* of fresh water. Our present knowledge oftheseminute creatures is chiefly due to Raspail, the distinguishedFrench naturalist and chemist, whose researches into thestructure of Alcyonella Stagnorum, are characterized bymuch patient observation, † while in these countries the subject has been totally neglected . Not so, however, with theascidian zoophytes of the ocean; these interesting animalshave had both here and on the continent some able investigators, among whom none deserve to be mentioned before

• The zoophyta ascidioida of Johnston are synonymous with the bryozoa of

Ehrenberg, and the ciliobrachiata of Farre, and include all those zoophytes whoseorganization is referrible to the molluscan type.† Compte rendu des seances de l'Academie des Sciences. 4 Fevrier, 1839.VOL. II. 2 D320Milne Edwards, and Farre, and it is especially to the latterindefatigable and accurate observer that we are indebted fora knowledge of the minute anatomy of these most curiousand highly organized polypes. Though in my own investigations into the anatomy ofthe fresh water zoophytes ofthisorder, I have not restricted myself to any particular structures, I yet intend, in the following remarks, confining myobservations to their muscular system; reserving for someother occasion the pleasure of directing the attention of theAcademy to those points of their anatomy not dwelt upon inthe present paper." In the remarks which I am about to offer, it will beseen how closely the ascidian zoophytes of our fresh waterscorrespond in organization with the marine species; andthough in minute anatomical detail certain differences willbe observed, yet these differences are far from invalidatingthe unity of the type of structure, -a unity which will befound from the following observations to pervade, in a remarkable degree, the entire order. I would wish it to beunderstood too, that if I should in any respect differ fromthe statements of Dr. Farre, I offer no opposition whateverto his observed facts, but solely to one or two of the conclusions to which they have induced him to arrive ."The animal of the present order, to the muscular anatomy of which I have chiefly attended, is one which has notas yet been recorded as a native of the British Islands .About two years since I was sent, by Mr. William Thompsonof Belfast, to whose researches into the natural history ofthis country we are so much indebted, a small portion ofthe dried polypidom of a zoophyte, which he found , in September, 1837 , cast upon the shore of Lough Erne. Fromthe dried condition of the fragment, -a condition in whichthe fresh water zoophytes lose all their most interestingcharacters, I was unable at the time to arrive at anything satisfactory in the investigation of the species; I321therefore contented myself by sketching in my note-book,the few imperfect external characters which continued visible on the dry and shrivelled zoophyte. No farther thanthis did my knowledge of Mr. Thompson's discovery extend ,when an opportunity fortunately occurred in October last,of obtaining living specimens of the animal. These I discovered in the Grand Canal, near Dublin, and have thusbeen enabled to pursue my investigations , from which Ifind the species to be one of great interest. I find , moreover, that although it has been hitherto unnoticed, as aBritish animal, it is identical with the alcyonella articulataof Ehrenberg, for which Gervais, who found the animal nearParis, subsequently constituted a new genus, under the nameof Paludicella. * It is also noticed by Van Beneden, whomet with it near Louvain, and gives a figure of it,† which ,though not very good , will yet be found of use in the identification of the species. Though Ehrenberg's appellationpossesses the claim of priority, yet, as it refers the zoophyteto a genus into which its structure will not admit it, it mustbe rejected, and I shall accordingly adopt the name Palludicella, by which it has been designated by Gervais." In the following remarks upon the muscular system ofthe fresh water ascidian zoophytes, my description of thissystem is chiefly derived from observations made upon Paludicella articulata, as there are certain points in the muscularanatomy of other species, upon which I cannot as yet speakwith certainty, and for completing my observations on which,I must wait until the approaching Spring shall afford mefresh objects for investigation." In describing the muscles of these animals, I haveavailed myself of Dr. Farre's phraseology, applying to theseveral sets of muscles in the fresh water ciliobrachiate zooBulletin de l'Acad. Roy. de Bruxelles, an. 1839.† Mem. de la Société d'Hist. Nat. de Paris, tom. 4.2 D 2322phytes, the same terms which Farre has given to the analogous sets in the ciliobrachiates of the sea." In Paludicella then, three groups of muscles may bedetected. These are strictly analogous to muscles whichhave been demonstrated in the salt water zoophytes ofthesame order, and for a description of which, we are indebtedto an admirable paper of Dr. Farre, in the PhilosophicalTransactions, an. 1837. The first of these groups to whichI shall direct your attention, corresponds with the anteriorset of retractor muscles of Farre. It may be observed (fig. 3and 4, h, h) to take its origin from the internal surface ofthewalls ofthe cell near the middle, and thence to pass upwardsin order to be inserted into the margin ofthe tentacular disk,and upper part of the pharynx. The action of this group isobvious, it is the true retractor apparatus of the polype, andit is worthy of remark, that neither in this nor in any otherfresh water zoophyte whose anatomy I have studied, could Idetect muscular fibres analogous to those described by Farre,as inserted into the remote extremity of the stomach in thosezoophytes of the sea which had come under his observation." The second set of muscles to be described in Paludicella, consists of four bundles of fibres (fig. 3 and 4, i, i, i)which arise from the inner walls of the cell near the top,two at each side, having the tubular orifice between them.From this origin, they pass towards the aperture of thecell, slightly converging, and are inserted by distinct attachments, which are all placed in the same plane, intothe inner surface of the tube near the margin of the orifice.These are in every respect analogous to the muscles whichFarre describes under the name of opercular, and to whichhe ascribes the office of assisting in the inversion of thepolype tube drawing in its margin after the retreating polype, and by their continued action, closing the orifice of thecell. Reasons will presently be given for dissenting fromthis view of the action of the opercular muscles, and in the323meantime I shall proceed to the description of the thirdgroup."Thethird group is analogous to one detected by Dr. Farre,in the ascidian zoophytes ofthe sea, and to which he has giventhe name parietal. The parietal muscles take a transversecourse, and originate and terminate in the internal membraneof the cell. In paludicella (fig. 3 and 4, k, k, k, k) they arerather numerous, and consist ofshort fibres of variable length,which pass transversely round the internal tunic, beingcapable of detection through nearly the entire length ofthecell, and sometimes passing one another in their course, theymay be seen to surround the cell with a contractile tissue.Dr. Farre is of opinion, that these muscles in the zoophyteswhich he has examined, are attached by their extremitiesonly, being free in the intermediate space . In paludicellahowever, I saw nothing which would lead me to suspect, thatin this zoophyte such was their disposition . I shall nothere, however, speak positively, as it will require more extensive observations before any decisive conclusion can bearrived at." Such are the three great groups ofmuscles which I havesucceeded in detecting in paludicella, and so far as my observations have gone, analogous groups are to be found in theother fresh water ciliobrachiates. It will at once be seen, byany one acquainted with Dr. Farre's paper, that while themuscles just described correspond in all their importantfeatures with those of the ascidian zoophytes of the sea,thus beautifully demonstrating the unity of type by whichthe order is characterized, yet in the details of the severalgroups, some remarkable modifications will be found toexist."The first thing which strikes us is the absence, probablyamong all the fresh water ascidian zoophytes of that welldeveloped fasciculus of muscular fibres, which is observed inthose ofthe sea, to arise from the bottom of the cell, and32466pass upwards to be inserted into the fundus of the stomach.It is true, that Trembley describes in alcyonella stagnorum, acertain appendage to the fundus of the stomach, to which heassigns the office of a retractor muscle; "J'ai vu," says Trembley, distinctement, lorsque les polypes à panache etaientbien au dehors de leur cellules un fil qui tenait d'un côté al'extrémité inferieure de l'estomac et de l'autre au fond de lacellule. "* Raspail supposes this an erroneous observation,and conceives that Trembley mistook for a distinct organ,the appearance presented under the microscope, by a foldofthe reflected tunic. Notwithstanding, however, the criticism of Raspail, I believe the observation of the celebratedhistorian of the green polype to he perfectly correct, thoughhis reasoning is erroneous." I have myself witnessed in Plumatella repens, an organin every respect corresponding to Trembley's description; Ibelieve this organ to be an ovary, though from its positionand attachments, Trembley's opinion might at first appearcorrect, and the structure in question might be supposedanalogous to the posterior set of retractor muscles in theciliobrachiate zoophytes of the sea. This supposition, however, is untenable, and I have satisfied myself by repeatedobservations, that no such function is performed by it; it isobserved to undergo no contraction, and its motions are entirely passive and dependant on those of the body of thepolype." In the same animal, Trembley also describes as retractormuscles, filaments attached by one extremity to the base ofthe plume of tentacula, and by the other to the bottom ofthe cell; but this, likewise, is considered by Raspail as anand referrible to the same source as the former. Hereagain I must dissent from the French naturalist; the filaerror,

• Hist. des Polypes d'Eau douce, p. 216.

Mem. de la Soc. d'Hist. Nat. de Paris, tom. 4, p. 92.Op. cit. p. 216.325ments alluded to by Trembley correspond closely with fasciculi described above, as existing in paludicella, and whichI have also witnessed in other fresh water zoophytes; and Icannot but think, notwithstanding the high authority ofRaspail, that they are really such as Trembley describesthem. It is worth remarking, that Raspail denies the existence of retractor muscles in alcyonella, believing that, withthe general contractility of the animal, such a contrivancewould be superfluous. I have not yet succeeded in obtainingany specimens of alcyonella, so that upon this point I cannotspeak from direct observation. Since these muscles, however, are particularly well marked in all the fresh waterascidian zoophytes, whose anatomy I have studied , as wellas in those of the ocean, I must still adhere to the originalobservation of Trembley; for it can hardly be supposed, thata genus so nearly allied to those in which the system inquestion is well developed , and which Raspail, by the way,would consider but as a different grade of evolution , shouldbe altogether destitute ofthem."In Plumatella repens I have examined, with much care,the retractor apparatus. In this species it consists of twofasciculi of muscular fibres, which arise from the sides of thecell near the bottom; and thence passing upwards symmetrically, one along each side of the body of the polype, receivean extensive attachment, being inserted into the wide part ofthe tentacular crescent, into the pharynx for its entire length,and into the upper part of the stomach; a few fibres appeardetached at each side from the main fasciculus, to be insertedmore externally near the base of the tentacular lobes. Thefunction of these muscles is evident, acting from their morefixed attachment to the side of the cell, they become powerful retractors, by which the body of the polype is drawninwards and concealed in the more internal parts of the polypidom ." In the opercular muscles, paludicella offers no remark-326able deviation from the general arrangement of these musclesin the salt water species. In plumatella repens, however,and perhaps in most other species of fresh- water ciliobrachiates, their arrangement is very peculiar. In this zoophyte, they consist of a series of about twenty-five distinctdelicate fasciculi , which arise from the internal surface ofthecell at regular intervals, and in a plane perpendicular to itsaxis, and thence radiating inwards are inserted into the opposed surface of the reflected tunic." In assigning their proper office to the muscles which havebeen already described as the true retractor apparatus ofthepolype, no difficulty whatever is met with; neither can webe at a loss in discovering the true function of the parietalmuscles, for these acting upon the flexible internal tunic ofthe polype cell, must necessarily, by their contraction, diminish transversely the space included between this tunic andthe body of the polype, a function the great importance ofwhich, in the economy of the little animal, will presently beapparent. When, however, we attempt to explain the actionof the opercular muscles, the task will perhaps be found notquite so easy. It has been stated that Dr. Farre assigns tothese muscles the office of drawing in the flexible portion ofthe polype tube after the retreating polype, and by their continued action closing the orifice of the cell. I cannot helpthinking, however, that in ascribing this office to the opercular muscles, Dr. Farre is correct but to a very limitedextent, and that their chief use is directly opposite to thatassigned to them by this excellent observer. The use whichI would assign to the opercular muscles is, first, that ofassisting the polype in its protrusion, an office which theyaccomplish by fixing and preserving in the axis of the polypetube that portion of the reflected tunic (fig. 4, c, c) whichis included , during the retracted state of the animal, betweenthe summit ofthe fasciculus ofapproximated tentacula, andthe orifice of the cell; and, secondly, what is a still more327important function, that of affording to the respiratory surface, when the polype is retracted within the recesses of itscell, a constant supply of fresh water, of which the littleanimal would be deprived, were it not that some meansexisted of dilating the tubular reflection of the tunic, anoffice to the performance of which these muscles are fullyadequate, acting then in a state of antagonism to the parietalmuscles, which tend to keep the orifice of the tube closelyshut."My objections to Dr. Farre's view of the function performed by the muscles in question are referrible to threeheads: first, want of necessity in ascribing to them the officefor which this anatomist believes them destined; secondly,their inability to perform the function which he ascribes tothem; and thirdly, the possibility of assigning to them anotheroffice in full accordance with the necessities of the animal." That we are not obliged to seek for opercular muscles,in order to account for the closing of the orifice when thepolype has retired into the recesses of its cell, is evident, ifwe give the slightest consideration to the action of the trueretractor muscles. It is quite plain that the retraction ofthepolype itself, which is effected by the muscles which act directly upon it, is amply sufficient to produce the completeinvagin*tion of the flexible termination of the cell; and, accordingly, observation will convince us that this invagin*tionfollows exactly the retraction of the polype, and is evidentlyrelated to the latter action as an effect to a cause. That theopercular muscles cannot, except in a very partial manner,produce the effect ascribed to them by Dr. Farre, is alsoevident, when we reflect upon their course and attachments.Arising from the circumferential portion of the cell, andthence passing inwards, to be inserted into a point nearer tothe axis, they must, after the invagin*tion of the tunic hasproceeded beyond the plane of their insertion, possess uponthe reflected tunic a decidedly dilatable action , —an action328which is antagonized, first, by the parietal muscles , as willbe presently explained, and , secondly, by the true retractormuscles; for these muscles, acting through the medium ofthepolype, in most instances nearly centrally, or in the axis ofthe tube, will not, in their ordinary action, possess any dilating power, but, on the contrary, will tend to close theaperture by approximating the sides of the tubular reflectionof the cell." Since we have thus seen that the opercular muscles areincapable of producing the closure of the orifice , it becomesan interesting subject of inquiry to determine by what meansthe act in question is performed , and indeed a slight consideration will render manifest the simple yet effective mechanism appropriated to this purpose. The great agents bywhich the closure of the cell is effected are to be found inthe parietal muscles, for these fibres, by pressing the fluid ofthe cell against the tube ofinvagin*ted membrane (fig . 4, c, c),will approximate the sides of this tube to one another, at thesame time that the membrane will be thrown upwards againstthe aperture of the cell, thus completely closing the orifice,and enabling the little animal to rest secure from all intrusionin the recesses of the polypidom." Afterthis account ofthe muscular system ofthe polypes,the mechanism will now be easily understood by which theanimal is protruded from its cell when hunger calls itforth to seek its food in the surrounding medium, or whendesirous of exposing its respiratory surface still more perfectly to the vivifying influence of the aerated water.66 Previously to the discovery of the parietal muscles nosatisfactory explanation had been given of the protrusive actofthe polype, and even since the detection of these musclesby Dr. Farre, their share in effecting the protrusion of theanimal would appear to be underrated. Dr. Farre considerstheir influence in this respect as of secondary importance,and would seem to attribute the act in question mainly to the329straightening of the oesophagus, which in the ciliobrachiatesof the sea is bent upon itself during the retracted state ofthe polype. In none of the fresh water species, however,which I have examined, with the exception of Paludicellaarticulata, does this curvature of the oesophagus appear toexist; we therefore cannot in these instances have recourseto its agency in accounting for the phenomenon now underconsideration, and we are consequently driven to the parietalmuscles, or to the general contractibility of the internal tunic,as the only provision by which this important act can beeffected. I mention the general contractibility of the internaltunic as a probable agent in protrusion, for I do not thinkthe existence of the parietal muscles throughout the entireorder as yet sufficiently established." We shall now suppose the polype withdrawn into therecesses of its cell, and that hunger or some other stimulusimpresses on it a desire of protrusion. The parietal muscles,which appear to me to be the direct agents in effecting theprotrusive act, now begin to contract, and thus exercise apressure on the fluid which surrounds the polype, and is included between the latter and the internal membrane ofthecell. The compressed fluid in its turn acts upon the polype,and by its upward pressure against that portion of the flexible tunic which is carried in by the animal during its retreat, will tend to produce an eversion of this membrane,which, in the completely retracted state, constitutes a tubeof some length between the summit of the fasciculus of approximated tentacula and the orifice of the cell. The opercular muscles at the same time coming into play will, by theirnicely adjusted action, keep the invagin*ted tunic exactlyin the axis of the orifice, and thus materially assist in effecting the necessary protrusion , which, by the continued actionof the parietal muscles, will go on increasing till the complete evagin*tion of the reflected membrane has taken place.This, then, I conceive to be the true account of the protru-330sive act, and that the apparatus just mentioned is amplysufficient for the purpose, without having recourse to theagency of the bent œsophagus, -an agency which in plumatella repens, and other fresh water zoophytes, which I haveexamined, assuredly does not exist, as in these the oesophagusis straight during the retracted state of the animal. In theremarks now offered, however, I do not deny that some influence is exercised by the straightening of the oesophagusin those species in which this tube is bent upon itself previously to the commencement of protrusion; I merely wishto assert that we are not necessarily obliged to have recourseto this agency, but that in some instances, at least, the parietal muscles, or, in their absence, the general contractilityofthe internal tunic, are agents perfectly effective." Such are the observations which I have had an opportunity of making on the muscular system of the ascidianpolypes of fresh water. I am fully aware that they are farfrom being perfect, but for this my excuse must be found inthe extreme difficulty of such investigations, made, as theyall necessarily are, under a high power of the microscope,with an illumination most carefully adjusted, and which canbyno means be at all times obtained , in order that structuresof such extreme tenuity and transparency may not entirelyescape detection. The observations have all been made onthe living animals, and no one who has not devoted himselfto such investigations can form any idea of the close and patient attention which they require, -the constant watchingto obtain the animal in the exact condition or position, inwhich alone certain peculiarities of structure are apparent;and, finally, the mortification of finding the conclusions towhich we had arrived on one day, after hours of painful attention, invalidated by some more favourable observation onthe next." In the present communication I have confined myself tothe muscular system; on some other occasion I may perhaps331again entreat the indulgence of the Academy, while I laybefore it my observations upon other not less interestingparts of the structure of these curious animals. "*DESCRIPTION OF THE PLATE.Fig. 1. Paludicella articulata; natural size.Fig. 2. Portion of the polypidome magnified.Fig. 3. A cell with the polype exserted.a, a, a. The polype cell.b. The orifice of the cell.c. That portion of the internal tunic which is carried out bythe polype during its egress from the cell.d. The stomach of the polype.e. The rectum.f. The oesophagus.g. The crown of tentacula exserted and expanded.h, h. The proper retractor muscles of the polype; they arenow relaxed, and carried out by the animal in the act of protrusion.i, i. Two ofthe four sets of opercular muscles, also in a stateof relaxation.k, k, k, k. The parietal muscles, preserving, by their contraction, the membrane c, in a state of tension, and thus maintaining theexserted condition of the polype.After the present account had been written, I happened to meet with apaper by M. Dumortier, in the Bul. Ac. Brx. an. 1835 , on the Polype à Panacheof Trembley, a polype belonging to the order now under consideration, and forwhich M. Dumortier constitutes a distinct genus under the name Lophopus,characterized by the tentacula, being destitute of cilia. So remarkable an exception, however, would this character offer to that of the entire order, that Icannot but suppose Dumortier in error; an opinion in which I believe myselffully born out by the phænomena subsequently described by this naturalist, andwhich are evidently the result of imperfectly observed cilia.Dumortier details, at considerable length, the anatomy of the zoophyte, andhas witnessed fibres corresponding with the retractor and opercular musclesdescribed in the present communication . His paper is well worth perusal, thoughsome of his statements will require further corroboration.332Fig. 4. A cell with the polype retracted.a, a, a. The polype cell.b. The orifice of the cell.c, c. The inverted membrane, which, in the completely retracted condition of the polype, consists of that portion of theinternal membrane which had been carried out in the act of exsertion, together with the more flexible termination of the externaltunic of the cell.d. The stomach of the polype.e. The rectum.f. The oesophagus. Both rectum and oesophagus are herecurved upon themselves, and thus accommodated to the retractedstate of the polype.g,g. The crown of tentacula retracted, and the tentaculaapproximated into a close fasciculus.h, h. The proper retractor muscles of the polype in a stateof contraction.i, i, i. The opercular muscles also contracted.k, k, k, k. The parietal muscles relaxed.Dr. Robinson gave a brief account of meteors observedat Armagh on the 10th of August, 1842, apologizing for theimperfect nature of the observations, while he felt that itwas desirable that they should be placed on record.The sky had been overcast, but became clear a little afterten, of which Dr. R. was availing himself to try an eyepiece of a peculiar construction, when the appearance of twolarge meteors, travelling in nearly the same direction, reminded him of the peculiar character of the 10th, and inconjunction with T. F. Bergin, Esq. and another observer,he proposed to watch for others. The roof of the dwellinghouse afforded an excellent position. Mr. Bergin lookedsouth-west; he ( Dr. R.) east; and the third north. From10h.55m. Armagh time, till 12h, seventy- eight were seen; ofwhich about twenty were in Dr. Robinson's district, and fiftyin Mr. Bergin's. With scarcely any exception, their ten-333dency was in tracks converging at Ophiuchi. The greaterpart of them were larger than ordinary falling stars, and lefta red train; in some instances a luminous cloud markedfor a few seconds the place of their disappearance, and thenwas faint Aurora towards north-west. The night was occasionally cloudy, and after twelve became completely overcast.DONATIONS.Report oftheLimerick Philosophical and Literary Society.Presented by Dr. Gore.Supplementary Appendix to the Report ofthe Poor LawCommissioners on the Medical Charities, Ireland. Presentedby the Commissioners.February 13.SIR Wм. R. HAMILTON, LL.D. , President, in the Chair.Robert Culley, Esq. , James Magee, Esq. , and H. L.Renny, Esq. , were elected members ofthe Academy.Apaper on the Action of certain Salts as Manures, bytheRev. Thomas Knox, was read by the Secretary of Council.A small meadow, containing about an English acre, wasdivided into six plots, and in last Spring, were manured asfollows:1st. 2nd. 3rd.Ashes.manure.Stable Burnedgypsum,4 stone.4th.Muriate of ammonia, 6 lbs.; pearl ash, 6 lbs.; 8 lbs . ofbones, burned anddissolved in halfa pint of sulphuric acid, and dilutedlargely.5th.Guano,2 stone.6th.2 barrels of lime mixedwith earth.331Plots 1st, 2nd, 3rd, and 6th, were top dressed in March;plots 4th and 5th in April. Mr. Knox first remarks, about thecomposition of No. 4, that the quantity of muriate of ammonia was calculated (according to Liebig) on the suppositionthat the decomposition of the ammonia furnished all thenitrogen required for the plant, and was sufficient to give aheavy crop with the addition of the ammonia derived fromthe rain. The quantity of bones was sufficient to furnish allthe phosphates required, at the rate of from three to fourtons to an acre, and were, as Liebig suggested , first dissolved in sulphuric acid, and having been mixed with alarge quantity of water, were sprinkled evenly over the land.At first, plots 1st and 2nd, those manured with ashes andstable manure, appeared much the most luxuriant, and evenup to the time of cutting, that top dressed with manureseemed far a finer and heavier crop, and had a richer colour.When ripe, the plots were mowed and saved quite separately,and that there might be no mistake, pegs had been drivendown deep into the ground at the time of laying on the topdressing. When the hay was quite dry and saved, the produce of each plot was weighed separately, and I was thensurprised to find, that though the stable manure was to allappearance the best, yet the plot manured with the mixedsalts and dissolved bones much surpassed it; also that onwhich the ashes had been used. This, in case of plot 1st, Iconsider to be due to the potash (which the ashes contain) ,enabling the plant to take up more silica from the soil; andin the case of plot 4th, to the potash and phosphates, bywhich greater firmness of stalk was acquired by the plant,and it was prevented from losing weight in drying, as theone that was top dressed with the stable manure did . I wasprevented at that time from determining this analytically,which might have been done, simply by weighing the ashesresulting from burning equal weights of hay. I here givethe weights of hay, the exact quantity of land, which was re-335gularly surveyed, and also the weight of hay calculated atwhat it would be per acre.1st Plot.Hay, 8 cwt.Land, 244 perch Hay, 94 cwt.Land, 27 perch2nd Plot. 3rd Plot. 4th Plot.Hay, 8 cwt. Hay, 8 cwt.Land, 25 perch Land, 22 perch .5th Plot. 6th Plot.Hay, 6 cwt. Hay, 5 cwt.Land, 21 perch Land, 20 perch .Produced at the Rate per Acre,Ton Cwt. St. Ton Cwt. St. 2 15 4 2 15 1Ton Cwt. St. 2 9 7Ton Cwt. St. 2 18 2Ton Cwt. St. 2 4 6Ton Cwt. St. 2 0 0"The results of the above experiments point out the advantage of the salts of ammonia and potash when combinedwith dissolved bones, but the nature of the land and crop towhich it is applied , must be considered , as it might be positively injurious in some cases. In the instance given above,the meadow was an old one, which had not been broken upfor many years, and the grass was close and fine in texture,so that great advantage was gained by the additional silicaand phosphate oflime; but in the case of a new meadow, thehay is often, for the first year or so, too strong and wiry. Insuch a case, were the same applied, it would be rendered toocoarse for the use of horses or cattle; it might, therefore, befound better, for the first two seasons , to apply simply thesalts of ammonia, which would increase the sappiness of theplant and the general growth, without adding to the harshness of texture.66 I hope to be able, on some future occasion, to lay beforethe Academy the result of further experiments on the subject, and (should time permit me) accompanied with anaccurate analysis ofthe ashes of the plant in each case."Mr. Webber made an inquiry as to the cost of the manures mentioned, and suggested that Mr. Knox should berequested to annex to his paper, a statement of the relativeexpenses of the manure employed.Dr. Kane and Dr. Apjohn made some remarks on thegeneral subject.VOL. II. 2 E336Mr. J. Huband Smith gave an account of some ancienttiles found in the ruins of Bective Abbey, near Trim, andexhibited specimens of some raised and incaustic tiles, withdrawings of others.Dr. Todd, V. P. , gave an account of an ancient Irish MS.preserved in the Bodleian Library, Oxford.This MS. , which is a large quarto on vellum, was formerlyin the collection of Archbishop Laud, by whom it was presented to the Bodleian. It was also once in the possession of Sir George Carew, as appears from the autograph"G. Carew" on the margin of the first page. It contains alarge collection of miscellaneous pieces, historical, genealogical, theological, and poetical, in different hands, and of different dates; such a collection was called by the ancient Irish"a Psalter," and in an entry, which shall be consideredpresently, this volume is called " the Psalter of Mac- RichardButler."Pasted down on the inside of the cover is the followingnote:"Oxford ye 9th of August 1673."This booke is a famous coppie of a greate part of SaltairCarril, the booke of St Mochuda of Rathin & Lismore, andthe chronicles of Conga; wherein is contained many divine.thinges, and ye most part of ye Antiquities of ye ancientesthouses in Ireland , a Cathologue of their Kings, of the comingin of ye Romans vnto England, ofye coming ofye Saxons, andof their lives and raygne; a notable Calender of the IrishSaints composed in verse eight hundred yeares agoe, wth theSaints of ye Romane breviary vntill that tyme; a Cathologueof ye Popes of Roome; How ye Irish and English were converted to ye Catholique faith; wth many other things as thereader may finde, and soe understanding what they containelett him remember" TULLY CONRY .66 Tuileagna o Maolionaire."337This account of the contents of the volume is very inadequate, as well as erroneous. There seems but little reasonto think that the book contains a copy of any part of thePsalter of Cashel, although that celebrated Collection issometimes referred to or quoted; no traces of the book ofSt.Mochuda, or the Chronicles of Cong, are now to be found inthe volume; if Tully Conry therefore was not mistaken , thereis ground to suspect that the MS. may have lost somethingsince the foregoing account of its contents was written.On the upper and lower margins, in several places, thereare entries and memorandums by various possessors of thebook, which serve to give us its history, and to fix the date.of a great part of the documents of which it consists. Themost remarkable of these entries must now be noticed.1. On the lower margin of fol. 4, b, there is the followingnote, which is here given in the original, with a translation:Or andro do sigraio mc. A prayer here for Sighraidhreain, mc. topna, mc. maoilin son of John, son of Torna, sonmoir ui mail-conaire, fil ag of Mailin Mor O'Mulconry; whoLerugad an libaisse do muiris is restoring this book for Maumc. tomais.. iarla desmuṁan, rice, son of Thomas, i . e. thegus se an e as geibtine a .... Earl of Desmond, who is nowtaiti na bealltaine tap eis residing at Askeaton . . . . . atdeisceart erinn da riarugad the beginning of May, after theiter gall agus gaeidil.south of Ireland has submittedto him both English and Irish.2. Another entry of a similar kind occurs on the lowermargin of fol. 34, as follows:Os, insodom ferir.1 . Muirismctomais, me semais, in ti d'arleirugiusan becso tuasle droċinstrumentaib.Aprayerhereformypatron (?),i . e. Maurice, son of Thomas,son of James, the person forwhom I am restoring the littleportion above, with bad instruments.The Maurice mentioned in these extracts was the tenth338Earl of Desmond, who succeeded his elder brother James inthe Earldom in 1481. He was the son ofThomas, the eighthEarl, who was beheaded at Drogheda, 5th February, 1467 .He died 1497, according to O'Clery's book of Pedigrees: andas the foregoing entries were manifestly made during hislife- time, it is evident that this volume was of some antitiquity, so as to require the ink to be revived and restored, inthe latter end of the fifteenth century. This was a processvery common with Irish scribes, as is evident from the inspection of our ancient vellum MSS. , many of which havesuffered great damage by ignorant attempts to restore them.3. A memorandum of peculiar interest occurs on the upper margin of fol . 110, b. It is as follows:Salvamp me purpoeno buirilen...emonnbuitiles, ind t-saltairseo,no god-tucad maidin bailein spoill ar iapla upṁuṁanagus ar me puisderd buitilerle iapla desmuman .1 . tomas,agus do baineaò inleabar soagusleabar na carruigi as fuasglad mc ruisderd, agus issein mesuisderd sin do chuir naleabair sin da scribad do fein,no gur bain Tomas [de iad].This Psalter was the Psalter ofMac Richard Butler, i . e. Edmond Butler, until after the defeat at Bally- in- spoill , of the Earlof Ormond and of Mac RichardButler, by the Earl of Desmond,i. e. Thomas; and this Book andthe Book of Carrick were givenin ransom of Mac Richard, anditis this MacRichard that causedthese books to be transcribed forhimself, until Thomas took themfrom him.Thus it appears that this book, and the book of Carrick,(now unknown) were in the fifteenth century considered asa sufficient ransom for the person of a great chieftain, —a remarkable proof of the preservation of a love of literatureamongst the native Irish nobles, in the midst of all their warand faction at that period . Nor is this a solitary instance inIrish history. The Leabhar na h-Uidhri, a manuscript ofthe twelfth century, in the collection of Messrs. Hodges andSmith, contains an entry of a similar kind.339The foregoing memorandum, however, shows that thisvolume was written originally for Sir Edmund, son ofRichard,Butler, commonly called Mac Richard; and that on his defeat by Thomas, eighth Earl of Desmond, who, as we havealready seen, was beheaded in 1467, it passed into the handsof the Desmond family.In the book of Pedigrees of the O'Clerys, an unpublishedwork, of which the autograph MS. , in the original Irish, isin the Library of this Academy, the following account ofThomas, eighth Earl of Desmond is given (p. 247):" The fate of Thomas, son of James, Earl of Desmond,i. e. the ninth [eighth] Earl. Thus did it happen unto him,viz.JohnTipto [ Tiptoft] Earl of Worcester, came into Irelandas Lord Justice, called by proclamation of the English ofIreland to the great Council at Drogheda. And bad was thecounsel there agreed upon, viz. to behead Thomas, son ofJames, the Earl, without impeachment of crime , right, orlaw, but merely from envy and hatred; the man of best mienand form, wisdom, and intelligence of either English or Irishof his time. No praise bestowed upon him could be toohigh. The sorrow and affliction of that death was feltequally by the English and the Irish. This Thomas theEarl invariably overthrew and put down his enemies and opponents on every occasion whenever he fought with them.Great indeed was the battle in which he overthrew the Butlers, on the Suir, and innumerable were the hosts of themthat were slain and drowned on that occasion. He likewisegave several overthrows besides, that are not here enumerated . A Lord intellectual and learned in Latin, English ,and ancient Irish writings, was that Thomas. It was hethat gave the great overthrow to the Mac Carthys at Reidhan-Eich-bhuidhe . The 5th day of February the Earl wasbeheaded, and 42 years was his age at that time. At Traleewas he buried, 1467. "*

• This is a strictly literal translation of the original Irish. -See Grace's

340This extract, taken in connexion with the entry in theOxford MS. , is exceedingly curious, as it notices the factthat Thomas Earl of Desmond was learned in ancient Irishwritings; and therefore incidentally confirms the probabilityof his accepting ancient MSS. as a ransom for the MacRichard. The place called Bally-in- spoill is now unknown;but from the record in the Book of Pedigrees it seems probable that it was a village on the banks of the Suir.4. Another interesting entry, which enables us to dateone portion ofthe volume, occurs on fol. 86, a, in the handwriting of the original scribe , at the end of a very valuablefragment of Cormac's Glossary:I h- e analad in tigerna inuair do scribad in sanasan sona saltraċ, .1 . mile bliadanagus ceizri .c. bliadan agustri bliadna dec, agus da .xx . incuiced la do mi Febra agus intockmad la don esca. mir:seaan buiỏi o cleiri do scrib,agus o'emann buitiler me risterd do scribaỏ.The year of our Lord whenthis Glossary of the Psalter waswritten, was 1453; on the 5thday of the month of February,and the eighth day of the moon.I am John Boy O'Clery whowrote it, and for Edmund ButlerMac Richard was it written.It appears therefore that this portion of the volume wastranscribed (doubtless from much more ancient documents,perhaps from the veritable Psalter of Cashel itself) in themiddle of the fifteenth century for Sir Edmund Butler,commonly called Mac Richard; and that it subsequentlypassed into the family of Desmond, having been received inransom of Mac Richard by Thomas Earl of Desmond.This MS. having been for the last two centuries in England, appears to be wholly unknown to our historians. Therules of the Bodleian Library do not permit its MSS. to belent, and as there is no accurate catalogue of the valuable,Annals, printed by the Irish Archæological Society, p. 165 , note , for a furthermention of Earl Thomas.341but unknown, and, in Oxford, unappreciated collection of IrishMSS. which it contains, the MSS. there preserved are almostas inaccessible for the purposes of Irish historical research,as those ofthe Vatican or the Escurial.Dr. Todd did not pretend to give a complete account ofthe contents of the " Psalter of Mac Richard, " as it may perhaps for convenience be called . He was able only to carryaway a very few memoranda of such articles as appeared, ona very hasty inspection, likely to prove most interesting.On fol. 7 is a religious tract, known as the Life of St.Margaret, a work of no value, except to the philologist.Fol. 9. The Genealogy of St. Mochoemog.Fol. 11 , b. A religious tract, entitled , in Irish, " TheHistory of the Image of our Lord, " and also, in Latin , " Incipit Libellus Anastasii [ Athanasii] Archiepi Alexandriæurbis, de passione imaginis Dni. nri. Jhu. Xi. " This is probably an Irish version of the tract attributed to St. Athanasiusat the second Council of Nice, although now admitted to bespurious. It is published in Greek and Latin in the Benedictine edition of the works of St. Athanasius.Fol. 14, a. A curious legend of Donogh O'Breen, abbotof Clonmacnois. The story is, that having gone on a pilgrimage to Armagh, he was miraculously detained there untilhis death, A. D. 987. He is said to have been the last ofthe Irish saints who performed the miracle of raising thedead. See Annals ofthe Four Masters in an. 987.Fol. 15. An account of the ancient tract called theFelire, or Festilogium, of Angus the Culdee; being a Martyrology, or Calendar of the Saints' days observed in theancient Irish Church, compiled in the eighth century.Fol. 18, b. " The Destruction of Jerusalem by Titus, sonof Vespasian, in revenge for the Blood of Christ. "There is a copy of this tract in the Leabhar Breac in theLibrary of the Academy, and a fragment of it in the Book ofLismore.342Fol. 23. A legend ofthe Infancy and Life of Christ, asrevealed by the Virgin Mary to St. Bernard.Fol. 29. A sermon in Irish on the text, " Omnia quæcunque vultis ut faciant vobis homines, et vos facite illis. "" Fol. 30, b. A sermon on the text, "Cum ergo facieselimosinam. "There are copies of these sermons in the Leabhar Breac.Fol. 33, a. The celebrated Chronological Poem of GiollaComgin, beginning with the Creation, and carried down tothe year 1072, when its author flourished. -See O'Reilly'sIrish Writers (Trans. Hiberno- Celtic Soc. vol. i . ) , p. lxxx.There is a very ancient copy of this poem in the Libraryof Trinity College Dublin, MS. H. 2, 18.Fol. 38 to 42.Fol. 43, a.b.66Genealogies of the Irish Saints.The three sons of Moses, &c .Incipit inventio sanctæ crucis."Fol. 57, b. A tract containing the fabulous history ofIreland before the Deluge, as related by Fintan, one of theante-diluvian colonists of Ireland , who, under various transmigrations, is supposed to have survived the deluge . Thiswork ends with an account of a convocation of the states ofIreland held at Tara, in the sixth century, under DermotM'Cearbhaill (Carroll). There is a fine copy of it in theLibrary of Trinity College, MS. H. 2, 16.Fol. 58. The history of Mac Datho's hog. Mac Dathowas king of Leinster in the first century. He invited thekings of Connaught and Ulster to a feast, with a view to sowdissensions between them for his own political ends. At thisfeast there was served up an enormous hog, the cutting upof which, and the assigning to each chieftain his propershare, became a matter of fierce contention between theguests, and produced the effect intended by their crafty entertainer.There are two copies of this legend in the Library ofTrinity College, MS. , H. 2, 18, and H. 3, 18.343Fol. 59. A very fine and ancient copy ofthe Felire, orFestilogium of Angus the Culdee. This part of the volumeis much more ancient than the rest, and was probably writtenin the twelfth century. It ends fol. 72, a.There is a fine copy of this work, with the gloss, in theLeabhar Breac.Fol. 72, b. A poem addressed to Cormac Mac Cuillionan, king and bishop of Cashel, in the ninth and beginningofthe tenth century, on the duties of a king.There are good copies of it in the Library ofTrinityCollege, MS. , H. 2, 18, and H. 3, 18.Fol. 73, b. A poem on the sons of Oillil Olum, king ofMunster in the third century.There is a good copy of it in the Library of Trinity College, MS. , H. 2, 18.Fol. 74, a. A poem on the succession of the kings ofEmania, by Cinaeth O'Hartigan, who died A. D. 975. Itbegins Fianna bazar in emain. This poem appears to havebeen unknown to O'Reilly.-Irish Writers, p. lxii.Fol. 75, a. A tract beginning " Hibernia insola interduos filios principales Militis, i . e. Herimon et Eber, in duaspartes divisa est." The remainder is in Irish.Fol. 81 , b. An account of the great plague in A. D. 633,beginning Anno dominice incarnationis dc.xxx . Apa mopa hisarain buaiscert ond anbthine rucad paulinus edilberta illuingco cantia agusso haipimed co honopach. " In the year ofourLord's incarnation 633, a great mortality in North Saxony,to avoid which Paulinus Edilberta was carried away in aship to Kent, and was there honourably received . "After this are a number of short poems.Fol. 83. An imperfect but very ancient copy of Cormac'sGlossary, beginning with the word Mindech, which is thusexplained, quasi mendic ab eo quod est mendicur. It endsfol. 86, a; after which is the entry already quoted, fromVOL. II. 2 F344which we learn a very remarkable fact, hitherto I believeunnoticed by our historians, that Cormac's Glossary wascompiled from the notes or glosses added by Cormac MacCuilionan, the celebrated king and bishop of Cashel, to themiscellaneous compilation called the Psalter of Cashel. Cormac was killed in the battle of Belach Mughna, now Ballaghmoon, in the County of Kildare, near Carlow, A. D. 903.Fol. 93, b. A tract, with the following Latin title, " Decausis quibus exules aquilonensium ad mumonienses adductisunt," beginning Iseò cetamus foċond toirgi, &c.Fol. 94, b. The history of the war between Oilill Olumand Mac Con. This is a most valuable document. OilillOlum was king of Munster in the third century. He deprived Mac Con, his stepson, of his lawful inheritance .Mac Con rebelled , assembled his followers, but was defeatedby Oilill at the battle of Ceannabrat, a place on the bordersofthe counties of Cork and Tipperary. The defeated princefled to Scotland, where he had influence enough to raise alarge force of foreign adventurers, with whom he returnedto Ireland, and again encountered the troops of his stepfather in the bloody battle of Moy Mocroimhe, in the countyof Galway. In this battle Oilill was aided by Art, son ofConn ofthe hundred battles, then monarch of Ireland; butwas defeated . Art was slain, and with him the six sons ofOilill, with the flower of the Irish chiefs. Mac Conn assumedthe sovereignty ofIreland, and continued to reign until drivenback to Munster by Cormac Mac Art, several years afterwards, who thus revenged the death of his father.There is an imperfect copy of this tract (a MS. of theearly part ofthe twelfth century) in the Library of TrinityCollege, Dublin, H. 2, 18 .Fol. 96, a. The history of the battle of Mucruimhe, beginning Zuid eugan mor do ċath mucruime.Fol. 99, b. The Expulsion of the Decies from Tara byCormac Mac Art.345Fol. 102, a. The coming of St. Finian from abroad intoIreland with the Gospel.Fol. 104. The History of Oriell, with the genealogies ofmany Irish families.Fol. 109, a. A poem on the sons of Conor Mac Nessa,king ofUlster in the first century; by Mongan, a celebratedpoet.Fol. 109, b. Pedigrees of the families of Fermoy, CountyCork.Fol. 111 , a. Pedigree of O'Dunlevey.Fol. 112. Lists of Roman emperors, kings of Egypt,Assyria, and Israel; bishops of Rome, Armagh, &c.In the margin offol . 117, b , there is written in faint red ink,rale. carril: by which we may infer that the tract there transcribed was preserved also in the Psalter of Cashel. This isapparently the only reason for supposing that the presentMS. contains extracts from the Psalter of Cashel.Fol. 118. The actions and deeds of Finn M'Cumhaill.Fol. 122. A very important tract, which appears fromthe handwriting to be much more ancient than any otherpart of the volume, containing the derivation of the names,local traditions, and other remarkable circ*mstances ofthehills, mountains, rivers, caves, rocks, carns, and monumentalremains in Ireland: more especially such as relate to thedeeds of Finn Mac Cumhaill and his heroes.There is an imperfect copy of this tract in the Book ofLismore, in the possession of His Grace the Duke of Devonshire, of which a copy was lately made for the Academy byMr. Curry.Fol. 127, a. A Finian tale, entitled , " The Elopement ofthe Daughter of the King of Munster with Oisin."The remainder of the volume is occupied with a series ofthese tales, which are of great interest and importance.Many modern copies of them on paper are preserved, especially in the valuable collection of Messrs. Hodges and Smith,345which is particularly rich in this branch of Irish literature:but with the exception of the fragment in the book of Lismore, the present volume is the only vellum MS. of such taleswhose existence is known.The special thanks of the Academy were voted to theBoard of Ordnance and to Captain Portlock for the presentation of the Ordnance Geological Survey of Tyrone, Londonderry, and Fermanagh.DONATIONS.Abhandlungen der Akademie der Wissenchaften zu Berlin, 1840. Presented by the Academy.Bericht über die zur Bekanntmachung geeigneten Verhandlungen der Königl. Preuss. Akademie der Wissenschaften zuBerlin. Presented by the Academy.Account of the Induction Inclinometer and of its Adjustments. By the Rev. H. Lloyd, D.D., F. R.S., V.P.R.I.A.Presented by the Author .Regulations ofthe School ofEngineering in the UniversityofDublin, with a Syllabus ofthe Course. Presented by Professor Lloyd.PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1843. No. 39.February 27.SIR Wм. R. HAMILTON, LL.D. , President , in the Chair.Sir William Betham exhibited to the Academy an ancientshoe, found in a bog on the property of Sir Nicholas Fitzsimon, in the King's County.Professor Lloyd read a supplement to a former paper66 on the Determination of the Intensity of the Earth's Magnetic Force, in Absolute Measure. "In a paper recently communicated to the Academy, theauthor had shown that the ratio ofthe coefficients of the firsttwo terms, in the expression for the moment of the forceexerted by a deflecting upon a suspended magnet, was generally given by the formulaM3 h = 2MM'3 3M'in which м and м, denote certain integrals depending on thelaw of distribution of free magnetism in the deflecting magnet, and м' and ' , the corresponding quantities for the suspended magnet. It was further shown, that when the magnets were small, this formula was reduced toVOL. II.3h = } (21² — 31²²);2 G3487 and denoting the half lengths of the two magnets. Thisratio being thus known à priori, the two unknown quantitiesin the equation of equilibrium of the suspended bar are reduced to one; and we are thus enabled not only to dispensewith the observations of deflection at two separate distances ,but also to infer the quantity sought with much greater accuracy than in the received method, by superseding the process of elimination.The preceding value of the ratio, h, has been derivedfrom an approximate law of magnetic distribution , which canbe regarded as physically exact only in the case of verysmall magnets; and the truth of the formula has been verified, in that case, by direct experiment. It was interestingto inquire, therefore, how far the same formula representedthe law of action of large magnets, and whether, by any modification, it might be applied to the results obtained withsuch instruments.For this purpose the following deflection experimentswere made:-The magnets employed were rectangular bars,12 inches, 9 inches, and 7½ inches, in length; } of an inchin breadth; and of an inch in thickness. The observationswere made with the aid of the Unifilar Magnetometer of theMagnetic Observatory , which has been elsewhere described;and simultaneous observations were taken with the Declinometer, in order to eliminate the changes of declination whichoccurred in the interval of the opposite deflections . In thefirst and second series, the position of the suspended bar wasobserved by means of a collimator attached; in all the rest,it was observed by the help of a mirror connected with thestirrup, which reflected the divisions of a scale placed at adistance of nearly six feet.The angles of deflection were calculated , in the case ofthe collimator bar, by the formulatan u = ½ (ne — Nw) k;-where ne and n denote the observed readings of the scale,349with the marked end of the deflecting bar to the East and tothe West respectively. The value of the constant k is givenby the formulak =い1 + 1 tan 0;O denoting the angle corresponding to one division of thescale, and the ratio of the torsion force to the magnetic H-Fforce. When the mirror is employed , the formulæ of reduction are similar, if only we substitute 2u and 20 for uand 0. The following Table gives the values of the constantsemployed in the reduction:1 0HFНlogk-5 (coll. )49"-158 ·00180 6.37795• 5 (mirr. )58-766 00162 6.75643.375 ⚫00255 6.75684313 www ⚫00292 6.75700The following Tables contain the calculated results: thevalues of (ne - nu) are corrected for the changes ofdeclinationwhich occurred in the interval of the two readings ne and no.SERIES I. and II. 7 = l' = • 5.I. II.D.(ne - nw)и (ne - nw)И4.50066.0010194.7882.512° 39′ 45″1° 7′43″194.22 2°39′18″82.26 1° 7'30"-5SERIES III. and IV. 75, l' = · 375.III. IV.D.(ne - nw)И (ne - nw)и4.0010 242.30 3°56' 25" 242.52 3°56′ 38″5.0015 123.31 2º 0'53" 123.50 2° 1' 4"6.0019 71.40 1° 10'4"-5 71.38 1° 10′ 3″2 G 2350SERIES V. and VI. 15, l' = ' 313.V.VI.D.(ne - nw) И (ne --- nw) И4.0005 243.58 3°57' 44"-5 242-74 3°56′ 56"5.0008 123.65 2° 1' 15"-5 123.36 2° 0′58″-56.0010 71.41 1 ° 10' 6"-5 71.25 1° 9'57"SERIES VII. and VIII. 7 = • 375 , l' = • 5.VII. VIII.D.½ (ne — nw)- И (ne - nw)И3.3762 211.18 3°26' 10"-5 210.50 3° 25' 30"-54.3754 97.885.3757 53.241 °35' 55"0°52′ 13″97.5652.881°35' 36"-50°51'51"-5SERIES IX. and X. 1 = l' = · 375.IX. X.D.(ne - nw)И | (ne - nw)и3.37664:37 60212.37 3°27′31″ 212.52 3°27′40″97.52 1°35'39"-5SERIES XI. and XII. 7 = 375, l' · 313.97.55 1°35'41"-5• 375,XI. XII.D.| (ne - nw)2 32 (ne - no) И3.37664.3760214.1698.053°29′21″1°36′ 13″213.8397.903°29' 1"5.3765 52.85 0°51'54" 52.821°36'3"-50°51′52″The following Table contains the calculated results ofthe foregoing observations. The values of the coefficients,Q and Q' , are deduced from the formulatan u =D³by the method of least squares.3517 νh.•5 •5 S4.2800 4.2662--0.8240.7900.193 ---- 085.5 .375 (4.3934 + 0.293 + 0.0674.3976 + 0.293 + 0.067.5 ( 4.3791 .313 + 0.887 + 0.202 4.3760 + 0.692 + 0.158375 2.3830 -⚫5 -2.3702•375 •375 ( 2.34072.3402.375 .313 S2.3456 2.3428 + 0·027+ 0·005-―- 0.823- 0.7610.161-0.1350.345- 0.321- 0.069 --- 0.058+ 0.012+ 0.002The values of h thus obtained are not adequately represented by the formula which has been already deducedfor the case of small magnets, the differences between thecalculated values and the means of the two observed resultsbeing, in general, greater than the differences of the latterinter se. It was accordingly natural to inquire whether theagreement might not be rendered more complete by pushingfarther the approximation in the value of the function whichrepresents the law of magnetic distribution. This was foundto be the case on trial. But it was also found that the observedresults were represented , with nearly equal exactness, by theempirical formula,h = 2 (1c)² - 3 ( l' — c)²;a formula which agrees with the hypothesis, that the wholeforce of each magnet is concentred in two points, or poles, atgiven equal distances from the ends. If we expand the preceding formula, and add together the resulting equations, wehave for the determination of c,6c² + 2 (21—31′ ) c + Eh − Σ (21² —31′²) = 0;or, substituting the numerical values of the coefficients deduced from the preceding Table,352c²- 0.625 c + 0· 0425 = 0;from which we deduce c⚫078.The following Table contains the values of h thus calculated, together with the means of the observed results . Thedifferences barely exceed the probable errors of the latter;and the corresponding error in the calculated value of q isless than the probable error of the same quantity, as deducedin the ordinary method from the observed deflections at twodistances.h (obs.) h (calc.)Diff.•5 •5 -- 0.189•5 •375•5 313.375 •5•375 375+ 0.067 +0.180 - - 0.333- 0.063- 0.178+ 0.092+ 0.191 -- 0.358+ .025+011- .025+011.375 313 + 0.007- 0.088+0.011-.025+004It follows from the preceding formula, that the relationbetween the half lengths of the two magnets, which will causethe coefficient of the fifth power of the distance to vanish, isl — c = 1 · 224 ( l' — c);or, substituting for c its value,70175 1 · 224 l'.It will appear evidently from the foregoing results , thaton account of the large probable error of h, its value shouldbe determined in each case from the mean of a much greaternumber of observations, before we can obtain thereby a satisfactory verification of any formula for its calculation . Asfar as the comparison has been here carried , the results appear to indicate that the value of h cannot be obtained àpriori, in the case of large magnets, with that precisionwhich would justify us in superseding observation, althoughwe may obtain thereby an approximate value, comparable inexactness with the result of a single observation.353Mr. T. Oldham read a paper " on the Tiles found in theancient Churches in Ireland."Mr. Oldham commenced by drawing attention to specimens of old tiles , from various places , which were on the table;and having alluded to the fact, that there has hitherto beenno published representation of these tiles from any place inIreland, proceeded to show that there were three distinctvarieties:-1st. Impressed or indented, in which the patternis formed by being sunk below the general surface of thetile. 2nd. Encaustic, in which the pattern is produced by adifferently coloured substance inlaid; and 3rd. Tiles in relief, or embossed, in which the pattern is raised above thegeneral surface or ground.From the great simplicity of the patterns in the indentedtiles, from their interlacing character (Fig. 1 ) , and from thefact, that several of these patterns occur also in the morecarefully formed encaustic tiles, it was shown that the impressed variety was the earliest in date; and, from a consideration ofthe history of the establishments where they occur,probably belonged to the twelfth century; that the encausticvariety was a subsequent improvement on this more simpleform, and that the embossed tiles belonged to an era whenthe knowledge of the arts had very much declined . This354was proved by several from Bective Abbey, the date ofwhichwas fixed by the occurrence of the tudor, or double rose, andby an heraldic tile from the same place, representing thearms of the Fitzgeralds, having the motto, " Crom abo- SiDien plet," and the initials G. E. It was shown, from thehistory of this family, that the tile could only be referred toa date subsequent to 1496 (in which year the Earls of Kildare, previously attainted , were restored to their honours,and again allowed to use their motto), and to either Geraldthe eighth or Gerald the ninth Earl, both of whom hadwives whose Christian name was Elizabeth, correspondingto the initials G. E.-Gerald and Elizabeth.සිදාදායිThe identity of several of the patterns from differentplaces in Ireland, and the strong resemblance of many tothose found in England and Normandy were then alluded to ,and several peculiarities in the Irish pattern, which tendedto prove that they were manufactured on the spot, werepointed out.Speaking of the comparative cost ofthese tiles now andformerly, Mr. Oldham showed from the account of the repairs at Hampton Court in 1536, and allowing for the diffe-355rence in the value of money, that the price at presentcharged was somewhat less than in the sixteenth century;R&RER&RABEREand concluded by soliciting the assistance of the members inbringing together as complete a series as possible of the patterns still remaining in many of the ruined churches ofIreland.The President read a Supplementary Notice of his Examination of Signor Badano's Memoir on the Resolution ofEquations of the Fifth Degree, and described the successfulapplication to cubic and biquadratic equations ofthe methodproposed by Badano, but which had been shown to be unsuccessful with equations of higher degrees than the fourth.Rev. Dr. Marks, on the part of the Bishop of Cashel,presented the seal used by the latter as Dean of St. Patrick's.356March 16. (Stated Meeting) .SIR WM. R. HAMILTON, LL.D., President, in the Chair.The Secretary of Council read the following Report,which was ordered to be entered on the Minutes:" The affairs of the Academy during the past year have been,for the most part, of a similar character to those which have formedthe subjects of former Reports. It is , however, satisfactory to theCouncil to be able to state, that our proceedings have been distinguished by still increasing activity and zeal among our members ,and that some important measures have been entered upon, andothers brought to completion, which it is to be expected will tendpermanently to sustain the reputation of the Academy, and extendits useful influence." The second part of the nineteenth volume of the Transactionsof the Academy is now printed , and the Council is enabled to placebefore the Academy an early copy. In a few days it will be readyfor distribution among the members." The twentieth volume, which will altogether consist of Mr.Petrie's Essay on the Round Towers, is progressing through thePress; and a portion of the twenty- first volume is in the hands ofthe printer." The Council have with great pleasure to report, that the valuable collection of Irish antiquities amassed by the late Dean ofSt. Patrick's, having been purchased by a subscription, has beenpresented by the subscribers to the Academy. The amount subscribed having slightly exceeded the cost of the Collection, thebalance was applied to the purchase of some other valuable relicsof antiquity, which were also presented to the Academy, and nowform part of its Museum. The detailed circ*mstances connectedwith the collection and application of this subscription, and theeminent services rendered to the Academy and to Irish Archæologyby various gentlemen, to whose exertions final success was mainlydue, have already been brought under your notice in the Reportdrawn up by the Committee of Antiquities, and presented to theAcademy in November last by Dr. Todd. The Council have there-357fore, on the present occasion, only to congratulate the Academy andthe country on the acquisition of this Collection, which it is to behoped will prove a centre to which may be attracted the variousobjects of antiquarian interest now scattered through the country,or which may hereafter be discovered , and thus be laid the foundation of a truly national Museum of Antiquities." Besides the actual Dawson Collection, our Museum has beenenriched by donations from His Excellency the Lord Lieutenant,and from various private individuals, to whom on the several occasions of presentation well merited thanks were voted by the Academy." The necessity of arranging our Museum in such a form asshould do justice to its intrinsic value, and adapt it for those purposes of reference and exhibition on which much of the influenceit is calculated to exert must depend, has rendered the present accommodation of the Academy House totally inadequate to ourwants, and the Council has consequently directed its attention toascertaining how far our accommodation in rooms can be extended.It has been found that at a moderate cost the present Board Roommay be converted into a Museum Room sufficient for our objects,and that under the Library and the adjoining spaces, there existsground now of little use, on which a Board Room, rather larger thanthe present, may be constructed. A model and drawings ofthe arrangement proposed have been already laid before the Academy,and met with its approval, but circ*mstances connected with our tenure of this house have induced the Council to postpone for a shorttime entering upon any outlay in building."In the Report of the last Council, the Academy was informedthat an application had been made to His Excellency the LordLieutenant, that he might recommend to the Government to increaseour Annual Grant by the sum of £ 100 , or to allow that sum peryear, specially for the purchase of Irish antiquities . No decisiveanswer has been as yet received to that application, but it is to behoped that as we have now made so excellent a beginning to ourMuseum, and that the sphere of our public utility has thus beenmuch extended, so small an increase to our exceedingly scantymeans may not be finally refused.358" In November last, the Academy authorized the Council toemploy Mr. Curry to draw up a Catalogue Raisonné of the Irishmanuscripts in the Library of the Academy. This work has beenever since in progress, but will still require some months for itscompletion." Some time ago the Council became aware that it was contemplated by Her Majesty's Government to withdraw from the Irishbranch of the Ordnance Survey those grants of money which havehitherto been made to the departments of Geology and NaturalHistory, as well as of Topographical Antiquities and Statistics, sothat the future operations of the Survey should be limited to thecompletion of the Maps. Sensible of the great benefit that mustaccrue to the country at large by the continuance of those departments, for which already a vast body of materials have been collected, which, if publication were now abandoned, may be totallylost, and feeling that independent of its interest, as positively extending the domain of science, and of which so brilliant an example hasbeen already presented to the Academy, on the part of the Board ofOrdnance, by Captain Portlock, the Geological branch of the Survey is of the highest practical importance to Ireland, as makingknown the true position and limits of our mineral wealth, andguarding enterprize from those latent perils on which, from wantof such scientific knowledge, it has been so often wrecked, theCouncil did not hesitate to interpose its voice against the relinquishing of that undertaking. A deputation of the Council waitedon His Excellency the Lord Lieutenant with a memorial, in whichthe more evident reasons in favour of the continuation of this trulynational work were embodied. His Excellency received the deputation with his usual courtesy, and was pleased to express his sympathy with its objects. He undertook to forward the memorial tothe heads ofthe Government in London, and the Council is notwithout sanguine hopes that the Memoir of the Ordnance Surveymay be finally continued on its original extended scale." In obtaining this result, the Council believe that the voice ofthe Royal Irish Academy will have afforded some assistance." Since the date of the last Report, the Library of the Academyhas been increased by numerous donations of books, for which359thanks have been voted to the donors, at the meetings of the Academy. The Academy continues in communication with the principal scientific bodies of Europe and America, with which an interchange of Transactions and other publications is kept up." During the past year the accession of new members to theAcademy has been such as to show, that notwithstanding the usuallyabstract nature of its proceedings, its importance is fully recognized. As honorary members, two have been elected on the recommendation of the Council: the one a philosopher of Europeaneminence, Professor Wheatstone; the other, an Irish woman, whosename adorns the roll of the Academy, as her works have long shedlustre on the literature of her country, Miss Edgeworth. The namesof the gentlemen who have been elected ordinary members of theAcademy are:Rev. Richard Butler.Dr. Robert Law.John Toleken, Esq. , F.T.C.D.William Blacker, Esq.Rev. James Booth.Arthur Cane, Esq.B. J. Chapman, Esq.F. M. Jennings, Esq.Sir Thomas Staples, Bart.Stewart Blacker, Esq.Thomas Cather, Esq.W. V. Drury, M. D.W. R. Gore, M. D.J. E. Hodder, Esq. , R. N.Rev. John Homan.H. Hutton, Esq.R. Leslie Ogilby, Esq.Hon. Frederick Ponsonby.George Salmon, Esq. , F.T.C.D.Robert Culley, Esq.James Magee, Esq.H. L. Renny, Esq." In a body so numerous as ours , it could not be expected thata year should pass away without the loss of some from amongst ourranks . Unhappily within the last twelve months we have had occasion to deplore the deaths of several valued members." From the list of honorary members three have been removed,Sir James Ivory, Mr. Allan Cunningham, and Professor Heeren.Of our ordinary members we have lost the Hon. Judge Foster, theRight Rev. Charles Dickenson, late Lord Bishop of Meath, Dr.Macartney, Mr. David Aher, and Mr. Bowles. It is fit to noticebriefly their career and their connexion with this Academy." Sir James Ivory was a native of Dundee, and studied in theUniversity of St. Andrew's, where he first distinguished himself in360those mathematical studies on which the elements of his subsequentdistinction rested. Although intended for the Church, circ*mstances threw him into the totally different career of managing anextensive flax and spinning concern. But even the engrossing nature of commercial industry could not wean him from scientificpursuits, and on the dissolution of the company he devoted himselfexclusively to mathematical investigation. He passed to London,and was appointed Professor in the Military College of Sandhurst,which he retained until ill health, occasioned by his untiring researches , obliged him to resign. His merits were so well recognized that he received the retiring pension, although he had notserved the time required by the War Office. Subsequently a royalpension was conferred upon him, and at the same time he receivedthe honour of Knighthood of the Guelphic Order of Hanover." Sir James Ivory was elected by this Academy an honorarymember on the score of his eminent mathematical discoveries .These it is unnecessary to detail . They embraced the solution, inabstract mathematics and in physical astronomy, of problems ofthe greatest difficulty and importance; and the Royal Society ofLondon sufficiently indicated their opinion of his merits by awarding to him at different periods the Royal and the Copley medals." Mr. Allan Cunningham, although occupying a totally differentfield of intellectual exertion from that trod by Ivory, and cultivatingrather the faculties of imagination and invention than those oflogical thought, is also an example of learning, pursued as an enjoyment in the first instance to relieve the weary practice of amechanical trade, and finally adopted as a profession . Born inScotland, he was early apprenticed to a stone-mason, for whom heworked many years. His mind, imbued with the traditions andtales of the Border district in which he resided, soon applied itsvigorous though somewhat rugged poetic faculties to their arrangement; and although it is said that many of the traditions he hasrendered popular, had their first origin in his own fertile brain, yetthere is no doubt but that his verses have preserved a great body ofpopular Scottish story, that otherwise might have been lost. Wouldthat the abundant sources of poetical composition which the earlierchronicles of this country present were similarly utilized. The361varied results of Mr. Cunningham's literary life need not here bedetailed. He subsequently became connected with Sir FrancisChantrey, in whose workroom he acted as manager and superintendant. Called thus to intimate association with the most elevated inart, all his subsequent literary works had for object, more or less,its illustration , and his final labour, concluded but a few days before his death, was the life of his countryman and friend, Sir DavidWilkie. Mr. Cunningham was elected an honorary member of thisAcademy on the score of his various literary merits." The death of Professor Heeren of Göttingen is felt throughEurope as the removal of one of the brightest luminaries of classicalliterature. A reputation, already brilliant, bequeathed to him byhis father, received additional lustre from his elaborate investigations into the commerce and social condition of the nations of antiquity. He was appointed first Professor of Philosophy, and afterwards of History, in the University of Göttingen; and his deceasein the past year has added another to the crowd of illustrious dead,by whose memory that seat of learning is rendered sacred. "" Our recollection ofthose members whom we have lost fromthe ordinary roll of the Academy during the past year is yet so fresh,the time that has elapsed since they assisted at our meetings is soshort, that the notice, necessarily so brief, that can be here made oftheir career must be imperfect, and may appear unjust. In the instances, however, of two eminent members, whose recent loss weall deplore, the Right Rev. the Lord Bishop of Meath, and the Hon.Justice Foster, it may be said, that although numbering them amongits members, this Academy was not the scene of their labours ortheir glory; devoted to the pursuit of most important and engrossing professions, in which by their varied talents they attained thehighest dignities, time was not available for the prosecution of anyof those objects which this Academy has more especially in view.Neither contributed to our Transactions, but the purposes of thisInstitution, and its progress, were always subjects of their warmapprobation and support."Mr. Bowles, a young member of the Academy, must be deeplyregretted, as from his extensive knowledge of languages, and theenlightened assiduity with which he was, up to the period of his362death, engaged in acquiring statistical information, much was to beexpected." In Mr. David Aher the country has lost one well conversant,as a civil engineer, with its physical circ*mstances , and anxious andeffectual in promoting industry. He was principally engaged in theworking ofthe coal district of Kilkenny and the Queen's County, butwasconcerned in many otherengineering operations in thatneighbourhood. He supplied a great deal of valuable information embodiedin the Reports onthe Irish Bogs, drawn up by order of Government;and recently, I believe his last work, at the time when the plans forrailway intercourse through Ireland were much discussed, he surveyed and proposed a line extending from Dublin to Kilkenny.Owing to the purely practical nature of Mr. Aher's labours, he didnot contribute any memoirs to our Transactions, but his career wasnot on that account the less valuable. This Academy, necessarilylimited in its scope to the more general and abstract contemplationof scientific questions, is still most fully cognizant of the merit,and anxious to express its admiration of those men, who practicallydeveloping the sources of useful employment and industrial wealthwhich our country holds, may become important agents in increasingthe comfort and happiness of our people." Dr. James Macartney was born in March, 1770, in Armagh,where his family had long been resident. He was educated in thecountry, where he received the rudiments of an ordinary education ,but was not at college, nor was he intended for a profession.Forced, however, in 1790, by the death of his father, to decide uponhis future course of life, he chose the profession of surgery, ' not,'as he used to say, ' because he had any peculiar aptitude for thebusiness, but that he thought it would harden his feelings, whichhe had found on many occasions painfully acute. ' In 1794 he wasapprenticed to Dr. Hartigan, who was at that time Professor ofAnatomy to the Royal College of Surgeons in Ireland . Passing toLondon for the completion of his professional studies, he was appointed, in 1798, Demonstrator of Anatomy at Bartholomew's Hospital; and in 1800, having become a member of the Royal College ofSurgeons in London, he began to lecture on Comparative Anatomyand Physiology, which he continued up to 1810. During the greater363part of this time he was Surgeon to the Radnorshire Militia, whichoffice, however, was not allowed to interfere with his scientific orprofessional pursuits. In 1811 he accompanied that Regiment toIreland, and in 1813, the Professorship of Anatomy and Surgery inTrinity College having become vacant by the death of Dr. Hartigan ,he presented himself as a candidate, and was elected ." For twenty- four years Dr. Macartney discharged the duties ofthat important office with unexampled zeal and industry, and usedhis utmost exertions to improve medical education. He endeavoured to establish a course of lectures on Comparative Anatomy,but circ*mstances prevented his plan being at the time carried out.He was, however, successful in arranging a separate course on Pathology, and in conjunction with Dr. Jacob, then his Demonstrator,he instituted a dispensary for the special treatment of diseases ofthe eye and ear. As a lecturer, his manner, though unadorned bythe arts of verbal eloquence, became highly popular from the soundideas which he imparted, and the distinct and logical language inwhich they were clothed. His classes were always very large, andby his means the reputation of the Medical School of the Universityof Dublin was materially elevated."He resigned his Professorship in 1837, but still continued hisapplication to scientific pursuits. On the 5th ofthe present month(March) he was seized with apoplexy, and died on the followingmorning."" In a literary point of view, Dr. Macartney's contributions tomedical and zoological science were numerous and important. In1803 he commenced writing for Rees ' Cyclopædia, to which hesupplied the articles- Comparative Anatomy. Vegetable Anatomy. Bezoar. Anatomy ofBirds. Classification ofAnimals.Anatomy of the Egg. Anatomy ofFishes. Incubation. Anatomy ofMammalia.' In the Philosophical Transactions he published a memoir on Luminous Animals, and contributed manyminorpapers to the British Association, and to the Academie de Medicine.of Paris. His large work on Inflammation, containing his chiefdiscoveries in physiology and surgery, was published in Dublinin 1838; and in the Transactions of this Academy there are by himtwo valuable memoirs, the first in vol. xiii. , on Curvature of theVOL. II. 2 H364Spine, and the second, on the Anatomy of the Brain of the Chimpanzee, inserted in the second part of the nineteenth volume, whichhas been this evening laid before the Academy, but of which, unfortunately, he did not live to witness the formal publication." Dr. Macartney was a Fellow of the Royal Society, and of theLinnean Society of London, and an Honorary Fellow of the Kingand Queen's College of Physicians in Ireland. He was also a Foreign Associate of the Academy of Medicine of Paris, and memberofmany of the most eminent scientific societies of the Continent ofEurope and of America." The Reverend James Horner, D. D. , engaged in the constantpractice ofthe sacred duties of his profession, did not take any partin the proceedings of the Academy, but will be long remembered bymany amongst us for the interest he always manifested in our success, the amenity of his manner, and the benevolence of his heart."The engrossing occupations of an active political life had alsoso completely removed the Right Hon. Sir John Newport, Bart.from the pursuits to which this Academy is devoted, that it is onlynecessary formally to record his loss, and that he had not contributed to our proceedings."The Treasurer presented the following Abstract of hisAccount with the Academy for the year ending this 16th ofMarch, 1843:JAMES PI ,JUN .Treasurer inAccount with the ROYAL IRISH ACADEMY ,16TH MARCH ,1843 .Dr.ToBalance ,asperudit 16th March 1842£dS. .16971 Sundries Bypaid •"" Cash for sundries received , 7161 Balance inBank ofIreland , """" Annual Subscriptions , 2750 99 inTreasurer's hands Do. ,99 Life Compositions , 9915 0"" Entrance Fees , 110 50"" Cash ,per Boone &Co. Balance ofAccount 817 4"" Rent ofStable for one year , 21 0 Dividends on3Stock per cnt ., 5613ووDo. ,cent Cosols .per 3"" Treasury Warrants ,3113114678927 £176Cr.£s.d636 11288 110211 91927 £176,SignedJAMESUN PIM ,.Treasurer366The auditors appointed by Council to examine the Treasurer's accounts reported as follows:"We have examined the original Account, * with the vouchersproduced, and found it to be correct; and we find that there is abalance in bank of £288 11s. 10d. , and in the Treasurer's hands,£2 11s. 9d. , making a total balance of £291 38. 7½d." (Signed,)" FRANC SADleir." SAMUEL LITTON. "" March 16, 1843."" The treasurer reports that there is £ 1085 17s. 1d. in 3 perCent. Consols, and £1665 4s. 2d. in 3 per Cent. GovernmentStock, to the credit of the Academy in the Bank of Ireland; thelatter known as the Cunningham Fund. He also reports, thateleven members owe their annual subscriptions, due 16th Marchlast, and that two members are owing their two years' subscriptionsto the same date. There are no other arrears due. He has also toreport, that the Annual Parliamentary Grant for the current year,amount £300, has not yet been placed to the credit of the Academyin the Bank of Ireland , but that there is no reason to doubt that itwill be done within a few days." (Signed, )" JAMES PIM, JUN. ," Treasurer. "The ballot for the Annual Election having closed, thePresident requested the Rev. Charles Strong and Mr. Callwell to assist the officers in examining the balloting lists.The Scrutineers reported that the following gentlemenwere duly elected Officers and Council for the ensuing year:President-Sir William Rowan Hamilton, LL.D.Treasurer-James Pim, Jun. , Esq.Secretary to the Academy-J. Mac Cullagh, Esq. LL.D.Secretary to the Council-Robert Kane, M. D.

• Entered in Treasurer's book.

367Secretary of Foreign Correspondence-Rev. HumphreyLloyd, D.D.Librarian-Rev. William H. Drummond, D.D.Clerk and Assistant Librarian- Edward Clibborn.Committee ofScience.Rev. Franc Sadleir, D.D., Provost of Trinity College;Rev. Humphrey Lloyd , D.D.; James Apjohn, M.D.; JamesMac Cullagh, LL.D.; Rev. William Digby Sadleir, A.M.;Robert Ball, Esq.; Robert Kane, M.D.Committee ofPolite Literature.His Grace the Archbishop of Dublin; Rev. Joseph Henderson Singer, D.D.; Samuel Litton , M.D.; Rev. WilliamHamilton Drummond, D.D.; Rev. Charles Richard Elrington, D.D.; Rev. Charles William Wall, D.D.; John Anster,LL.D.Committee ofAntiquities.George Petrie, Esq. , R. H.A.; Rev. J. H. Todd, D.D.;Henry J. Monck Mason, LL.D.; Samuel Ferguson, Esq.;Joseph Huband Smith, Esq.; James Pim, Jun. Esq.; Captain Larcom, R.E.The President then appointed, under his hand and seal,the following Vice-Presidents:Rev. Humphrey Lloyd, D.D.; Rev. James HenthornTodd, D.D.; Rev. Joseph Henderson Singer, D.D.; JamesApjohn, M. D.368April 10.RICHARD GRIFFITH, Esq. , in the Chair.George James Allman, Esq. , Henry Lindsay, Esq. , JohnM'Mullen, Esq. , Hon. and Very Rev. Henry Packenham,Dean of St. Patrick's, Goddard Richards, Esq. , and JohnWynne, Esq. , were elected Members ofthe Academy.Dr. Todd, V. P. , read a translation of an Irish deed oragreement made in the year 1526, between Conla Mac Geoghegan, chief of the Kinel Fiacha, and Breasal Sionnach,alias Fox, chief of the Clan Tadgan, -both of Westmeath.The agreement was, that Mac Geoghegan should belord over Fox and his country under certain conditions,which are specified , and of which the principal is, that MacGeoghegan is to do his best for the protection and defenceof Fox and his country. The deed adds, " if Mac Geogheganshould on any occasion fail to do his best for the protectionand sustainment of the Fox in his lordship, that he woulddo for himself; that he no longer have rent, nor privilege,nor lordship over him, but every one be for himself. "One passage proves that the custom of holding the halfyearly assemblage (oreactar) on the 1st of November andthe 1st of May was then kept up. " Every general assemblyof Samhan [ All Saints' day] or of Bealtine [ May day] thatshall be in Mac Geoghegan's country, shall be held atBaileath-an- Urchair, or at Corr-na-Sgean, and the Fox andthe nobles of his country shall attend."inIt is known from other sources that the Brehon laws, andthe authority of the hereditary Brehons, were kept upmany parts of Ireland to a much later period: the followingpassage therefore, which contains an allusion to the Brehon,is not surprizing. " And whenever either an Englishmanor an Irishman sues the Fox or any one of his country, they369shall submit to pay whatever is decided upon by MortoghMac Egan, or whoever may be the Brehon at the time, &c."The original of this deed, which is in Irish, is in the possession of Sir Richard Nagle, the lineal representative ofMac Geoghegan, who has kindly permitted a copy of it tobe taken and deposited in the Library of the Academy.The great body of the document is uninjured and legible;the only imperfection which occurs is in the following passage at the end, which contains the signatures and date ofthe agreement.·" These are they ofthe Foxes' country who are presentwith us, viz. the Fox himself, and the two sons of Edmund,viz. Murtogh and Phelim; and the two sons of Brian Fox,viz. Breasal and Cucogry; and Murtogh, son of Owen, sonof . . . . . i. e. the Ollamh (poet or historian) of Foxand myself James O'Cionga [or king] the son of CarbryO'Cionga, who was present at the making ofthis agreement,and who wrote it. And it was on the Fast [i. e. the Eve] ofSt. Adamnan this agreement was made; and particularly onWednesday; and it was on a Friday it was written . Andthis is the year of the Lord at this time, viz. six years, andtwenty, five hundred and one thousand years [ 1526] , andthe 22nd day of the month of August.66 " I am the Mac Geoghegan. I am the Fox." [Herefollows a line in the characters of the consonant Ogham, butso much effaced that although the key is known, it has beenfound impossible to decipher it. The last word only is legible, which is Graine, or Grace, a woman's name: thenfollows] are in Ireland . We are the sons of EdmundFox.66We are the sons of Brian Fox. "Mr. Mallet gave a notice of recent improvements in theformation of Mosaic pavements.370April 24.SIR WILLIAM BETHAM, in the Chair.The Chairman informed the Academy, that Sir RichardO'Donnell had consented to deposit the Cathach, containinga MS. of the Psalms in Latin, by St. Colombkill, in the Museum of the Royal Irish Academy.- RESOLVED, That the marked thanks of the Academy bereturned to Sir Richard O'Donnell for his kindness.Read, a letter from the Rev. T. R. Robinson, accompanying a box containing an original Pyrometer of Wedgewood, presented to the Academy by Miss Edgeworth,(H. M. R. I. A.)" DEAR MAC CULLAGH," Our friend, Miss Edgeworth, has requested meto present from her to the Academy a Wedgewood's Pyrometer, which, as unfortunately I cannot attend this evening,I commit to your care . This instrument is remarkable, asbeing the first attempt to place within reach of the manufacturer and the chemist an easy method of measuring, atleast approximatively, the temperature of their furnaces. Itconsists, as is well known, of a pair of converging bars, whichmeasure, by a graduation on them, the contraction of claycylinders that have been heated; this remains permanent,and were it, as Mr. Wedgewood supposed, a function oftemperature alone, would suffice for all practical purposes.Many circ*mstances, however, have interfered with its general employment. The set of clay pieces which were used inthe first instance were made of natural clay found in Cornwall. By these the numbers given in treatises of chemistryfor the fusing points of the more refractory metals were determined, and I think it probable that Mr. Kirwan used themin his researches; Sir James Hall, I think, did not. Mr.371Wedgewood had stated in his memoir that the supply of theclay was inexhaustible; but when the stock first made wasdisposed of, he was unable to find the identical spot whereit had been obtained, and the contraction of the new specimen was different. Had he used it as he did the other, andmerely directed the employment of a number by which tomultiply the indications of the scale, no inconvenience wouldhave resulted; but he thought he might bring it to an identity by adding ' earth of alum, ' obtained by precipitatingalum by carbonate of potassa; a product which Apjohn orKane will tell you is very far indeed from being pure alumina.This unhappily made the contraction irregular, and the claypieces much less capable of resisting a high heat. Its indications were found to differ from those of the first set, andit fell into disuse , especially for two reasons . The first thatWedgewood had assigned to his degrees, a value enormouslytoo large, so that he supposed the extreme heat of a furnaceto be about 30000 of Fahrenheit, when it is only 4000 .Many years since, in our Transactions, I had pointed outthis error, and corrected it, with tolerable success, as waslong afterwards confirmed by Daniell and Prinsep . The second, that a long exposure to a low heat produces the samecontraction as a short exposure to a high. This is said bySir James Hall to have been established by Dr. Kennedy,whose experiments, however, are no where published; andI confess that I doubt the fact. Guyton De Morveau haseven made an observation which may account for the mistake.He found that similar pieces exposed for half an hour in apowerful furnace, one surrounded by siliceous sand, theother by powdered charcoal, marked 90 and 60, in consequence ofthe different conducting powers of these media.Now it is possible that the Scotch philosopher may haveoverlooked this influence, and not allowed time enough forthe higher temperature to be fully transmitted . The pyrometers of Daniell and others which have since been conVOL. II. I372trived, are so much more cumbrous and elaborate than this,that I hope it may yet be revived; and if so, the chemists ,who may construct pieces for themselves, would find it usefulto compare them with Wedgewood's old standard. A singlecylinder is sufficient for this, as after measuring a comparatively low temperature, it will still contract when submittedto a higher. This I know to have been one of the originaland genuine set presented to the late Mr. Edgeworth by itsinventor, and therefore, independent of its probable utility ,precious as a relic oftwo such men, and still more so as thegift of our illustrious countrywoman to a body, of whosescientific triumphs she is proud, and in whose welfare I knowher to be deeply interested."April 24, 1843."-"T. R. ROBINSON.RESOLVED, That the letter be referred to Council, forspecial notice and attention.H. Smith, Esq. exhibited an ancient dress , found in abog at a considerable depth, near the Abbey of Kilkenny.A number of interesting antiquities , found at Ballyrowan ,in the Queen's County, by Mr. Harrison, were presented bythe Rev. B. I. Clarke, to the Academy.The thanks of the Academy were presented to Mr. Clarkefor his donation.Sir Wm. Betham made a communication on the antiquityof certain languages.DONATIONS.Astronomical Observations made with Ramsden's ZenithSector, and Catalogue ofthe Stars which have been observedat the different stations of the Ordnance Survey in England373and Scotland. London, 1842. Presented by the MasterGeneral ofthe Hon. Board of Ordnance.Ordnance Survey ofthe County ofClare, in seventy- sevensheets, including the Title and Index. Presented by His Excellency the Lord Lieutenant.Battle ofMagh Rath. Presented by the Irish Archæological Society.Memoires de la Société de Physique et d'Histoire Naturelle de Genéve. Ninth volume. 1841 , 1842. Presented bythe Society.On the Public Institutions for the Advancement ofa*gricultural Science which exist in other Countries. By CharlesDaubeny, M. D. Presented by the Author.Transactions of the Cambridge Philosophical Society.Vol. VII. Part 3. Presented by the Society.Proceedings ofthe Academie Royale de Bruxelles. Nos.1 to 9 inclusive. Vol. IX.Comptes Rendus des Seances de l'Academie des Sciences.Nos. 1 to 7 inclusive, from 2 Janvier to 13 Fevrier, 1843.Presented by the Academy.Annales de l'Observatoire Royale de Bruxelles, Tome II .Presented by M. Quetelet.Archives du Museum d'Histoire Naturelle de Paris. Livraison 3. Presented by the Museum.

PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1843.May 8.No. 40.SIR WM. R. HAMILTON, LL.D. , President , in the Chair.I. G. Abeltshauser, Esq. was elected a member of theAcademy.The special thanks of the Academy were voted to MissEdgeworth for her donation of Wedgewood's Pyrometer.Professor Mac Cullagh read the following communication.On the Laws ofMetallic Reflexion, and on the Mode ofmakingExperiments upon Elliptic Polarization.Several years ago, as the Academy are aware, I made anattempt to investigate the laws according to which light isreflected at the surfaces of metals, and I then proposed certain formula which represented, with sufficient accuracy, allthe facts and experiments which I was able to collect uponthe subject (see the Proceedings of the Academy, vol. i . p . 2,October, 1836; Transactions, vol. xviii. p. 71 , note) . Butin order to test these formulæ satisfactorily, it was necessary to obtain measurements far more exact than any thathad previously been made; and for this end I devised aninstrument, which was constructed for me by Mr. Grubb,and ofwhich a brief description has been given in the Proceedings, vol. i. p. 159. I regret to say, however, that noVOL. II . 2 K376thing of much consequence has yet been done with theinstrument. Some preliminary trials of its performance wereindeed made in the summer of 1837 , and the results of oneof these shall presently be given; but an accidental strainwhich it suffered , while I was preparing to undertake a seriesofexperiments, caused me to discontinue the observationsat the time; and being then obliged to superintend theprinting of my essay on the Laws of Crystalline Reflexionand Refraction (Transactions R. I. A. , vol. xviii. p. 31 ) ,my attention was drawn afresh to this latter subject, respecting which some new questions suggested themselves, whichI thought it right to discuss in notes appended to the essay.I was not afterwards at leisure to take up the experimentalinquiry, until the beginning of the year 1839, when I beganto think of putting the instrument in order for that purpose.The strain which it had suffered rendered some slight alterations necessary; and I now resolved to make additions toit also, with the view of operating upon the fixed lines ofthespectrum, as a few trials had convinced me that measuressufficiently precise could not be obtained without employinglight of definite refrangibility. I wished, moreover, to takethe opportunity which the nature of the proposed experiments presented, of verifying the theory of Fresnel's rhomb,or rather of verifying, by means of the rhomb, the formulæwhich Fresnel has given for computing the effects of totalreflexion, when it takes place at the common surface oftwo ordinary media. I wrote therefore to Munich for several articles which I wanted; among others , for a set ofrhombs cut at different angles, out of different kinds ofglass. But while I was waiting for these some monthselapsed, and in the meantime I got sight of a new theory,which, from its connexion with my former researches, possessed more immediate interest, and the pursuit of which,in conjunction with other studies and various engagements,caused me again to suspend the inquiry respecting the lawsof metallic reflexion. I allude to the Dynamical Theory377of Crystalline Reflexion and Refraction, communicated tothe Academy in December, 1839 (Proceedings, vol . i . p. 374) .This was followed soon after by a general Theory of TotalReflexion (Proceedings, vol. ii . p. 96) , founded on the sameprinciples. The latter theory, forming a new departmentof physical optics, and involving the solution of questionsnot previously attempted, was analytically complete when itwas communicated to the Academy in May, 1841; but itsgeometrical development has since required my attentionfrom time to time, and has not yet been brought to that degree of simplicity of which it appears to be susceptible(see Proceedings, vol. ii . p. 174). Indeed I have found that,in this instance, the geometrical laws of the phenomena areby no means obvious interpretations of the equations resulting from the analytical solution of the problem; and inendeavouring to verify such supposed laws I have often beenled to algebraical calculations of so complicated a nature thatit has been impracticable to bring them to any conclusion,and I have been obliged , from mere weariness, to abandonthem altogether. On returning, however, to the investigation,after perhaps a long interval of time, I have usually perceived some mode of eluding the calculations, or of directlydeducing the geometrical law; and when the theory comesto be published in its final form, no trace of these difficultieswill probably appear.From the causes above-mentioned, combined with frequent absence from Dublin, the researches which I hadentered upon, respecting the action of metals upon light,have been hitherto interrupted; and as it may still be sometime before they are resumed, I venture, in the meanwhile,to submit to the Academy the results already spoken of,which were obtained on the first trial of the instrument, andwhich afford the best data th can yet be had for comparison with theory.The results, it must be confessed , are those of very2 K2378rough experiments, made one evening (about the monthof July, 1837) in company with Mr. Grubb, before I hadreceived the instrument from his hands, and merely withthe view of showing him, when it was finished , the kind ofphenomena that I proposed to observe with it, and the modeof observing them. But the instrument was so far superior(in workmanship at least) to any apparatus previously employed for this sort of experiments, that it was impossible,without great negligence in using it , not to obtain measuresof considerable accuracy. I did not, however, at the time,set much value on these measures, because I expected shortlyto possess a series of observations made with every possibleprecaution; but having chanced to preserve the paper onwhich they were noted down, I was tempted , a few days ago,to try how farthey agreed with my formula; and the agreement turns out to be so close, that I think myself justified inpublishing them. Besides, it will be curious hereafter tocompare them with more careful measurements.Before we proceed, however, to the details ofthe experiments, it may be well to give the formulæ in a state fitted forimmediate application . The light incident on the metalbeing polarized in a certain plane, let a denote the azimuthof this plane, or the angle which it makes with the plane ofincidence; and as the reflected light will be elliptically polarized, or, in other words, will perform its vibrations in ellipsesall similar and equal to each other, as well as similarly placed ,put 0 for the angle which either axis of any one of theseellipses makes with the plane of incidence, and let ẞ be anotherangle, such that its tangent may represent the ratio of oneaxis of the ellipse to the other. Then when the optical constants м and X (of which I suppose the first to be a numbergreater than unity, and the second an angle less than 90°)are known for the particular metal, the angles 0 and ẞ maybe computed for any value of a, at any given angle of incidence, by the following formulæ:379tan 20 =(v' -v) sin 2a2f+ ( v' + v) cos 2a'sin 28 =2gsin2av' +v + 2fcos 2acos X, g== (x + 1 );M M.(A)in which ƒand g are constant quantities given by the expressions sin x, (B)and v, v' are quantities depending on the angle of incidencei, in the following way. Let i' be an angle such thatsin i=sin i'Mcosx andputcosicosi'= μl,then will 1 ƒ² + g² V = vμบ(c)(D)(E)The angles and ẞ are given by immediate observation withthe instrument; and from their values at any incidence, andfor any azimuth a ofthe plane of primitive polarization, wecan find the constants м and x, which we may afterwardsuse to calculate the values of 0 and ẞ for all other incidencesand azimuths, in order to compare them with the observedvalues. It is indifferent, in the formulæ, whether ◊ be referred to the major or the minor axis of the elliptic vibration,as also whether tan ẞ be the ratio of the minor to the majoraxis, or the reciprocal of that ratio; but in what followswe shall suppose to be the inclination of the plane of incidence to that axis, which, when a is 45° or less , is alwaysthe major axis; and ẞ shall be supposed less than 45°, inorder that its tangent may represent the ratio of the minoraxis to the major.Whenthe azimuth a is equal to 45°, the formulæ (A) becometan 20 =v'. ν2f2º sin23 =

v'+vfrom which we may deduce the remarkable relationtan26 gcos 20(F)(G)380showing that, in the case supposed, the ratio of tan 23 tocos 20 is independent of the angle of incidence. In the experiments which I made with Mr. Grubb this azimuth wasalways 45°; and the following Table contains the resultsof observation compared with those obtained by calculationfrom formulæ (F). The experiments were made upon asmall disk of speculum metal; and in the calculations I havetaken м = 2.94, x = 64° 25′.Value of 0. Value of B. Angle of Incidence. Observed. Calculated. Observed. Calculated.65° 27° 55' 27° 53' 28° 0' 28° 0'70 15 41 15 44 33 7 33 175 - 8 45 - 9 16 34 10 34 680 -30 15 -29 25 27 0 26 5384 -37 22 -37 25 16 47 17 17The light used in these observations was that of a candleadmitted through small(See the description ofplaced at a short distance, and wasapertures at the ends of the tubes.the instrument in the Proceedings, vol. i. p. 159). The Nicol'sprism inthefirst tube having been secured in a position in whichits principal plane was inclined 45° to the plane of incidence,and the two arms having been set at the proper angle withthe surface of the metal, the Fresnel's rhomb and the Nicol'sprism in the second tube were moved simultaneously, untilthe image of the candle became as faint as possible . Hadlight perfectly hom*ogeneous been employed, the image couldhave been made to vanish altogether; but instead of vanishing, it became highly coloured , and our rule in observing wasto make the blue at one side of it, and the red at the other,equally vivid, so as to get results which should belong, asnearly as possible, to the mean ray of the spectrum. Whenthis was done, the angles 0 and ẞ (subject however to certaincorrections which will be hereafter explained) were respectively read off from the divided circles belonging to therhomb and the prism. The observations were made at large381incidences, because it is within the last thirty degrees ofincidence that the phenomena go through their most rapidchanges.If we now cast our eyes on the above table, making dueallowance for the uncertainty arising from the dispersion ofthe metal, we shall be struck with the agreement betweenthe calculated and observed numbers. The differences aregreatest in the last two observations, which however werereally the first; for the observations were made in the inverse order of the incidences, and their accuracy may haveimproved as they went on. However that may be, the differences are quite within the limits of the errors of observation; and they are actually less than those which Fresnelfound to exist between calculation and experiment in themuch simpler case ofreflexion at the surface of a transparentordinary medium, when he proceeded to verify the formulawhich he had discovered for computing the effect of suchreflexion. See the Table which he has given in the Annalesde Chimie, tom. xvii. p. 314.It may seem extraordinary that these experiments shouldhave been in my possession for nearly six years, before I became aware of their close agreement with my formulæ; butthe fact is, that I did not regard them with much interest,because, from the circ*mstances in which they were made, Idid not expect more than a general accordance with theory.And even now, I am in no haste to infer the absolute exactitude of the formulæ, though they are found to representthe phenomena so well. It was far more allowable to inferthat the formula of Fresnel was exact in the case just mentioned, though it appeared to represent the phenomena lessperfectly. For, to say nothing of the small number of our experiments, the present is a much more complicated case, andthe phenomena depend on two constants instead of one , so thatthe formulæ might be slightly altered , and yet perhaps continue to agree very well with rough experiments. Wherethere is only one constant this is not so probable. Again,382there is one of the quantities in the preceding formula whichmay be greatly altered without producing more than a slighteffect on the values of 0 and B. This quantity is the ratioof sin i to sin i' , which, according to the value in formula (c) ,is a number so large as to make the angle i' always small, sothat its cosine never differs much from unity; and thereforeif the above ratio were taken equal to any other large number, the value of µ in formula ( D) would remain nearly thesame, and consequently the values of 0 and ẞ would be butslightly changed.It is with regard to the value of μ as a function of theincidence that I entertain the greatest doubts, and if anydefect shall be found in the formulæ I think it will be here.The relations (c) and ( D) , from which u may be deduced interms of i , were not indeed adopted without strong reasons;but I am not entirely satisfied with them, because, when wereverse the problem, and seek to determine the constants Mand x from the observed values of 0 and ẞ at a given incidence, the results are rather complicated and involved,though the approximate determination is easy enough. Asthe formulæ are in a great measure built upon conjecture,we must not be disposed to receive them without thestrongest experimental proofs; and it will certainly requireexperiments of no ordinary accuracy to decide some of thequestions which may be raised respecting them.When plane-polarized light is incident on a metal, if itsvibrations be resolved in directions parallel and perpendicular to the plane of incidence, the effect ofthe reflexion is tochange unequally the phases of the resolved vibrations; andit may be useful to have the formula which express the difference of phase after reflexion , and the ratio of the amplitudesof vibration. Put for the difference of phase; and supposing, for simplicity, the incident light to be polarized inan azimuth of 45°, let o be angle less than 45°, such thattan σ may represent the ratio of the reflected amplitudes383respectively perpendicular and parallel to the plane of incidence; then we shall have2g tan = cos 2σ =-2f;v'+ v(H)from which we may infer thatsino tan 2σ = (1)or that the product on the left side of the last equation isindependent ofthe angle of incidence. It is to be observedthat the relations (G) and ( 1) are independent of the value ofμ, and may hold good though that value should require to bechanged.All the preceding formulæ are merely mathematical consequences of those which I published long ago in the Transactions of the Academy (vol. xviii . p. 71 ) . The formulawhich I had previously given in the Proceedings (vol . i. p. 2)are slightly different, and, I think, less likely to be exact,because they are less simple, and do not lead to any of theremarkable relations which may be deduced from the others.Having had occasion, in the course of the few experiments which I made with the instrument before mentioned,to study the nature of Fresnel's rhomb, which constitutes animportant part of it, I shall here describe the method whichmust be followed in order to obtain true results, when therhomb is employed in observations on light elliptically polarized. A ray in which the vibrations are supposed to beelliptical is given , and what we want is to determine theratio ofthe axes of the elliptic vibration, and their directionswith respect to a fixed plane passing through the ray; inother words, to determine the angles which we have denotedby ẞ and 0 in the case of a ray reflected from a metal. Forthis purpose the ray is admitted perpendicularly to the surface at one end of the rhomb, and after having suffered twototal reflexions within, passes out perpendicularly to the sur-384face at the other end. Then causing the rhomb to revolveabout the ray, we shall find two positions of it in which theemergent light will be plane- polarized , these positions beingreadily indicated by a Nicol's prism interposed between therhomb and the eye; for such a prism, by being turned roundthe ray, can make the light totally disappear when it isplane-polarized , but not otherwise. These two positions ofthe rhomb will be exactly 90° from each other; in one ofthem the principal plane of the rhomb (the plane of reflexionwithin it) will be parallel to the major axis of the elliptic vibration, and the angle which it makes with the plane of incidence on the metal will be equal to 0: while in the sameposition the angle which the principal plane makes with theplane of polarization of the emergent ray (as given by theNicol's prism) will be equal to ß. In the other position, theprincipal plane will be parallel to the minor axis of theelliptic vibration, and the corresponding angles will be equalto 90° -0 and 90° -ẞß respectively. This, however, proceedson the supposition that the rhomb is exact. When it is notso, which is of course the proper supposition, and a very necessary one inthe experiments with which we are concerned,there will still be, generally speaking, two positions of it inwhich the emergent ray will be plane- polarized, or in whicha disappearance of the light may be produced by the Nicol'sprism; but these positions will no longer be 90° from eachother, nor will the principal plane, in either of them, coincidewith an axis of the elliptic vibration . If we now measure theangles between the different planes as before, and denotethem by ' , ' in the first position, and by 90° —0″, 90° —ß”in the second, we shall find that 0' and 0" are unequal, butwe shall have ẞ' equal to ẞ" . The values of 0 and ẞ willthen be given by the formula0' +0"0 =2cos 28 =cos23'cos (0' -0")(K)The error ofthe rhomb may easily be found. Supposing385the vibrations to be resolved in directions parallel and perpendicular to its principal plane, the rhomb is intended toproduce a difference of 90° between the phases of the resolved vibrations, or to alter by that amount the differenceof phase which may already exist; but the effect really produced is usually different from 90° , and this difference, whichI call ɛ, is the error of the rhomb. The value of ε is given bythe formulatan ɛ =sin (0'-- 0")tan 28; (L)and as the error of the rhomb is a constant quantity, wehave thus an equation of condition which must always subsist between the angles ' -0" and B. For any given rhombthe sine of the first of these angles is proportional to thetangent of twice the second, and therefore 0' -0" constantlyincreases as ẞ increases towards 45° , that is, as the axes ofthe elliptic vibration approach to equality. When ẞ is equal to45°-ε, we have 0′— 0" =90°; and for values ofẞ still nearerto 45°, the value of sin ( 0′ - 0″) becomes greater than unity,that is to say, it becomes impossible, by means of the rhomb,to reduce the light to the state of plane-polarization . Thisis a case that may easily happen with an ordinary rhombin making experiments on the light reflected from metals;because at a certain incidence, and for a certain azimuth ofthe plane of primitive polarization, the reflected light will becircularly polarized .The rhomb which I used in the experiments tabulatedabove, was made by Mr. Dollond, and was perhaps as accurate as rhombs usually are; it was cut at an angle of 544°, asprescribed by Fresnel. Its error was about 3º, and the valueof 0'-0", at the incidence of 75° , was about 7°. But inanother rhomb, also procured from Mr. Dollond, and cut atthe same angle, the value of ' -0", under the same circ*mstances, was about 20°, and the value of & was therefore386about 8°. The angle given by Fresnel was calculated forglass of which the refractive index is 1.51; and the errorsofthe rhombs are to be attributed to differences in the refractive powers of the glass . I was not at all prepared toexpect errors so large as these when I began to work withthe rhomb, and they perplexed me a good deal at first,until I found the means of taking them into account, and ofmaking the rhomb itself serve to measure and to eliminatethem. The value of the rhomb as an instrument of researchis much increased by the circ*mstance that it can thus determine its own effect, and that it is not at all necessary toadapt its angle exactly to the refractive index of the glass.It may also be remarked, that this circ*mstance affords amethod of directly and accurately testing the truth of theformulæ which Fresnel has given for the case of total reflexion at the separating surface oftwo ordinary media; for wehave only to measure the angle of the rhomb and the refractive index of the glass, and to compute, by Fresnel's formula, the alteration which the rhomb ought to produce inthe difference between the phases of the resolved vibrations;which alteration of phase we may then compare with thatdeduced, by means of the formulæ (K) and (L) , from directexperiment.If, in each position of the rhomb, we measure the anglewhich the plane of polarization of the emergent ray makeswith the plane of incidence on the metal, and call the twoangles respectively y', y", we shall havey' = 0' - B', y" = 0″ + ß' ,and therefore(M)y' + y" = 0' +0″ = 20, 2B' = y" —y' + 0' — 0"; (n)from which it appears that if the rhomb were perfectly exact,that is, if 0′ and 0" were equal to each other, the anglewould be half the sum of y' , y", and the angle ẞ half theirdifference. It would then be sufficient to measure the anglesy' and y", in order to get 0 and ẞ accurately. And if the387rhomb were erroneous, the true value of 0 would still behalf the sum of y', y"; but the true value of ẞ would not bediscoverable without measuring the angles 0' , 0", by the helpof which it can be deduced from the second of formulæ ( N) ,combined with the second of formulæ (K) . Nor can we discover whether the rhomb is erroneous or not, without measuring the angles 0', 0"; and therefore as these angles mustbe measured in any case, the former method of determiningand ẞ is to be preferred .In making experiments on elliptically polarized light, aplate of mica or any other doubly refracting crystal, placedperpendicular to the ray, may be used instead of Fresnel'srhomb. If the thickness of the crystalline plate be such thatthe interval between the two rays which emerge from it isequal to the fourth part of the length of a wave, for lightof a given refrangibility, the plate will, for such light, perform all the functions ofthe rhomb; the principal plane ofthe rhomb being represented by the plane of polarization ofone ofthe emergent rays. But unless the light be perfectlyhom*ogeneous, this method is liable to great inaccuracy inpractice, since the effect of the plate in producing or alteringthe difference of phase between the two rays which interfereon their emergence from it, is inversely proportional to thelength of a wave, and will therefore be extremely differentfor light of different colours, and will change very perceptibly even within the limits ofthe same colour. It is true,the effect of the rhomb also varies with the colour of thelight: but this variation is trifling compared with that whichexists in the other case. It was for this reason that I employed the rhomb in my experiments, instead of a crystallineplate. The apparatus, however, is much simplified by usingsuch a plate; and if any one chooses to do so, and to workwith hom*ogeneous light, he must take care to follow, in everyrespect, the directions which I have given for conductingexperiments with the rhomb. The two cases are precisely388similar; and if it be necessary not to neglect the errors ofthe rhomb, it is certainly not less necessary to take into account those which may arise from a want of accuracy in thethickness of the plate, considering how difficult it is to makethe thickness correspond exactly to the particular ray whichwe wish to observe.I have been induced to enter into these particulars, respecting the mode of making experiments on elliptic polarization, because the subject is one which has not hithertobeen studied; nor does it seem to have occurred to any onethat any precaution was requisite beyond that of getting therhomb cut as nearly as possible at the proper angle, or thecrystalline plate made as nearly as possible of the properthickness . This, indeed, was quite sufficient for ordinarypurposes. For example, light polarized in a plane inclined45° to the principal plane of the rhomb or of the plate,would, as far as the eye could judge, be circularly polarizedafter passing through either of them. Notwithstanding acertain error in the angle of the one, or in the thickness ofthe other, such light would, when analysed by a rhomboid ofIceland- spar, give two images always sensibly equal in intensity. But an error which could not be at all detected in thisway, might produce a very great effect in such experimentsas those uponthe metals, and, for the purpose of comparisonwith theory, might render them entirely useless, if in thefirst method of observing we relied upon one set of observations, taking (suppose) the values of 0' and B' for the truevalues of 0 and ẞ; or if, inthe second method, we contentedourselves with merely measuring the angles y' and y".The necessity of attending to the foregoing rules and remarks will appear from an examination of the experimentsof M. de Senarmont, published in the Annales de Chimie,tom. lxxiii. pp. 351-358. In these very elaborate experiments, which were made upon light reflected at various incidences from steel and speculum metal, the author followed389a plan similar to that which I have adopted, and which, in ageneral way, I had previously sketched in the Proceedingsof the Academy (vol . i . p. 159) . There was this difference,however, that he used a plate of mica instead of Fresnel'srhomb. Now as he worked with common white light, theuse of the mica plate must have rendered two kinds of errorsunavoidable. In the first place, it would be impossiblealways to take the observations for the same ray of thespectrum; and next, as a consequence of this, the thickness of the plate would be generally inexact for the particular ray to which the observations happened to correspond.If the thickness of the plate were exact for a certain ray, itwould be very sensibly inexact even for the neighbouringparts of the spectrum; and as the part of the spectrum towhich the observations belonged was continually changing,the results obtained for different incidences and azimuthswould not be comparable with each other, even though, ineach separate case, the error of the plate were allowed forand eliminated. The values of 0, however, as determinedby M. de Senarmont, would be correct, so far as this error isconcerned; those of ẞ alone would be erroneous. For thevalues of 0 were determined in two ways: by measuring theangles 0′, 0″, and taking their sum for 20; also by measuring the angles y' , y", and taking their sum for the same quantity. Now each of these methods gives a true value of 0,because by the preceding formulæ we have 20 0′ + 0″ =' +y"; and this accounts for the agreement, shown by thetables of M. de Senarmont, between the values* of 20 obtained by these different methods. But the values ofẞ werededuced from the angles y', y", by simply making their dif

• Or rather the values of 180° +20; because the angle w, the double of which

appears in the tables of M. de Senarmont, is equal to 90° +0. The angles whichhe calls y, and y, are equal to 90º + y″ and 90º + y' respectively. It thereforecomes to the same thing, whether the one set of angles or the other is supposedto be measured. The letter ẞ has the same signification in both notations.390ference equal to 2ß; and we see by the second of formulæ (N)that, when the plate is not of the proper thickness , this valueof2ẞ is erroneous by the whole amount of the angle ' 0",the difference between B' and ß being supposed so small thatit may be neglected . As M. de Senarmont proceeded on thecommon assumption that when the thickness of the plate hasbeen adjusted to that part of the spectrum to which the observations are intended to refer, it may afterwards, throughthe whole series of experiments, be regarded as exact, henecessarily conceived 0' and 0" to be the same angle; and itwas on the principle of taking an average between two measures ofthe same quantity, that he made the supposition200' + 0", which happened to be correct. When therefore he found 0' and 0" to be different, he of course lookedupon the difference as merely an error of observation , whichit would be superfluous to tabulate. Not having the valuesof this difference, therefore, we have not the means of immediately correcting the values of 28. But as observationswere made for several azimuths at each angle of incidence,we may use the values of 0to determine those ofß; for whenat any incidence (except that of maximum polarization , where0=0 for all azimuths) the values of 0 are known for two givenvalues ofa, we can deduce the corresponding values ofß, without any other theory than that ofthe composition of vibrations.The values of ẞ so deduced must indeed be expected to bevery inaccurate, partly because of errors in the observed valuesof0, partly because the observations in different azimuths donot answer to the same ray of the spectrum; but they willbe accurate enough to show the great amount of the errorcommitted by neglecting the difference ' -0". For example, putting 0。 and Bo for the values of and ẞ whena = 45°, M. de Senarmont gives, at the incidence of 60° uponsteel, 20。 = 64° 15′ (taking the mean of his two determinations), and for the azimuths 55°, 30°, 25° , he gives 20 equal to88° 5′, 37° 2′, and 29° 36′ respectively. Combining these391values of 20 in succession with that of 200, we get for 23.the series of values 32° 38' , 33° 28' , 34° 30'; the differencesbetween which are to be attributed to the causes abovestated. The mean value of 23, thus found is 33° 32'; whileits value, as given by M. de Senarmont, is only 28° 41'.The difference 4° 51' is the value of 0' 0", which, dividedby the tangent of 2ß。, gives 7° 19′ for the mean value of ɛ,the error of the mica-plate corresponding to that part of thespectrum which was observed at the incidence of 60°.At incidences nearer the angle of maximum polarization,the errors are probably much greater. Beyond that anglethey again diminish , and in some cases they almost vanish.Thus, at the incidence of 85° upon steel, with the valueof 20, and the value of 20 corresponding to a = 20°, we get,by computation, a value of 2ß, which differs only by a fewminutes from that given by M. de Senarmont. Nearly thesame thing happens at the same incidence when we takea = 25°. In these cases therefore the results belong to thatparticular ray for which the thickness of the plate wasexact.The observations of M. de Senarmont on speculum metalwere not carried beyond the incidence of 60° . He statesthat he was unable to observe at higher incidences, on account of the uncertainty arising from the dispersion of themetal; but though this cause operated in some degree, hisembarrassment must have been really occasioned by the increasing magnitude ofthe difference 0′ - 0″, as he approachedthe angle of maximum polarization; that difference beingperhaps twice as great as in the case of steel. My own experiments on speculum metal were all made, as has beenseen, at incidences greater than 60°.The experiments of M. de Senarmont do not at all agreewith the formulæ; and therefore I have been obliged to analyse his method of observation, and to show that it couldnot lead to correct results. It is to be regretted that hisVOL. II. 2 L392method was defective, as the zeal and assiduity which hehas displayed in the inquiry would otherwise have put us inpossession of a large collection of valuable data.I shall conclude by saying a few words respecting the intensity of the light reflected by metals. The formulæ forcomputing this intensity have been given in the Transactionsof the Academy, in the place already referred to; but theymay be here stated in a form better suited for calculation .If we suppose and to be two angles, such thatMcotan = "cotan Mu,μand then take two other angles w, w' , such that(0)cos sin 24 cos x, cos ' sin 24' cos x, (P)we shall haveT = tan 1 w, T = tan w ', (Q)where is the amplitude of the reflected rectilinear vibration,when the incident light is polarized in the plane of incidence,and is the amplitude of the reflected vibration when theincident light is polarized perpendicularly to that plane; theamplitude of the incident vibration being in each case supposed to be unity. Hence when common light is incident, ifits intensity be taken for unity, the intensity I ofthe reflectedlight will be given by the formula1 = (tan² + tan² w '). (R).If with the values of м and x determined by my experiments we compute, by the last formula, the intensity of reflexion for speculum metal at a perpendicular incidence, inwhich case μ = 1 , we shall find 1.583. This is considerably lower than the estimate of Sir William Herschel, who,in the Philosophical Transactions for 1800 (p. 65) , gives .673as the measure of the reflective power of his specula. Thesame number, very nearly, results from taking the mean ofMr. Potter's observations (Edinburgh Journal of Science ,New Series, vol. iii . p. 280). It might seem therefore that393the formula is in fault; but I am inclined to think that themetal which I employed had really a low reflective power.Its angle of maximum polarization was certainly much lessthan that ofthe speculum metal used by Sir David Brewster(Phil. Trans. 1830, p. 324), who states the angle to be 76°,whereas in my experiments it was only about 7310; and anyincrease in this angle, by increasing the value of м, raisesthe reflective power. On the other hand, the maximum value ofẞ (when a = 45° ) was greater than that given by SirDavid Brewster, namely, 32°; and any increase in ẞ tendsalso to increase the reflective power. Now it is not unreasonable to suppose that the highest values of both angles maybe most nearly those which belong to the best specula; andaccordingly if we take 76° for the incidence of maximum polarization, and retain the maximum value ofß, namely 34° 37′,which results from my experiments, we shall get м = 3.68 ,x = 66° 16' , and the value of I at the perpendicular incidencewill come out equal to .662, which scarcely differs from thenumber given by Herschel.It is clear from what precedes that the optical constantsare different for different specimens of speculum metal, andthis is no more than we should expect, from the circ*mstance that the metal is a compound, and therefore liableto vary in its optical properties from variations in the proportion of its constituents; but I am disposed to believe thatthe same thing is generally true, though of course in a lessdegree, ofthe simple metals, so that in order to render thecomparison satisfactory, the measures of intensity shouldalways be made on the same specimen which has furnished.the values of M and x. There is one metal, however, withrespect to which there can be no doubt that the experimentsof different observers are strictly comparable, when it is pure,and at ordinary temperatures; I mean mercury. For thismetal Sir David Brewster states the angle of maximum pola-394rization to be 78° 27' , and the maximum value of ß, whena = 45°, to be 35°; from which I find м= 4.616, x = 68° 13′ ,and, at the perpendicular incidence, 1.734. Now Bouguerobserved the quantity of light reflected by mercury, but not ata perpendicular incidence. His measures were taken at theincidences of 69° and 7810, for the first of which he gives, bytwo different observations, .637 and .666; for the second, bytwo observations, .754 and .703, as the intensity ofreflexion.(See his Traité d'Optique sur la Gradation de la Lumière,Paris, 1760; pp. 124, 126) . If we make the computation fromthe formula, with the above values of м and x, we find thequantities of light reflected at these two incidences to be, asnearly as possible, equal to each other, and to seven-tenthsofthe incident light, the intensity of reflexion being a minimum at an intermediate incidence; and if we suppose thesequantities to be really equal at the incidences observed byBouguer, we must take the mean of all his numbers, which is.69, as the most probable result ofobservation. This resultdiffers but little from one ofthe two numbers given by him ateach incidence, and scarcely at all from the result ofcalculation.The angle at which the intensity of reflexion is a minimum, when common light is incident, may be found from theformula11( + ) ( + ) = (m - i) + B )-4cosx, ( ) MM--M. √ (ƒ²which gives the value ofu, and thence that ofi. This incidencefor mercury is, by calculation, 75° 15', and the minimum value of 1 is .693, which is less than its value at a perpendicularincidence by about one-eighteenth ofthe latter. Accordingto the formulæ, the reflexion is always total at an incidenceof 90°.Rev. Charles Graves communicated certain extracts from395a work of the late Dr. Cheyne, on a Deranged State oftheFaculty of communicating by Speech or Writing. *Dr. Allman read a paper " on a New Genus of Hydraform Zoophytes."The author discovered the animal on which he foundedthe new genus in the Grand Canal near Dublin, in October,1842. The genus of which this zoophyte constitutes as yetthe only known species, will find a place in the family ofthetubulariada, and occupies a position between coryne andtubularia, differing from the former in the possession ofpolypedome, and from the latter in the scattered arrangement of its tentacula. The tentacula, as in both the lastmentioned genera, are filiform; and in this character a pointof distinction is at once found between the new genus andHermia, Johnst.aTo the new zoophyte Dr. Allman assigned the nameCordylophora lacustris.May 22.SIR WM. R. HAMILTON, LL.D. , President, in the Chair.Right Hon. the Earl of Dunraven was elected a memberof the Academy.Dr. Osborne read some observations on the deprivationof the faculty of speech while the intellect remains entire,and in which the defect does not arise from paralysis of thevocal organs. The communication was intended as a sequel

• This work having been since published, the extracts are not here given.

396to Dr. Cheyne's observations read at the last meeting, andwas chiefly intended to refer to a case published by Dr. Osborne, which afforded some peculiar opportunities of investigating the nature of this affection.The subject of this case was a gentleman of about 26years of age, and of very considerable literary attainments.He was a Scholar of Trinity College, and also a proficientin the French, Italian, and German languages. When residing in the country, one morning, after bathing in a neighbouring lake, he was sitting at breakfast, when he suddenlyfell in an apoplectic fit. A physician was immediately sentfor, and after being subjected to the appropriate treatment,he became sensible in about a fortnight. But although restored to his intellects, he had the mortification of findinghimselfdeprived of speech. He spoke, but what he utteredwas quite unintelligible, although he laboured under no paralytic affection, and pronounced a variety of syllables withthe greatest apparent ease. When he came to Dublin hisextraordinary jargon caused him to be treated as a foreignerin the hotel where he stopped; and when he went to theCollege in quest of a friend he was unable to express his wishto the gate-porter, and succeeded only by pointing to theapartments which his friend had occupied. The circ*mstance of his having received a liberal education , and histractable disposition, rendered this case peculiarly favourable for ascertaining the true nature of the affection, andthe result of Dr. Osborne's observations during severalmonths were as follows:1. He perfectly comprehended every word said to him,and his conduct and habits were those of a man in a soundstate of mind, and were exactly those which his friends statedto be peculiar to him before the seizure. He had no paralysis, and the motions of his mouth and tongue were executed with the force and rapidity of ordinary health.3972. He perfectly comprehended written language. He continued to read his newspaper every day, and when passingevents were spoken of, proved that he had a clear recollectionof all that he read. Having procured a copy of Andral'sPathology in French, he read it with great diligence, havinglately intended to embrace the medical profession.3. He expressed his ideas in writing with considerablefluency, and when he failed it appeared to arise merely fromthe want of the association with spoken language, whichcaused confusion and uncertainty, the words being orthographically correct, but frequently not in their proper places.He translated Latin sentences accurately, and also wrotecorrect answers to historical questions .4. His knowledge of arithmetic was unimpaired, he addedand subtracted numbers of different denominations with uncommon readiness; also played well at the game of drafts.5. His recollection of musical sounds appeared to be unimpaired, for when the tune of Rule Britannia was played hepointed to the shipping in the river.6. His power of repeating words after another personwas almost confined to certain monosyllables; and in repeating the letters of the alphabet he could never pronouncek, q, u, v, w, x, and ≈, although he often uttered those soundsin attempting to pronounce the other letters. The letter ialso he was very seldom able to pronounce.7. In order to ascertain and place on record the peculiarimperfection of language which he exhibited, the followingsentence from the By-laws of the College of Physicians wasselected, viz. " It shall be in the power ofthe College to examine or not examine any Licentiate previously to his admissionto a Fellowship, as they shall think fit." Having set him toread this aloud, he read as follows: " An the be what in thetemother ofthe trothotodoo to majorum or that emidrate eineinkrastrai mestreit to ketra totombreidei to rafromtreido asthat kekistret." The same passage was presented to him in398a few days afterwards, and he then read it as follows: " Bemather be in the kondreit ofthe compestret to samtreis amtreitemtreido am temtreido mestreiterso to his eftreido tum briedrederiso ofdeid dat drit destrest."We observe here those monosyllables which are of mostfrequent use in our language, as the, be, what, in, that, his,and was, along with several syllables almost peculiar to theGerman language, which he was engaged in studying at thetime ofthe apoplectic seizure; but the main feature in thecase was, that although he knew when he spoke wrong, yetthat he was unable to speak right, notwithstanding he articulated very difficult and unusual syllables .As in this case the recollection of the meaning of wordswas retained, and it was proved that there was no paralyticaffection interfering with pronunciation, but that even in theact of endeavouring to imitate another person, he could notpronounce the right word, Dr. Osborne concluded that theaffection was not (as has been usually described) a loss ofthefaculty of language or of the memory of names, while thememory ofthings remains, but that it consisted in a loss ofthe recollection how to use the vocal apparatus.In stammering it is obvious that the patient knows themode in which the word is to be pronounced; he begins itrightly, but is prevented from finishing it by debility orspasm on the part of the muscles, causing them to resist hisefforts. In this patient, on the contrary, the words which hecould write, and understood perfectly, he was unable to commence the first syllable of, and instead of them utteredwords compounded from other languages. His ear affordedhim very little assistance, as his attempts to repeat what hadbeen read were scarcely better than his reading. The organs were not paralysed, neither were they affected byspasm, nor was he ignorant of the sounds to be uttered: itonly remains then that he was ignorant of the art of pro-399ducing those sounds, and as he was previously in possessionof this art, we are justified in asserting that he forgot it.It may appear unaccountable why we should be liable toforget the use of the vocal organs, but never forget the useof the other voluntary muscles. Thus while we have thoseinstances of persons pronouncing one word when they intended another, we have no instance of an individual runningwhen he wished to stand , or leaping when he wished to sitdown. This, however, admits of being adequately explained ,by the nerves concerned in the muscular apparatus of speechbeing derived from the brain and highest portions of thespinal cord, and consequently liable to be disturbed by apoplectic affections; while the nerves of the limbs being derivedfrom the cervical plexus, or lower portions of the spine, areunaffected, except by such causes as may produce paralysis.Dr. Osborne referred to the Ephimerides Curiosæ for acase in which the art of writing was retained , while that ofspeaking was lost; and also alluded to that of Zacharias inthe Sacred Scriptures, who, although deprived of speech, isrelated to have written " The child's name is John."Those instances which have been recorded of personsafter wounds or apoplectic seizures ceasing to speak theirusual language, and resuming the use of some other language with which they had been familiar at a former period ,appear to be of the same nature as the present. The recollection of one language, and its train of associate actionsbeing lost, it was most probable that the vocal organs shouldmove in that train to which they had formerly been accustomed ,and fall into the use of another language. It is highly probable that a similar occurrence would have taken place inthis patient if he had only cultivated one language besidesEnglish, but having been conversant with five languages,the muscular apparatus ranged among them, forming a kindof polyglot jargon, which was formed without any rule, wasinconsistent with itself, and wholly unintelligible.VOL. II. 2 M400Although Dr. Osborne did not enter upon the medicaltreatment of the case, yet he considered that the effect ofthe plan adopted to recover his speech afforded an additionalproof that this patient had not lost the faculty of language,but only the art or knack of speaking. He commencedlearning to speak de novo like a child, by repeating afteranother person first the letters of the alphabet, and subsequently words. This was a very laborious task. Sometimeshe was able to pronounce words which at other times hefound impracticable, but his progress may be estimated byhis repeating after another the same By-law of the Collegeof Physicians in the following terms: " It may be in thepower ofthe College to enhavine or not ariatin any Licentiateseviously to his amission to a spolowship as they shall thinkfit." A month or two afterwards he repeated the same Bylaw perfectly well, with the exception of the word power,which on this occasion he called prier. This gentlemansoon afterwards went to the country, where in a few monthshe was carried off by a fever, and Dr. Osborne learned nofurther particulars respecting him after he left Dublin.Sir William Hamilton remarked that Dr. Robinson's meanrefractions, published in the second Part of the NineteenthVolume ofthe Transactions of the Academy, might be represented nearly by the formula,R = 57,546 tan ( 0-4" XR);or by this other formula,R cot0 +R2 sin 3",8 = 57,346;(1)(2)R being the number of seconds in the refraction corresponding to the apparent zenith distance 0, when the thermometeris 50°, and the barometer 29,60 inches.The first formula seems to give a maximum positive deviation from Dr. Robinson's Table, of about a quarter of asecond, at about 80° of zenith distance; it agrees with the401Table at about 83° 10'; is deficient by a second at about84° 30'; and by " at 85°.The second formula, which may be reduced to logarithmiccalculation by the equations,log tan 20 = log tan 0 + 2,81296,log R = log tano + 3,24657,(3)does not agree quite so closely with Dr. Robinson's Table,in the earlier part of it; but the error, positive or negative ,seems never to exceed half a second, within the extent ofthe Table, that is, as far as 85°.It appeared to Sir W. H. worth noticing, that the resultsof such (necessarily) long and complex calculations , as thosewhich Dr. R. had made, could be so nearly represented byformulæ so simple: of which, indeed, the first is evidentlyanalogous to Bradley's well known form, but differs in itscoefficients. The second form is more unusual, and gives(approximately) the mean refraction as a root of a quadraticequation. It has been used (with other logarithms) byBrinkley, for low altitudes.DONATIONS.Address to the Geological Society of London. By Roderick J. Murcheson, F. R. S. A. Presented by the Author.Report ofthe Meeting of the British Association held atManchester in 1842. Presented by the Association.Statutes relating to the Admiralty, to the 8th of Geo. III.Presented by Captain Portlock.Proceedings ofthe Glasgow Philosophical Society. 1841-1842. Presented by the Society.Memoirs published by the Society of Sciences in Holland.Vol. II. Second Series.II.Proceedings ofthe American Philosophical Society . Vol.Parts 24 and 25.Transactions ofthe American Philosophical Society. Vol.VIII. New series. Parts 2 and 3. Presented by the Society.402Fifth Annual Report ofthe Loan Fund Board in Irelandfor 1843. Presented by the Commissioners.Communication to the Right Hon. Sir Robert Peel, Bart.By Jeffries Kingsley, Esq. Presented by the Author.Bulletin des Sciences de la Societé Vaudoise des SciencesNaturelles. Nos . 1-4. Presented by the Society.Sur les Figures Roriques et les Bandes Coloriées produitespar l'Electricité. Par M. P. Riess. Presented by the Author.Expériences sur la non caloricité propre de l'Electricité.Sur les relations qui lient la lumiere a l'Electricité.Sur les travaux recents qui ont en pour objet l'etude de lavitesse de propagation de l'Electricité. Par M. Le Prof.Elie Wartmann. Presented by the Author.Memoirs ofthe Literary and Philosophical Society ofManchester. New Series. Vol. VII. Part 1. Presentedby the Society.List of Premiums ofthe Society for the Encouragement ofArts, Manufactures, and Commerce, for 1843-45. Presentedby the Society.Transactions of the Geological Society ofLondon. Second Series. Vol. VI. Part 2. Presented by the Society.PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1843. No. 41.June 12.SIR WM. R. HAMILTON, LL.D. , President, in the Chair.Sir William Betham read the following letter from SirRichard O'Donel, Bart.:" MY DEAR SIR WILLIAM,66 April 24th, 1843."I have to apologise for all the trouble I havegiven you about the Caah, but several circ*mstances havecometo my knowledge within the last few days, which induceme to desire that it should be placed in the Royal IrishAcademy, next to the Cross of Cong; but I would not takeany step in the matter without first consulting you, andhaving done so, I write you this note to request you will beso good as to make known my wishes to the Dublin Societyupon the subject, and to have it removed to the Royal IrishAcademy, upon their taking charge of it as my property,placing it during the day beside the Cross of Cong, andhaving it each night placed in a fire proof box." I again beg leave of you to pardon me for all this trouble, and to accept my thanks for your kindness at all times,and believe me,"Dear Sir William," Sir William Betham,Record Tower, Castle."VOL. 11.66 Very sincerely yours," RICHARD O'DONEL.2 N404RESOLVED, That the thanks of the Academy be givento Sir Richard O'Donel, Bart. , for his valuable deposit, andthat the custody of it be accepted by the Academy on theterms proposed by him.Sir Wm. Betham gave an account of the Caah.Professor Kane read a notice of some recent Determinations ofthe Heat developed during the Formation of certainCompounds of Chlorine , by Dr. Andrews.The present results were obtained by a similar methodto that described in the last volume of the Transactions ofthe Academy. The chlorine, however, was employed in thedry state, and the compounds being formed without the presence of water, the heat of combination was deduced from asingle direct experiment. In the case of potassium, an important modification of the apparatus was required, whichwill be described when the full details of the experimentsare communicated to the Academy. The numbers in the firstcolumn are the immediate results of experiments, and express, in degrees of Fahrenheit's scale, the heat producedduring each reaction, in reference to the chlorine as unit,that is , the degrees through which a weight of water equalto that ofthe combining chlorine would be raised by the heatdeveloped in the formation of each compound. The numbers in the second column express the same heat, referredto the combining metal as unit, and are deduced by calculation from the others.KCl .. 5379° .. 5954°.SnCl2.. 1621 ° .. 1346°.Sb₂ + Cl .. 1570° .. 1145°.As₂ + Cl3.. 1268° .. 898°.Dr. Allman read a notice of a new species of Linaria.This plant was discovered growing on the banks of theRiver Bandon, and Dr. Allman considered it sufficiently dis-405tinct to entitle it to rank as a new species. Specimens oftheplant collected by Dr. Allman were seen in London by Mr.H. C. Watson, who recognized them as identical in specieswith a Linaria, gathered by himself in two English localities ,and, moreover, that they corresponded with the AntirrhinumBauhin of Gaudin's Flora Helvetica, L. Italica, Koch. Inaccordance with these views, a paper by Mr. Watson appeared in the second Number of Sir W. J. Hooker's LondonJournal of Botany, adding L. Bauhini to the Flora of Britain.To the claim, however, of L. Bauhini to be admitted intothe British Flora, Dr. Allman could not assent; so far atleast as this claim depended on the identity of the Irish withthe Continental plant. He had carefully examined the IrishLinaria, and convinced himself not only of its distinctnessfrom L. Bauhini, but of its claim to rank as a new species.To Linaria repens it is closely allied , indeed there is somedifficulty in separating it from this plant as a distinct species.Dr. Allman, however, conceived that specific characterswould be found in the flowers, which not only differ in colourfrom those of L. repens, but also in their larger size, and inthe greater relative as well as absolute length of the spur.To the new Linaria he gave the specific name sepium, anddescribed it as follows:LINARIA sepium. Lin. radice repente, foliis subglaucislineari-lanceolatis, calcare incurvo corollam æquante, seminibus trigonis.Radix repens. Caulis erectus simplex v. subramosus,Paniculatus. Folia subglauca, lineari-lanceolata , sparsa,inferiora sæpe verticillata . Bractea lanceolatæ, pedicellobreviores, Calycis lacinia lanceolatæ. Flores in paniculam exracemis erectis constantem dispositi, et odorem suavem attenuem exhalentes. Calcar incurvum corollam æquans, labium superius, tubus et calcar grisei, striis palidé purpureiseleganter signati: labium inferius diluté luteum, striis palidé purpureis et parum distinctis notatum: palatium villis2 N 2406saturatè luteis vestitum, villis purpureis quemque margineminvestientibus, Capsula globosa, dehiscens superne pluribusvalvulis lanceolatis. Semina nigra, trigona, lateribus inæqualibus muricatis, marginibus in alas tres productis.A L. repente differt hæc species calcare longiore, corollâmajori et labio inferiori luteo; a L. vulgari discrepat floribusminoribus corollâ striis signatâ et toto flore, præter labiuminferius et palatium, coloris lutei experti: ad hoc semina trigona signum certum præstant quo hæc species a L. vulgaridignosci potest; ab Antirrhino Bauhini differt caule erectiori,foliis angustioribus, colore florum pistillo glabro et seminibustrigonis.Habitat in sepibus juxta flumen Bandon. -FlorebatJunio, Julio et Augusto 4.Rev. Dr. Kennedy Bailie commenced the reading of apaper on " Certain Greek Inscriptions copied on the Sitesof Ancient Teos and Aphrodisias in Asia Minor.”DONATIONS.Journal of the Franklin Institute. Vols. III. and IVThird Series. Presented by the Institute.Proceedings of the Zoological Society of London. Part10. 1843. Presented by the Society.Tribes and Customs of Hy- Many. By John O'Donovan,Esq. Presented by the Irish Archæological Society.Astronomische Nachrichten. Nos. 462-477.Annales des Sciences Physiques et Naturelles d'Agricultureet d'Industrie, publiées par la Société Royale d'Agriculture,&c. de Lyon. Tomes I. II. and III. Presented by the Society.Second Mémoire sur les Kaolins. Par M. Brongniart.Presented by the Author.407June 26.SIR WM. R. HAMILTON, LL.D. , President, in the Chair.Present, His Excellency Earl De Grey, Lord Lieutenant,Visitor ofthe Academy.Dr. Kennedy Bailie read in continuation the Account ofhis Researches in Ancient Teos and Aphrodisias, in AsiaMinor.Previously to entering on his selection of notices withrespect to the Teian, &c. inscriptions, he thought it properto offer a few remarks on that part of his former essay whichrelates to the subject of the inscriptions from Sardes andPergamus.The passages more particularly referred to are those inpages 132-4, and 149-50, on which certain observations weremade either explanatory of, or modifying, the author's conclusions, as expressed therein. The result in the case oftheSardian titulus has been, that it must no longer be considered as referrible to the ages of Hadrian or ofthe Antonines,as he was at first led to suppose; and in that of the Pergamenian, that the document may be so interpreted as not to bein anywise connected with the question of Hadrian's adoptionby Trajan.The new readings illustrative of these points were submitted to the notice of the Academy.Theauthorthen proceeded to a detail of his researches onthe sites of the ancient Teos and the neighbouring port- townof Cherræïdæ, which is mentioned by Strabo. This last heconsiders as occupied by the modern village of Sighadjék.The most interesting ofthe inscriptions which he broughtfrom these sites is a fragment of one of an early date, atleast coeval with those which Chishull has published in hiscelebrated work on the Antiquities of Asia, from copies408made by the late Sir William Sherard in 1709 and 1716. Itrelated, as far as can be collected from the extremely mutilated state ofthe monument, to a treaty ofAsylumship (àovλía)between the inhabitants of this district of Asia Minor andcertain other States of Greek origin, amongst which thereare fragments of the names of the Agrigentines, the Coans,the Polyrrhenians ( of Crete) , also of the people of Delphi.This notice was concluded with a translation of theTitulus, which contained such supplementary matter as theauthor deemed requisite to complete the sense.He then proceeded to notice two other inscriptions, oneofwhich he regarded as marking the site of the Temple ofBacchus, in Teos, of which Vitruvius has made mention;and the other as a remnant of the inscribed monuments ofthe ancient Chalcis, which lay contiguous to Teos.The first of these is remarkable, from its containing anotice ofthe election of a female of rank to serve the officeof High Priestess of Asia.The second informs us of the existence ofa Gerusia, orHouse of Assembly for the Seniors, in the city to which itbelonged. Whether this was Chalcis (as conjectured above),or Teos, is uncertain.In proceeding to Gheyerah (the representative of Aphrodisias in Caria) , the site of Tralles was noticed; as also werethe Tituli, which Poco*cke and others have copied from theruin at present existing in the ancient acropolis.TheTemple ofAphrodite, extensive remains of which stillexist, in Aphrodisias, was then noticed; as also the probablesite of the Agora. Near this the first of the Aphrodisian inscriptions was copied, which is remarkable from its containing notices of a gradation in dignity amongst the Archons ofthe city, as also amongst the Neopæi, or Trustees of theTemple of Aphrodite.The inscription in honour of Constantius and one of hiscolleagues, over the west portal, was next explained, and409reasons were assigned for supposing that the name of Julian,the Apostate, had been erased by the Christian inhabitantsof the city, from this monument.The next inscription which was noticed contains an allusion to the office of Asiarch, which led the author of theMemoir to offer some explanations in reference thereto, principally on the mode of election to, and the duties, of, thatstation.The next brought under consideration was a fragment, capable of being restored so as to present the first two petitionsofthe Lord's Prayer; a supposition in perfect consistencewith the history of the town.Several others were also noticed; the most remarkableand interesting of which was a tomb-inscription of considerable length, copied from the eastern side of the rampart.The discussion of this led to many remarks on the modeadopted amongst the Greek colonists of Asia Minor to express degrees of descent, on the terms of their sepulchralarchitecture, and on the laws regulating tomb- property.Connected with this subject was a series of observationson the office of the Stephanephora. This appears to havebeen partly of a civil nature, partly pontifical, in accordancewith which the right of wearing diadems was granted tofunctionaries of this class, as to the Flamines amongst theRomans.The Memoir closed with some details respecting a seriesof reliefs, which the author discovered on the exterior of thesouthern wall. These, though placed in juxta- position, didnot all refer to the same subject. There are two interposed,which appear to be altogether symbolical in their meaning,or at least to possess a mythical character, and to have beenintended as illustrations of some mythical circ*mstance.A suggestion was offered, that perhaps it would beworthy the attention of archæologists, to adopt means tohave these sculptures removed from their present position,410and deposited in some museum. They appeared to the author to be curious and valuable specimens of ancient art, andare, in all probability, connected with the mythical legendsof the Cretan people, with whom the early inhabitants ofAphrodisias were closely connected.The Rev. Dr. Todd, V. P. gave an account of a Stonewith an Ogham Inscription, which was found with manyothers in a cave at Fortwilliam, in the county of Kerry, andsent up to the Provost and Senior Fellows of Trinity College.After having given a short account of the different kindsof Ogham spoken of by Irish grammarians, and exhibitedthe key usually given for reading the particular kind ofOgham to which the inscription on the stone found at Fortwilliam belongs, Dr. Todd proceeded to show the inapplicability of this key to the interpretation of the inscription.The whole subject of the Ogham inscriptions, he stated, wasone which was involved in great obscurity, and althoughvery abundant materials exist for investigating it, it has neveryet been fairly examined. Several treatises on the subjectare to be found in our ancient MSS. , but no Irish scholarseems as yet to have had the courage to enter upon thestudy of them. Numerous inscriptions on stones, similar tothat now exhibited to the Academy, are also to be found,particularly in the south and west of Ireland, but accuratecopies of these inscriptions are no where accessible. Dr.Todd suggested this as a suitable subject for a prize, if everthe Academy should return to the former practice of offeringa prize for an essay on a given subject. In this case, however, he recommended that the prize should be offered , notfor the best essay or theory for the explanation of the Oghamcharacter, but, in the first instance, for the most accurateand best authenticated collection of copies, or fac similes, ofthe inscriptions themselves.The following engraving gives a correct view of the stone,411which is four feet five inches high, and in its broadest partat the base four feet six and a half inches in circumference,and an exact copy of the inscription: 0000000AYE°0/.!..TreadRANLON00 00 DODD DODO 0000000 00000dinom etiãocarpoud andof emin JaimeDuNayerDebMr. Griffith read a notice by Mr. Hemans, of a Dislocation in the Calp near Killester.The President, on presenting to Dr. Kane the Cunningham Medal, awarded to him for his Researches on the Natureof Ammonia, gave an account of the progress of his discoveries.412It is now my duty to inform you, that a Cunningham Medal hasbeen awarded bythe Council to Dr. Robert Kane, for his Researcheson the Nature and Constitution ofthe Compounds of Ammonia, published in the First Part of the Nineteenth Volume of the Transactions of this Academy. It would, indeed, have been much moresatisfactory to myself, and doubtless to you also, if one of yourVice-Presidents, who is himself eminent in Chemistry, had undertaken the task which thus devolves upon me, of laying before you asketch of the grounds of this award; but at least, my experience ofyour kindness encourages me to hope, that while thus called uponofficially to attempt the discharge of a duty, for which I cannotpretend to possess any personal fitness, or any professional preparation, I shall meet with all that indulgence of which I feel myself tostand so much in need.Although, in consequence of the variety of departments ofthought and study which are cultivated in this Academy, and theimpossibility of any one mind's fully grasping all, it is likely thatmany ofits members are unacquainted with the details of chemistry,yet it has become matter of even popular knowledge, that in generalthe chemist aims to determine the constitution or composition ofthe bodies with which we are surrounded, by discovering the naturesand proportions of their elements. Few need, for instance, to betold that water, which was once regarded as itself a simple element,and which seems to be so unlike to air, or fire , or earth, has beenfound to result from the intimate union of two different airs orgases, known by the names of oxygen and hydrogen, of which theone is also, under other circ*mstances, the chief supporter of combustion, is an ingredient ofthe atmosphere we breathe, and is closelyconnected with the continuance and healthful action of our ownvital processes, by assisting to purify the blood, and to maintainthe animal heat; this same gas combining also, at other times, withsome metals to form rusts, with others acids, with others againalkalies and earths, entering largely into the composition of marbleand of limestone, and, in short, insinuating itself, with a more thanProtean ease and variety, into almost every bodily thing around usor within us; while the other gas which contributes to composewater, though endowed with quite different properties , is also ex-413tensively met with in nature, especially in organized bodies, and inparticular occurs as an element in that important substance, on theconfines of the mineral and organic kingdoms, to which the Researches of Doctor Kane relate; ammonia being, as all chemistsadmit, a compound of hydrogen and nitrogen, which last- namedgas is well known as being the other chief ingredient (besides oxygen) of atmospheric air.Again, it is generally known, to those who take an interest inphysical science, as a truth which is almost the foundation ofmodern chemistry, that the elements of bodies of well- marked anddefinite constitutions, such as pure ( distilled) water, or dry (anhydrous) ammonia, are combined, not in arbitrary, but in fixed anddetermined proportions; for example, the oxygen contained in anyquantity of pure water weighs exactly, or almost exactly, eighttimes as much as the hydrogen contained in the same quantity, butoccupies (when collected and measured) a space or volume onlyhalf as great; and the nitrogen contained in any given amount ofdry ammoniacal gas, is to the hydrogen with which it is combined,by weight as 14 to 3, and by volume in the proportion, equallyfixed,of 1 to 3.Yet such results as these, respecting the constitution of compound bodies, however numerous and accurate they may be, arestill not sufficient to satisfy the curiosity, or to terminate the researches of chemists. They aspire to understand, if possible, notonly the ultimate constitution of bodies, or the elements of whichthey are composed, and the proportions of those elements, but alsothe proximate constitution of the same bodies, or the manner inwhich they arise from other intermediate and less complex compounds. Water, for instance, is believed to enter, in many cases,into composition with other bodies, as water, not as oxygen andhydrogen. Has ammonia any such component, which itself iscomposite? It is admitted to consist of one volume of nitrogen,combined with three of hydrogen. Can any order be discovered inthis combination, any proximate constituent, any simpler and earlierproduct, from which the ammonia is afterwards produced? Untilexperiments decide, it appears not impossible, may seem even notunlikely, that nitrogen may combine (more intimately than by mere414mixture) not only with thrice but with twice or once its own volumeof hydrogen, and that thus other substances may be formed, fromwhich, by the addition of new hydrogen, ammonia may result. Itis interesting, therefore, to inquire whether either of these conceivedpossibilities is actually realized in nature; whether these two important gases do ever actually combine with each other in either ofthese two proportions. In the symbolic language of chemists, asusually written in these countries, the compound NH, is well known,being no other than ammonia; but does NH* or does NH, exist?An eminent French chemist, M. Dumas, in examining a substance, which he called oxamide, and which was one of the resultsof the action of oxalic acid on ammonia, was led to the conclusion,that the last mentioned compound of nitrogen and hydrogen, namely NH,, does really exist in nature, and he proposed for it the nameof amide. The same chemist considered it also to exist in thesubstance formed by heating potassium in ammoniacal gas; andthe same combination, amide, had been (I believe) regarded as aproximate constituent of certain other compound bodies, such asurea, sulphamide, and carbamide, before Dr. Kane's researches onthe White Precipitate of Mercury. Yet it has been judged byBerzelius, that the investigations of Dr. Kane have assisted in animportant degree to establish the actual existence (der wirklichenexistenz) of amide, or of amidogene (as Kane prefers to call it,from its analogy with oxygen and cyanogen), and have thrownmuch light upon its chemical history and relations.In fact, the body oxamide, which seems to have first led Dumasto infer the existence of amide, was one of those organic compounds, respecting which it has often been found difficult, by chemical inquirers, to pass with confidence from the empirical to therational formula; from the knowledge of the ultimate elements(or of those which are at present to be viewed as such), and of theproportions in which they combine, to a satisfactory view respectingthe proximate elements, or intermediate and less complex combi-

• The compound NH, or as it is otherwise better written, HN, has been suspected to exist, as one of the proximate elements of melamine and of some connected bodies. See Gregory's edition of Turner's Chemistry, 1840, page 757.

415nations on which the final result depends. Oxamide may be, andwas considered to be, probably composed of amide and carbonicoxide (in the foregoing notation, NH, +C₂O₂); but it was perceivedto admit also* of being possibly compounded of nitric oxide and acertain combination of carbon and hydrogen (NO, +C₂H₂); or ofcyanogen and water ( C, N+H₂O₂) . And even the amidides of potassium (KNH, ) and of sodium (NaNH,) , have, from the energeticaffinities ofthose metallic bases, been thought to prove less decisivelythe existence of amidogene itself, than the amidide of mercury(HgNH, ) discovered by Dr. Kane, in his analysis of the white precipitate ofthe last mentioned metal. (Trans. R. I. A. , vol. xviii. part iii. )Although this precipitate had been long known, and often analyzed, erroneous views (as they are now regarded) were entertainedrespecting its composition, and it had, for instance, been supposedto contain oxygen, till Kane pointed out the absence of this element,and showed, with a high degree of probability, that the proximateelements were the chloride and the amidide of mercury; white precipitate being thus a chlor-amidide of that metal ( HgCl +HgNH2, iftheBerzelian equivalent of mercury be adopted, instead of its double).Ullgren, a friend of Berzelius, obtained the chemical prize from theSwedish Academy of Sciences, for the year 1836, for a paper inwhich, having with great care repeated and varied the experiments,he confirmed this and other connected results of our countryman;and Berzelius himself, in his Report read to the above-mentionedAcademy in 1837, on the recent progress of the Physical Sciencesin Europe (to which Report allusion has been made above), expressed his opinion that these researches of Kane were among themost important of the preceding year. †In the essay for which your Council have awarded the present

• L'Oxamide peut donc, à volonté, être considérée comme un composé de cyanogène et d'eau, ou bien comme un composé de deutoxide d'azote et d'hydrogène

bicarboné, ou bien enfin comme un composé d'oxide de carbone et d'un azotured'hydrogène différent de l'ammoniaque. —Dumas, sur l'Oxamide, &c. Annales deChimie et de Physique, tome xliv. page 142.† Diese Untersuchungen von Kane gehören meiner Ansicht nach zu den wichtigeren des verflossenen Jahres. -Wöhler's German Translation of Berzelius'sReport, Jahres - Bericht über die Fortschritte der physischen Wissenschaften,17th year, page 179. ( Tübingen, 1838) .416

prize, Dr. Kane has pursued his researches on ammonia, and hasshown, with apparently a high probability, that there exist amidides (though not yet insulated) of other* metals besidesm ercury,especially of silver and copper; that is , combinations of these metals with the proximate element amide or amidogene. He has alsogiven, in great detail, a series of analyses performed by him on alarge number of compound bodies, of which some had been imperfectly examined before, while others were discovered by himself.But as it would lead into far too great length, and too minute detail,ifany attempt were made at present to review these laborious processes of analytical chemistry, and as indeed they derive their chiefphilosophical interest from the views with which they have beenassociated , it may be proper to attempt no more than a very brief(I fear that it will also be a very inadequate) sketch of those views.Dr. Kane considers that in ammonia, which, in the usual language of chemists, is said to consist of one atom of nitrogen andthree atoms of hydrogen, one of these atoms of hydrogen is moreloosely combined than the two others with the nitrogen, so as to becapable of a comparatively easy replacement, by many, perhaps byall, of the metals, as well as by organic radicals; the other twoatoms of hydrogen being already, in the ammonia itself, and notmerely in the products of such replacement of hydrogen by metals,combined in a particular way with the one atom of nitrogen, so asto form that substance named amide or amidogene, which was detected by Dumas (as has been mentioned) in performing the analysisof oxamide. From Dr. Kane's own study of the combinations ofthis substance amidogene (H, N) , with metals, he infers it to be acompound radical of feebly electro- negative energy, analogous tothat important one cyanogen (C, N) , of which the discovery by GayLussac has exercised so powerful an influence on modern chemistry.He considers this radical, amidogene, as existing ready formed, incombination with hydrogen, in ammonia; which latter substance isthus, according to him, to be regarded as amidide of hydrogen;and as, in this respect, analogous to water, and to the hydrocyanic, hydro- sulphuric, and muriatic acids, that is, to the oxide,

• Dr. Kane has since made it probable that there exist amidides of palladium

and platinum also. (Phil. Trans. 1842, part ii .)417cyanide, sulphuret, and chloride of hydrogen; from all of whichbodies it is possible, as from ammonia, to expel an atom of hydrogen, and to replace it by an atom of metal,-if indeed hydrogen benot (as there seems to be a tendency to believe it to be) itself ofmetallic nature, notwithstanding its highly rarefied form. By developing this view of the constitution and function of ammonia, Dr.Kane has offered explanations of a large number of replacements ofthat substance by others, some of which replacements ( I believe)were known before, while many have been discovered by himself.One of the most remarkable points in Dr. Kane's views is theway in which he considers the ordinary salts of ammonia. Manyof these are known to contain an atom of water, the existence ofwhich led to the proposition of the very remarkable theory by Berzelius , of the existence in them of a compound metal ammonium,which has not indeed been insulated, but has been found to form,in combination with mercury, a certain metallic amalgam. Dr.Kane looks upon these salts as double salts of hydrogen. He considers them to contain ammonia ready formed, united with a hydratedacid or with a hydrogen acid. He seeks to establish the similarityof the common ammoniacal salts to those complex metallic amidides, whose nature he has developed by analysis.Thus, for example, the well- known body, sal -ammoniac, is, inthe Berzelian view, regarded as chloride of ammonium; but, inthe view put forward by Dr. Kane, it is chlor-amidide of hydrogen.The former view supposes that the ammonia robs the hydrochloricacid of its hydrogen, to form, by a combination with it, a metallicbase, NH,, with whichthe chlorine unites; as this last element combines with the metal sodium, in the formation of common salt. Thelatter view supposes that in the action between hydrochloric acid anddry ammoniacal gas, there is no separation of the chlorine from thehydrogen, no breaking up of a previously existing union, -noovercoming of the affinity which these two elements (chlorine andhydrogen) have for each other; but an exemplification of a generaltendency of chlorides, oxides, and amidides of the same or similarradicals, to unite, and form chlor- oxides, chlor-amidides, or oxamidides. Sal-ammoniac is, according to Kane, a double haloid salt;he looks upon it as being a compound exactly analogous to thewhite mercurial precipitate, which was first accurately analyzed by418himself; the one being HCl + HAd (if Ad be the symbol of amidogene) , while the other is HgCl + HgAd, so that the mercury in thelatter takes the place of the hydrogen in the former.It was, however, in the oxysalts, such as the sulphate of ammonia, that the presence of an atom, or equivalent, of water, orat least of the elements required for the composition of such anequivalent, appears to have suggested to Berzelius the theory, thatwhat seemed to be hydrate of ammonia (NH, +HO) was really oxideof ammonium ( NH₁ + 0). There are, undoubtedly, many temptations to adopt this view, besides the high reputation of its propounder. One is, that it assimilates the constitution of sulphate ofammonia to what seems to be regarded by the greater number ofmodern chemists, as the probable constitution of other sulphates,nitrates, &c. , for example, the sulphate of iron. When greenvitriol is to be formed by the action of sulphuric acid upon iron,it is requisite to dilute the acid with water, before the action willtake place. The hydrogen of the water then bubbles off, but whatbecomes of the oxygen which had been combined with it? Doesit combine immediately, and as it were in the first instance, withthe iron, to form oxide of iron, on which the anhydrous sulphuricacid may act, to produce sulphate ofoxide of iron, according tothe view which seems, till lately, to have been adopted: or doesthis oxygen, from the water, combine rather with the sulphuricacid to produce a sort of oxide thereof, and does this sulphat-oxygenact on the pure metallic iron to form with it a sulphat- oxide, asmany eminent chemists now appear to think? Whatever maybe the final judgment of those who are entitled to form opinions onquestions such as these, it cannot, I conceive, be justly said, thatthe questions themselves are unimportant. They touch on pointsconnected with the philosophy of chemistry, are essentially connected with its theory, and cannot always be without an influenceupon its practice.Now according to the Berzelian view of sulphate of ammonia,that is the salt produced by the mutual action of sulphuric acid,water, and ammonia, this salt is properly a sulphat- oxide of thecompound metal ammonium (NH, +SO ), inthe same way as greenvitriol, on the view last mentioned, is sulphat- oxide of iron419(Fe + SO ), or as sulphate of potash is sulphat- oxide of potassium(K + SO ) , and this analogy is doubtless pleasing to contemplate.Dr. Kane does not entirely reject this Berzelian theory of ammonium; he acknowledges that the substance NH,, which he regards assubamidide ofhydrogen, and compares to some suboxides, possesses metallic properties, and is a proximate constituent of certaincompounds, especially of the ammoniacal amalgam; but he conceives that the evidence for the existence of ammonia itself, inmany of the ammoniacal salts , is too strong to be resisted: and helooks upon the hydrated ammonia, which is found to combine withsulphuric and other oxacids, as being not, in general, oxide of ammonium, but oxyamidide ofhydrogen; the sulphate of ammoniabeing thus a bibasic compound, of which one base is ammonia,while the other base is water.Between the conflicting opinions of such men, supported eachby powerful arguments and analogies, and it will easily be conceived that in so short a sketch as this , and upon such a subject, ithas been found impossible by me to mention even the names of allthe eminent chemists whose experiments and writings should bestudied, by persons inquiring for themselves, —not only do I not venture to express any judgment of mine, but I conceive also that yourCouncil did not desire to express on their part any decision. To justify the present award, it was, I believe, deemed by them sufficient,thatgreat research and great talents had been brought, in the investigations of the author to whom that award has been made, to bearon an important subject, which has derived, from those investigagations, an additional degree of importance. Whatever may be thefinal and unappealable judgment of those persons who shall, atsome future time, be competent and disposed to pronounce it, weneed not fear that the honour of this Academy shall have been compromised by the recognition which the Council have thought itright on the present occasion to make, of that combination ofgeniusand industry, which has already caused the researches of Kane toinfluence in no slight degree the progress of chemical science, andhas won for him an European reputation.The President then presented the Gold Medal to Dr.Kane, and the Academy adjourned for the summer.VOL. II. 20420July 31. (Extraordinary Meeting. )SIR WM. R. HAMILTON, LL.D. , President, in the Chair.RESOLVED, On the recommendation of Council, —Thatthe Treasurer be empowered to sell stock in the 3 per cent.Consols, to the amount of £300, in order to pay Mr. Gill'sbill for printing Transactions to March 16, 1843, amount£264 10s . 4d. , and the rent of the Academy House to 31stJuly, 1843.RESOLVED, On the recommendation of Council, -Thatthe Treasurer be empowered to sell such 3 per cent. stock,being the Cunningham Fund, as shall amount to £50, towards defraying the cost of medals.Sir William Betham presented to the Academy certaincasts from the sculptures on the inside of the tower ofArdmore.Dr. Lloyd having taken the Chair, the President gave anaccount of some researches in the Calculus of Probabilities.Many questions in the mathematical theory of probabilities conduct to approximate expressions of the formthat is,p ==== S.2 tdt et;p = 0(t),O being the characteristic of a certain function which has beentabulated by Encke in a memoir on the Method of LeastSquares, translated from the Berlin Ephemeris, in vol. ii .part 7 of Taylor's Scientific Memoirs; p being the probability sought, and t an auxiliary variable.Sir William Hamilton proposes to treat the equationp = 0 (t)as being in all cases rigorous, by suitably determining theauxiliary variable t, which variable he proposes to call the421argument of probability, because it is the argument withwhich Encke's Table should be entered, in order to obtainfrom that Table the value of the probability p. He showshow to improve several of Laplace's approximate expressionsfor the argument t, and uses in many such questions a transformation of a certain double definite integral, of the form,in which4stπ Sdr S" du en u cos (2s* ruv)-1 = 0 (r ( 1 + v₁ s−¹ + v2 s−² + . . . ) );uU = 1+ a₁ u² + α₂ u¹ + ...v = 1 +ß₁ u² +ß₂u¹ +...while v1, v2, ... depend on a₁, ... ẞ₁ , ... and on r; thusv₁ = & a₁ - B₁r².The function 0 has the same form as before, so that if, forsufficiently large values of the quantity s (which represents,in many questions, the number of observations or events tobe combined), a probability p can be expressed , exactly ornearly, by the foregoing double definite integral, then theargument t, of this probability p, will be expressed nearly bythe formula,t = r ( 1 + v₁ s−¹ +v2 s−²).Numerical examples were given, in which the approximations thus obtained appeared to be very close. For instance, if a common die (supposed to be perfectly fair) bethrown six times, the probability that the sum of the sixnumbers which turn up in these six throws shall not be lessthan 18, nor more than 24, is represented rigorously bythe integralp =2TOSπdx 27448 162) , or by the fraction 7}}};sin 7x (sin 6xsinx \6sinh 665while the approximate formula deduced by the foregoingmethod gives 27449 for the numerator of this fraction, or forthe product 66p; the error of the resulting probability beingtherefore in this case only 6-6. The advantage of the method422is that the quantity which has here been called the argumentofprobability, depends in general more simply than does theprobability itself on the conditions of a question; while theintroduction of this new conception and nomenclature allowssome ofthe most important known results respecting the meanresults of many observations to be enunciated in a simpleand elegant manner.DONATIONS.Historias e Memorias da Academia Real des Sciencias deLisboa. Tome XII. Parte 2.Discurso lido em 22 de Janeiro de 1843 na sessao publica da Academia Real des Sciencias de Lisboa. Por J. J. daCosta de Macedo. Presented by the Academy.Le Petit Agriculteur. Par N. C. Seringe. Presented bythe Author.Astronomical Observations made at the Radcliffe Observatory, Oxford, in 1840. By M. J. Johnson, Esq. Presentedby the Governors.Archives du Museum d'Histoire Naturelle. Tome III.Liv. 3, et Tome II . Liv. 4. Presented by the Museum.Remarks on Safety Lamps. By Doctor Reid Clanny,H. M. R. I. A. Presented by the Author.Transactions of the Royal Society of Edinburgh. Vol.XV. Part 3. Presented by the Society.Proceedings ofthe National Institution for the PromotionofScience at Washington. D. C. for 1840 and 1842. Parts 1and 2. Presented by Thomas Sewall, M. D., Professor ofMedicine in Columbia College, U. S.Memoirs ofthe Chemical Society ofLondon for 1841-3.Vol. I. Presented by the Society.Numismatic Chronicle. No. XXII. Presented by theNumismatic Society.Statistical Returns ofthe Dublin Metropolitan PoliceforPresented by the Commissioners.PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1843.November 13.No. 42.SIR WM. R. HAMILTON, LL.D. , President , in the Chair.Dr. Allman drew the attention of the Academy to certain undescribed peculiarities in the anatomy of Anthocephalus, a genus of Entozoal worms. The points especiallydwelt upon by Dr. Allman were the remarkably definite arrangement ofthe hooks with which the proboscides are furnished, and the singular apparatus destined to effect theretraction and exsertion of the latter organs. The proboscides were described as communicating each with a distincttube, which extending through the entire length of the animal, terminates posteriorly in an oval dilatation, with thickened walls. The retraction of the proboscides consists inan inversion, by which they become invagin*ted in the tubular appendage. This invagin*tion is effected by means ofa muscular filament, which is attached by one extremity tothe internal surface of the cul de sac of the proboscis, andmay be thence traced through the tube as far as the ovalbody in which the latter terminates.The mode by which the exsertion of the proboscides iseffected would appear to be as follows:-These organs,together with their tubular prolongation through the vermicular body of the Entozoon, are filled with a transparentfluid, which during the inversion of the proboscides is exVOL. II. 2 P424pelled into the more posterior parts of the tubular prolongations, and into the oval bodies in which these terminate.Mr. Bergin had pointed out to Dr. Allman the existence ofmuscular fibres in the walls of the oval dilatations. Thecontraction, therefore, of these muscles, will cause the contained fluid to impinge upon the inverted extremity of theproboscis, which will thus be forced outwards, and the proboscis injected with the fluid . The source of this fluid wouldappear to be in the oval bodies themselves, whose structureis, in all probability, glandular, and which, besides possessinga contractile power, by which the contents of their cavitiesare expelled, would seem also to be the secerners of the fluidwhich plays so important a part in the protrusion of theproboscides.The Chair having been taken pro tem. by the Rev. H.Lloyd, D. D., Vice- President,The President read a paper on a new Species of Imaginary Quantities, connected with a theory of Quaternions.It is known to all students of algebra that an imaginaryequation ofthe form 21 has been employed so as toconduct to very varied and important results. Sir Wm. Hamilton proposes to consider some ofthe consequences whichresult from the following system of imaginary equations, orequations between a system ofthree different imaginary quantities:¿² =j² = k² = − 1;ij = k, jk = i, ki =j;jik, kj = — i, ik = −j;(A)(B)(c)no linear relation between i, j, k being supposed to exist, sothat the equationin whichQ = Q',Q = w + ix +jy + kz,a' = w' + ix' +jy' + kx' ,425and w, x, y, z, w' , x ' , y' , z' are real, is equivalent to the fourseparate equations,w = w', x = x', y = y', z = 2.Sir W. Hamilton calls an expression ofthe form Q a quaternion; and the four real quantities w, x, y, ≈ he calls the constituents thereof. Quaternions are added or subtracted byadding or subtracting their constituents, so thatQ + Q' = w + w' + i ( x + x') +j ( y + y ) + k ( ≈ +≈') .Their multiplication is , in virtue of the definitions ( a) ( B) (c),effected by the formulæwhich giveQQ′ = Q″ = w" + ix" + jy" + kz",-w" = ww' — x x' — y y' — z z' ,xwx + xw' + yz' —zy',y' = wy' + yw' + z x' — x z' ,-z = wz' + z w' + xy' — yx' ,(D)w¹¹² +x/¹² + y/¹² + ≈¹¹² = ( w² + x² + y² + ≈²) .(w¹² + x²² + y/² + ≈¹²),and thereforeμ' = μμ' ,if we call the positive quantityμπ= √ w² + x² + y² + x²,(E)the modulus ofthe quaternion Q. The modulus of the product of any two quaternions is therefore equal to the productof the moduli. Letw = μ cos 0,X = sin cos 0,μy= μ sin 0 sino cost,≈= μ sin 0sin & sin;then, because the equations (D) givew'w" + x'x" + y'y" + z'x" = w ( w¹² + x^2 + y²² + 2′²),ww" + xx" + yy" + zz" = w' ( w² + x² + y² + ≈²),(F)2 P 2426we havecos " cos e cos 0' -sin 0 sin e' (cos cos p' + sin o sin o'cos ( 4')),cosecose' cos 0" +sin e' sin 0" (cosp' cos p" + sin o'sin p" cos (4'- 4′'´)) ,cos 0' cos 0" cos 0+sin 0" sin ( cos " cos +sin o″ sino cos ( 4" ))." (G)Consider x, y, ≈ as the rectangular coordinates of a pointof space, and let R be the point where the radius vector ofx, y, z (prolonged if necessary) intersects the spheric surfacedescribed about the origin with a radius equal to unity; callR the representative point of the quaternion Q , and let thepolar coordinates and , which determine R upon thesphere, be called the co- latitude and the longitude of the representative point R, or of the quaternion Q itself; let alsothe other angle ✪ be called the amplitude of the quaternion;so that a quaternion is completely determined by its modulus,amplitude, co -latitude, and longitude. Construct the representative points R' and R", of the other factor o' , and of theproduct q"; and complete the spherical triangle RR′R", bydrawing the arcs RR', R'R", R" R. Then, the equations (G)becomecos "coscos 0 cosesin 0 sin 0' cos RR' ,cos ' cos 0" + sin 0' sin 0" cos R'R",cos 0' cos 0" cos 0 + sin 0" sin 0 CosR" R,and consequently shew that the angles of the triangle RR′R"areR = 0, R'0 ' = 0'′,, R"″ = πT — 0";-(H)these angles are therefore respectively equal to the amplitudes of the factors, and the supplement (to two rightangles) ofthe amplitude of the product. The equations ( D)show, further, that the product-point R" is to the right orleft of the multiplicand-point R' , with respect to the multiplier-point R, according as the semiaxis of + ≈ (or its intersection with the spheric surface) is to the right or left ofthe semiaxis of + y, with respect to the semiaxis of + x:that is, according as the positive direction of rotation inlongitude is towards the right or left. A change in the427order of the two quaternion -factors would throw the product- point " from the right to the left, or from the left tothe right of RR'.It results from these principles , that if RR'R" be anyspherical triangle; if, also, a ẞyγ be the rectangular coordinates of R, a'B'y' those of R' , and a" B" y" of R", the centreof the sphere being origin, and the radius being unity; andif the rotation round +x from + y to + ≈ be of the same(right-handed or left-handed) character as that round RfromR' to R"; then the following formula of multiplication , according to the rules of quaternions, will hold good:{cos R + (ia +jẞ +ky) sin R } . { cos R' + (ia' +jß' +ky) sin R' }= cos R" +(ia" +jẞ" +ky") sin R". (1)Developing and decomposing this imaginary or symbolicformula (1 ) , we find that it is equivalent to the system of thefour following real equations, or equations between realquantities:- cos R" = cos R cos R' (a a' + ßß' +yy') sin R sin Rʼ;-- a" sin R" =asin R cos R' + a' sin R' cos R + (By′ —yẞ′ ) sin R sin R′;ẞ"sin R" ẞ sin R COS R′ +B′sin R' cos R + (y a' — a y') sin R sin R';y" sin R" ysin R cos R' + y'sin R' cos R + ( a ß' — Ba′ ) sin R sin R'.(K)Ofthese equations ( K) , the first is only an expression of thewell-known theorem, already employed in these remarks,which serves to connect a side of any spherical triangle withthe three angles thereof. The three other equations (K) arean expression of another theorem (which possibly is new) ,namely, that a force sin R", directed from the centre ofthe sphere to the point R", is statically equivalent to the system of three other forces, one directed to R, and equal tosin R Cos R' , another directed to R', and equal to sin R′ cos R,and the third equal to sin R sin R' sin RR' , and directed towards that pole of the arc RR' , which lies at the same side ofthis arc as R". It is not difficult to prove this theorem otherwise; but it may be regarded as interesting to see that thefour equations (K) are included so simply in the one formula428(1) of multiplication of quaternions, and are obtained soeasily by developing and decomposing that formula, according to the fundamental definitions (A) (B) (c). A new sort ofalgorithm, or calculus, for spherical trigonometry, appears tobe thus given, or indicated . And by supposing the threecorners of the spherical triangle RR'R" to tend indefinitelyto close up in that one point which is the intersection of thespheric surface with the positive semiaxis of x, each coordinate a will tend to become 1 , and each ẞ and y to vanish,while the sum of the three angles will tend to become=π;so that the following well known and important equation inthe usual calculus of imaginaries, as connected with planetrigonometry, namely,(cos R +isin R) (cos R' + isin R') = cos(R +R') + i sin (R + R),(in which i² = 1), is found to result, as a limiting case, fromthe more general formula (1) .In the ordinary theory there are only two different squareroots of negative unity ( + i and — i ) , and they differ onlyin their signs. In the present theory, in order that a quaternion, wix +jy + ks, should have its square = — 1 ,it is necessary and sufficient that we should havew = 0, x² + y² + s² = + 1;-we are conducted , therefore, to the extended expression,1 = i cosp +j sin o cos + k sin φ& sin 4, (L)which may be called an imaginary unit, because its modulusis = 1 , and its square is negative unity. To distinguish onesuch imaginary unit from another, we may adopt the notation,-iR = ia +jẞ + ky, which gives i = 1,(L')R being still that point upon the spheric surface which hasa, ß, y (or cos p, sino cos , sin 4 sin ) for its rectangularcoordinates; and then the formula of multiplication (1) be-429comes, for any spherical triangle, in which the rotation roundR, from R' to R", is positive,(cos R + iR sin R) (cos R' + i sin R) = — COS R" +iR" sin R". ( 1 )If p" be the positive pole of the arc RR' , or the pole towhich the least rotation from R' round R is positive, then theproduct ofthe two imaginary units in the first member ofthis formula (which may be any two such units) , is the following:iR iRCOS = RR' + ip" sin RR'; (M)we have also, for the product of the same two factors, takenin the opposite order, the expressionin iniR = — COS cos RR' - ip" sin RR',) N(which differs only in the sign of the imaginary part; andthe product ofthese two products is unity, because, in general,(w +ix +jy +k≈) (w−ix−jy− kz) = w² +x² +y² +x²; (0)we have, therefore ,iRig. in iR = 1 , (P)and the products iR iR and iR iR may be said to be reciprocalsof each other.In general, in virtue of the fundamental equations of definition, (A), (B) , (c) , although the distributive character ofthe multiplication of ordinary algebraic quantities (real orimaginary) extends to the operation of the same name in thetheory of quaternions, so thatQ (Q' + Q) = QQ' + qq" , &c. ,yet the commutative character is lost, and we cannot generally write for the new as for the old imaginaries,QQ' = Q'Q,since we have, for example, jiij. However, in virtue ofthe same definitions, it will be found that another importantproperty of the old multiplication is preserved , or extended4:30to the new, namely, that whichmay be calledthe associativecharacterof the operation, and whichmay havefor its typethe formula q. q'q″ . q, q¹ — QQ' . Q″ Q'"' QIV;thus we have, generally,Q. Q'Q" = QQ' . q",Q. Q'Q" Q""' = QQ' . Q" Q" = QQ'q" . q'"',(Q)(a)and so on for any numberof factors

the notation

o qʻoʻbeingemployedto expressthat one determinedquaternion,which, in virtueof the theorem(Q) , is obtained, whetherwefirst multiplyQ" as a multiplicandby o' as a multiplier, andthenmultiplythe productoʻq" as a multiplicandby Q as amultiplier

or multiply

first o' by Q, and theno″ by qoʻ.Withthe helpof this principle, we mighteasilyprovetheequation(P), by observingthat its first member12 - 2 = 1 .In the samemannerit is seen at once that• ¿½(n−1) i₂ = ( —1)",•2i₂iz i₂ =(P)whateverininn points . in iR" upon . in" igthe!” . . spheric . . surfacemay be denotedby R, R' , R", R" , ... R( -1); and by combiningthis principlewith that expressedby (M), it is not difficultto provethatfor any sphericalpolygon, R R' ... R(n -1) , the followingformula holdsgood:...(R)(cos R + i sin R) (COS R' + i sinR') (COS R" +i " sin R")(cos (n-1) + (n-1) sin R( -1) = (- 1)",whichincludesthe theorem( 1') for the case of a sphericaltriangle, and in whichthe arrangementofthe n points maybe supposed, for simplicity, to be such that the rotationsroundR from R′ to R", roundR' from R″ to R" , and so on,are all positive, and each less than two right angles, thoughit is easy to interpretthe expressionso as to includealso thecaseswhereany or all of theseconditionsare violated.Whenthe polygonbecomesinfinitelysmall, and therefore431plane, the imaginary units become all equal to each other,and may be denoted by the common symbol i; and the formula (R) agrees then with the known relation , thatπ - R + T - R' +π— R" + ... +π- R( -1) = 2π.Again, let R, R', R" be, respectively, the representativepoints of any three quaternions Q, Q' , Q", and let R , R , Rbe the representative points of the three other quaternions ,qa' , a'a″ , qa'a" , derived by multiplication from the formerthen the algebraical principle expressed by the formula (Q)may be geometrically enunciated by saying that the twopoints R, and R, are the foci of a spherical conic whichtouches the four sides ofthe spherical quadrilateral RR′R″ R,„,;and analogous theorems respecting spherical pentagons andother polygons may be deduced, by constructing similarlythe formulæ (q'), &c.In general, a quaternion Q, like an ordinary imaginaryquantity, may be put under the form,Q = µ (cos 0 + ( − 1 ) ³ sin 0) = w + ( −1)³r,-)s(provided that we assign to ( -1)³ , or √1, the extendedmeaning (L) , which involves two arbitrary angles; and thesame general quaternion Q may be considered as a root of aquadratic equation, with real coefficients, namely,Q²-2wQ + µ² = 0, (s')which easily conducts to the following expression for a quotient, or formula for the division of quaternions,Q"Q" 2w-μεQQ", (s")ifwe define q-¹q" or to mean that quaternion o' which Qgives the product o", when it is multiplied as a multiplicandby Q as a multiplier. The same general formula (s") of division may easily be deduced from the equation (o), by writingthat equation as follows,432(w +ix +jy +k2)−¹ =wix-jy- kzw² + x² + y² + x²;(0')or it may be obtained from the four general equations ofmultiplication (D) , by treating the four constituents of themultiplicand, namely, w', x', y' , ', as the four sought quantities, while w, x, y, z, and w" , x" y", ", are given; or from aconstruction of spherical trigonometry, on principles alreadylaid down.---The general expression ( s) for a quaternion may be raisedto any power with a real exponent q, in the same manner asan ordinary imaginary expression, by treating the squareroot of 1 which it involves as an imaginary unit i having(in general) a fixed direction; raising the modulus μ to theproposed real power; and multiplying the amplitude 0, increased or diminished by any whole number of circumferences, by the exponent q: thus,n(u (cos +ir sin 0) ) ª = µ¹ (cos q ( 0 +2nπ) + i¸ sing ( 0 +2nt)) , (T)if q be real, and if ʼn be any whole number. For example, aquaternion has in general two, and only two, different squareroots, and they differ only in their signs, being both includedin the formula,(µ (cos 0 + i, sin 0) ) * = µ³ ( cos ( + n )) + i, sin ( + ) ) , ( ')in which it is useless to assign to n any other values than 0and 1; although, in the particular case where the originalquaternion reduces itself to a real and negative quantity, sothat , this formula (T') becomes(−µ)³ = ± µ³ir, or simply ( —µ)³ = µ³ ir, (T )the direction of i remaining here entirely undetermined; aresult agreeing with the expression ( L) or (L') for √ —T. Inlike manner the quaternions, which are cube roots of unity,are included in the expression,2пп32nT 1cos + ir sin 3(T)433i denoting here again an imaginary unit, with a directionaltogether arbitrary.If we make, for abridgment,ƒ(Q) = 1 + 1 + +Q2 Q3 + &c. , 1.2 1.2.3 (v)the series here indicated will be always convergent, whateverquaternion Q may be; and we can always separate its realand imaginary parts by the formula,ƒ(w + ir r) = ƒ(w) (cosr +ir sin ”); (v')which gives, reciprocally, for the inverse function ƒ-¹, theexpressionƒ−¹ (µ(cos 0 + ir sin 0) ) = log µ + ir (0 +2nπ) , (U″)u being any whole number, and logμ being the natural, orNapierian, logarithm of μ, or, in other words, that real quantity, positive or negative , of which the function ƒ is equal tothe given real and positive modulus μ. And although theordinary property of exponential functions, namely,ƒ(Q) • ƒ(Q') = ƒ(q + q'),does not in general hold good , in the present theory, unlessthe two quaternions o and o' be codirectional, yet we mayraise the function f to any real power by the formula(ƒ(w +irr') )ª =ƒ(q(w + i₂ r + 2nπ)) , (U")which it is natural to extend, by definition, to the case wherethe exponent q becomes itself a quaternion. The generalequation,when put under the formQ,¶ = Q1, (v)(f(w +ir r))¹ = ƒ(w' + ir'r'), (v')will then giveq={ w' +in' (r' + 2n'π) } { w−iz (r +2nπ) };w² + (r + 2n π)²2 (v")and thus the general expression for a quaternion q, which is434隆one ofthe logarithms of a given quaternion q', to a given baseQ,, is found to involve two independent whole numbers n andn', as in the theories of Graves and Ohm, respecting the general logarithms of ordinary imaginary quantities to ordinaryimaginary bases .For other developments and applications of the newtheory, it is necessary to refer to the original paper fromwhich this abstract is taken, and which will probably appearin the twenty-first volume of the Transactions of the Academy.November 30. (Stated Meeting.)REV. H. LLOYD, D.D., Vice-President, in the Chair.The Rev. Dr. Todd, V.P., presented to the Academy, inhis name and that of Mr. O'Donovan, a volume containingtracings made from Irish MSS. preserved in the College ofSt. Isidore at Rome, by the Rev. Dr. Lyons, who had sentthem from Rome, some to Mr. O'Donovan, and the remainder to Dr. Todd.The thanks ofthe Academy were voted to Mr. O'Donovanand also to the Rev. Dr. Lyons, for the important servicehe has rendered to Irish literature, by making known theexistence of these MSS.The Rev. Dr. Todd made some remarks on the progressof the Catalogue, made by Mr. Eugene Curry, of the IrishMSS. in the Library of the Academy.The miscellaneous character of the MSS. , almost everyvolume of them containing tracts or poems, wholly unconnected with each other, rendered it impossible to attemptany previous classification . Mr. Curry, therefore, took theMSS. in the order in which they stood on the shelves of theLibrary, hoping that all the important objects of a classifica-435tion might be attained by the means of proper Indexes afterthe work is completed.The method pursued was to give a description of thecontents of each volume, enumerating the several tracts ofwhich it consists, describing its state of preservation , noticing, as far as possible, its defects or imperfections, andidentifying, whenever it could be done, the handwriting ofthe scribe or scribes by whom it had been written. Particularattention has been paid to the history of every importantMS.; the quotations made from it by historians or lexicographers have been verified , and, where practicable, thevarious hands through which it has passed, and the meansby which it became the property of the Academy, have beenaccurately detailed and recorded.In this way many opportunities have occurred ofcorrectingmistakes which have been made by various writers on Irishsubjects -mistakes, which must always be numerous in thehistory of a people, whose ancient literature is still in manuscript, and in a language which is every day becoming more.obsolete and obscure. These mistakes Mr. Curry has alwayscorrected with temper, and with due allowance for the difficulties under which the authors to be corrected must necessarily have laboured; although it must be confessed thatsometimes blunders may be found of a nature well calculatedto try the patience or rouse the indignation of an Irish scholar.Another object of great importance which Mr. Curry haskept steadily in view during the progress of the Catalogue,has been the noticing of other copies of the tracts or poemsdescribed, whenever the existence of such copies was knownto him and his accurate acquaintance with the contents ofthe Irish MSS. of Trinity College, and those in the possession of Messrs. Hodges and Smith, * the only two great collections accessible to him for this purpose, rendered Mr.Curry peculiarly well qualified for such a task.

Since purchased by the Academy.436In reference to the history of the MSS. , of such of them,at least, as are of any high antiquity, it was of great importance to collect together the numerous memoranda,short scraps of poetry, dates, signatures, and other entries,which are frequently to be found on the margins of MSS.These are often mere scribbling, and often written from purewantonness, or for the purpose of trying a pen; but theyvery frequently contain information of singular interest,shewing who were the ancient owners or possessors of theMS. , and sometimes giving facts and dates of which we haveno other record. A most remarkable example of the valueof these apparently trifling scribblings will be found in Mr.Curry's account of the Leabhar Breac, upon whose historythe most important light has been thus thrown.The autograph volume of the Four Masters, which isone of the glories of the Academy's Library, may also bementioned as a MS. , whose history Mr. Curry's researcheshave greatly illustrated . By a comparison of it with the MS.(also an autograph) in the Library of Trinity College, Mr.Curry has succeeded in identifying the handwritings of itsdifferent compilers, and to assign to each the portion oftheseAnnals which he appears to have compiled, or at least tohave transcribed.When any document occurred of peculiar interest, as anhistorical tale, or ancient deed, or singular narrative, Mr.Curry has very generally given an abstract of its contents.This has been sparingly done, from a wish to avoid swellingthe Catalogue to too great a bulk; but it is of more importance than it might seem to be at first view, especially ifthe Catalogue should ever be published, as furnishing to thosewho are at a distance, the means of identifying the worksdescribed with MSS. in other collections.Dr. Todd having read some extracts from Mr. Curry'sCatalogue in illustration of the foregoing remarks, concludedby stating, that about five volumes still remained to be cata-437logued, including the important volumes, the Books of Lecanand Ballymote, whose examination would take some months,and that the Council have therefore been under the necessityof applying to the Academy for a further grant of money toenable Mr. Curry to complete the work.It was resolved by the Academy that the sum recommended by the Council be granted for this purpose.December 11.SIR WM. R. HAMILTON, LL.D., President, in the Chair.Matthew Dease, Esq. , William M'Doughall, Esq., SirMontague Chapman, Bart. , James H. Pickford , M. D. , Edward Bewley, M.D. , and James S. Eiffe, Esqrs. , were electedMembers of the Academy.Professor Kane read a paper on the Chemical Composition of the plants of Flax and Hemp.In those plants which are cultivated for the purpose ofbeingultimately employed as food, it is found that certain constituents are withdrawn from the soil, partly of an organic andpartly of an inorganic character, which give to the plant, orto certain portions of it, the constitution that adapts it forsustaining the animal organism. Thus nitrogen, alkalies,and lastly, phosphates, &c. , are found as components ofplants, and the value of the crop yielded by a certain surfaceofground is proportional, generally speaking, to the materialswhich the crop has taken up. If, therefore, wheat, or oats,or potatoes exhaust a soil, the agriculturist does not sufferthereby, for he is paid for the materials of which they haveexhausted it , and when he replaces that loss of material byfresh manure he but invests a certain capital, to be deliveredat a profit in the next season.Many plants not employed as food, but ancillary to ourcivilization as luxuries , or as utilized in the arts, are similarly438circ*mstanced . Thus when indigo or tobacco is grown, theobject is to obtain the greatest possible development ofthe colouring or ofthe narcotic principle. For this purpose, elementsare necessary ofwhich the soil is thereby deprived , but theimpoverishing of the soil is paid for, by its materials beingsold as the valuable portion of the plant. In such cases,therefore, to sustain the fertility of the soil, a continued supply, from external sources, of the materials which the plantstake up is required . The farmer must supply in the manurethe elements which he sends to market in the grown plants.Dr. Kane then proceeded to point out that this principlewas limited as to certain classes of plants, by the fact, nowclearly established by the concurrent investigations of vegetable physiologists and of chemists, that certain vegetablesubstances, and those of high importance to mankind, werenot formed of materials abstracted from the soil, but wereproduced by the vital action of the plant upon the constituents of the atmosphere. This class of bodies he characterized as being constituted , generally, of carbon, united withhydrogen and oxygen in the proportions which form water.The carbonic acid of the atmosphere, with the watery vapourconstantly existing in it, supplies the elements of sugar, gum,starch, and ligneous fibre, and the oxygen of the carbonicacid, evolved by the vital action of the plants, tends, as it iswell known, to ameliorate the air we breathe. When, therefore, we take the sugar, or the woody fibre of a plant, wehave a material, formed, as to its elements, independent ofthe soil. For its formation is required a plant in healthyvegetation, and for the plant to be in healthy vegetation, itmayrequire to abstract from the soil various materials, so thatthe crop may actually be of a highly exhausting nature. Stillthose materials do not go to the sugar or to the fibre; theyexist in other portions of the plant; and if the sugar or fibrebe the valuable portion of the crop, as in reality usually occurs, the elements which render its production costly are rejected, and let to waste; they do not subserve any future439useful purpose, although nothing should be easier than toapply them thereto.Such is actually, according to Dr. Kane's idea, the condition ofthe growth of one plant ofthe highest importance toagricultural industry in Ireland—that offlax , and also ofanother, which although not now grown here, has been grown withsuccess, and, as he conceives, might still be cultivated with considerable advantage, the hemp. In flax and hemp the valuableportion ofthe plant is ligneous fibre; the purer this fibre is, themore its value increases; yet the pure fibre contains no element derived from the soil. It is well known to be producedsolely by the atmospherical constituents. Hence the intenseexhausting nature of the flax and hemp crops, which makesthem be dreaded by agriculturists, notwithstanding the highmoney value of the crops, arises, according to Dr. Kane,from causes of which the effects may be obviated by attentionto the true conditions of the growth and composition of theplants, so that those fibre- crops, such as flax and hemp,from being the most exhausting and expensive, may be rendered the least injurious to the land, and perhaps amongstthe cheapest that can be grown.As the chemical composition of these plants had neverbeen examined, Dr. Kane devoted himself to the determination, as well of their organic as of their inorganic constituents,and from an extensive series of analyses, of which the details are given in the memoir, arrived at the followingresults:Composition of the stem of hemp, dried at 212°. F.Carbon ·HydrogenOxygenNitrogenAshesVOL. II.•·39.945.0648.721.744.54100.002 Q440Composition of the leaves of hemp, dried at 212° .Carbon •Hydrogen •40.505.98NitrogenOxygenAshes1.82• · · 29.70• 22.00100.00The ashes ofthe hemp plant were found to consist ofPotash • 7.48Soda .72Lime • 42.05Magnesia • 4.88AluminaSilica· .376.75Phosphoric acid 3.22Sulphuric acid 1.10Chlorine 1.53Carbonic acid 31.90100.00Dressed hemp fibre was found to give but 1.4 per cent.of ashes, when dried at 212°. Its organic composition neednot be given, as it is identical with that of ordinary woodyfibre, which is well known. It therefore contains no nitrogen.The characteristic constituents of the hemp plant areseen to be nitrogen and lime. In these it is peculiarly rich ,and with these it is the duty ofthe agriculturist abundantlyto supply it.When hemp is steeped in order to separate the fibrousbark from the internal stem, it is known that the water dissolves certain substances out of the plants, and thereby acquires narcotic properties. Dr. Kane evaporated a quantityof the hemp liquor to dryness, and analyzed the extract so441obtained, in order to trace what action the steeping had exerted on the plant. He found the composition ofthe hempextract, dried at 212°, to be,Carbon • ·Hydrogen28.284.16NitrogenOxygen .• 3.2815.08Ashes 49.20100.00Ifwe exclude the ashes, the organic part consisted ofCarbon · ·HydrogenNitrogenOxygen .•55.668.216.4529.68100.00This composition approaches to that of the azotized animal substances , and surpasses the animal manures usuallysold. The water in which hemp has been steeped containsthus most ofthe nitrogen of the plant, and if poured overthe soil should serve efficiently to restore its fertile powers.The ashes of the hemp extract require also to be noticed ,for the plant, in steeping, gives up to the water especially itssoluble constituents. The ashes of the leaves of hemp contain in 22 parts only 1.77 soluble in water, or 8.05 per cent. ,whilst the ashes of the hemp extract contain in 49.2 parts,29.70 parts soluble in water , or 60.4 per cent. Thus almostall the alkaline constituents of the ashes are dissolved outby the water, whilst the earthy materials remain associatedwith the residual portions of the stem.Dr. Kane next examined the stem, as it remains aftertreatment for the fibre, by steeping and peeling. Dried at212° this hemp residue consisted of2Q 2442Carbon .Hydrogen • •NitrogenOxygenAshes56.806.48.4334.521.77100.00The ashes contained but a trace of alkali, and it is seenthat the nitrogen has almost disappeared.From these researches it is plain that, by the quantity ofnitrogen, of phosphoric acid , of potash, of magnesia, and oflime, which the hemp takes from the soil, it must be, as experience proves it, a highly exhausting crop; but as the materials so abstracted are not found in the valuable fibre, butin the residual stem, the chaff, and the steeping liquor, allthese are available for the purpose of restoring to the soilwhat had been taken up, and in fact, if it were possible tocarry on the processes ofthe preparation of the fibre withoutloss, the same nitrogen and inorganic constituents might, asit would appear from these chemical inquiries and from physiological researches, serve for any number of successivecrops ofhemp; the fibre alone, generated at the expense ofthe atmosphere, being sent out and sold , and thus the cropbe absolutely deprived of all exhausting quality to the soil.Dr. Kane's inquiries regarding the flax plant were of aprecisely similar character to those described already in thecase of hemp, and have led him to similar conclusions affecting the practical culture of this important plant. The general results of his analyses are as follows:Stem of flax dried at 212°; the plant had its usualamount of leaves, but the seed vessels had not ripened .Carbon · ·HydrogenNitrogenOxygenAshes38.72· 7.33• .56• • 48.395.00100.00443There is a great difference here shewn between the composition of the plants ofhemp and flax , though they resembleeach other so much in their uses. The hemp contains alarge amount of nitrogen, the flax very little . The hempcontains more oxygen than would form water with the hydrogen. Flax, on the contrary, contains an excess of hydrogen. The difference is also remarkable in the compositionof the ashes.The ashes of the flax plant consist ofPotash • ·Soda •LimeMagnesiaAlumina•·SilicaPhosphoric acidSulphuric acidChlorineCarbonic acid .• 9.78• 9.82· 12.33· 7.79• 6.0821.35· · 10.84• 2.652.41• · · 16.95100.00The great quantity of lime which characterized the hemphere disappears, and the peculiar quality of the ash is thepresence of soda and potash in equal quantities , much magnesia, and especially the large proportion of phosphoric acid.Dr. Kane has not met with any analysis of the ash of aplant yielding the same amount of phosphoric acid, andhence the exceedingly exhausting power ofthe flax crop iseasily understood.Dr. Kane notices in this ash of flax, that the potash,soda, sulphuric acid, and chlorine are in a very simple relation to each other, the numbers given above coincidingclosely with those of two atoms each of sulphuric acid andchlorine, six of potash, and nine of soda. So that if (in theash) all the soda be taken as carbonate, the potash will be444divided equally among sulphuric, muriatic, and carbonicacids. Dr. Kane thinks that this simplicity is probably accidental, but suggests it for attention in subsequent analysesofflax ashes from other localities.The steeping of flax to loosen the coat of fibrous bark isaccompanied by the solution of certain constituents of theplant, as in the case of hemp. The extract of the steepingwater was analyzed; it yielded , dried at 212° ,Carbon .HydrogenNitrogenOxygenAshes•• ••· ·30.694.242.2420.8242.01100.00The organic part of this extract consisted therefore ofCarbon .HydrogenNitrogenOxygen52.93• 7.313.8635.90100.00Here, as in the case of hemp, the nitrogen of the plant isconcentrated, but the total quantity of nitrogen is not half sogreat. In the ash of the extract, as in the case of hemp, thesoluble alkaline matters also preponderate. The ashes ofthe plant yielded 33.90 per cent. of matters soluble in water;whilst the ashes ofthe flax- steep extract yield 60 per cent.of matters soluble in water. The flax- steep is therefore richin all the materials necessary to produce a new generation ofplants; and Dr. Kane stated, as a satisfactory confirmationof the views put forward in his memoir, that in many instances where agriculturists have sprinkled land with thewater in which flax has been steeped, they have found it amost active manure.After the flax fibre has been removed from the rotted445stem, the residue, or chaff, was found to be composed asfollows:CarbonHydrogen• •·Nitrogen •OxygenAshes· 50.347.33.2440.521.57100.00This is almost identical in composition with the residual hempstem, and may therefore be applied to the same uses. Restoredto the soil with the steep water, it should give back all thatthe crop of flax had taken from the grounds, and thus thevaluable fibre being generated by the atmosphere, the greatsource of expense in the cultivation ofthe plant might beremoved.Dr. Kane finally placed before the Academy certaintables, in which, taking the average quantity of produce froma statute acre offibre- crops and offood crops, and comparing,from the data supplied by the analyses of Sprengel, Boussingault, and his own, the weights of materials of which thesoil is exhausted by each crop, it appeared that the fibrecrops were actually more exhausting than the food crops;whilst the agriculturist profits by the materials that the foodcrops take out of the ground, and the substances taken upby the fibre crops from the soil are at present actually rejected as waste and valueless . Hence it is , as Dr. Kaneconsiders, of much interest to the agricultural industry ofIreland that the views of economizing the residues of thepreparation of flax and hemp, put forward in his memoir, betested by practical men, as, if they be found correct, and thatthose residues may be applied with success to prepare andfit the soil for another crop, those fibrous plants will bepractically deprived of their exhausting qualities, and thegreatest disadvantage, under which their extensive cultivationin this country labours, may be removed.446Professor Mac Cullagh gave an account of his researchesin the Theory of Surfaces of the second Order, in connexionwith a former communication which he had made to the Academy on the same subject. These researches are containedin the following paper.ON THE SURFACES of the Second Order.There is hardly any geometrical theory which more requires to be studied, or which promises to reward betterwhatever thought may be bestowed upon it, than that ofthe surfaces of the second order. My attention was drawnto it, many years ago, by the consideration of mechanicaland physical questions. In the dynamical problem of theRotation of a Solid Body, and in the investigation of theproperties of the Wave- Surface of Fresnel, I found, so longsince as the year 1829, that the ellipsoid could be employedwith very great advantage; while the discussion of thesequestions, but especially of the former, * suggested properties of the ellipsoid and its kindred surfaces which Imight not otherwise have perceived . In this manner Iwas led to consider systems of confocal surfaces, and thenceto notice the focal curves, which I discovered to be analogous, in the theory of the surfaces of the second order, tothe foci in that of the plane conic sections. That theorynow began to interest me on its own account, and, guidedby analogy, I struck out the leading properties possessedby the surfaces in relation to their focal curves; but theinterference of other matters prevented me from continuing the inquiry. I had done enough, however, in this andother parts of the theory, to open new views respecting

• The Theory of Rotation , here spoken of, was completed in the year 1831;

but, from causes which need not be mentioned at present, it was not published. The investigations relative to Fresnel's Wave- Surface will be found inthe Transactions of the Royal Irish Academy, vol. xvi. p. 65; vol. xvii . p. 241 .See also vol. xxi . p. 32, of the same Transactions.447

it; and the results at which I had arrived seemed so fittedfor instruction, that when I was appointed Professor ofMathematics in the University, I made them the subject ofthe first lectures which I gave in that capacity, in the beginning of the year 1836. Next year the heads of theselectures were communicated to this Academy, in a paper ofwhich a very short abstract appeared in the Proceedings.The subject soon became afavourite one among the more advanced students in the University, who are, for the most part,excellent geometers, and in the present Article very littlewill be found which is not well known amongst them; verylittle, indeed, which was not communicated to the Academy on the occasion just mentioned, or which may not begathered, in the shape of detached questions, out of theExamination-Papers published yearly in the University Calendar. But as nothing has yet been published on the subject in a connected form, except the brief notice in the Proceedings of the Academy, and as mathematicians in othercountries attach some importance to researches of thiskind, and appear to be in quest of certain principles whichare familiar to us here, it seems proper to collect togetherthe chief results that have already been obtained, in orderthat persons wishing to pursue these speculations may bebetter able to judge where their inquiries should begin, andin what direction further progress is most likely to be made.PART I.- -GENERATION OF SURFACES OF THE SECOND order.§ 1. The different species of surfaces ofthe second orderare obtained , as is usually shown in elementary treatises,by the discussion of the general equation of the second degree among three coordinates; but it is necessary that weshould also be able to derive these surfaces from a commongeometrical origin, if we would bring them completely within

• Proceedings of the Royal Irish Academy, vol. i. p. 89.

the448graspofmay (with theexception ofthecircle)bedescribed inplanogeometry.Now asthedifferent conicsectionsbythemotion of apointwhosedistancefrom agivenpointbears aconstant ratio to itsdistancefrom agivenrightline,*it isnatural tosuppose thattheremust besomeanalogousmethod bywhich thesurfaces ofthesecondorder may begenerated inspace.Accordingly Ihavesought forsuch amethod,and Ihavefoundthat (withcertainanalogous exceptions)everysurface ofthesecondordermay beregardedasthelocus of apointwhosedistancefrom agivenpointbears aconstant ratio to itsdistancefrom agivenright line,provided thelatterdistance bemeasuredparallel to agivenplane;thisplanebeing, ingeneral,oblique totheright line.Thegivenpoint Icall,fromanalogy, afocus,andthegivenright line adirectrix;thegivenplanemay becalled adirectiveplane,andtheconstantratiomay betermedthemodulus.Tofindtheequationofthesurfacesodefined,lettheaxisofbeparalleltothedirectrix;lettheplaneofxypassthroughthefocus,andcutthedirectrixperpendicularlyinA,thecoordinatesbeingrectangular,andtheiroriginarbitrarilyassumedinthatplane;andlettheaxisof ybeparalleltotheintersectionoftheplaneofxywiththedirectiveplane,theanglebetweenthetwoplanesbeingdenotedby 4.Thenifweputx1 , y₁forthecoordinatesofthefocus,andX2Y2 forthoseofthepoint A,whilethecoordinatesofapointSuponthesurfacearedenotedby x, y , ≈,thedistanceofthislastpointfromthefocuswillbethesquarerootofthequantity(−x )+ (y − z )+ x;andif aplanedrawnthrough S,paralleltothedirectiveplane,beconceivedtocutthedirectrix in D,thedistanceSDwillbethesquarerootofthequantity

Thismethod ofdescribingtheconicsections isdue totheGreekgeometers.It isgivenbyPappus attheend oftheSeventhBook of hisMathematicalCollections.449(x− x2)² sec²p + (y—Y2)²;so that, m being the modulus, the locus ofthe point S will bea surface of the second order, represented by the equation-(x −x1) ² + (y —y1) ² + x² = m² { ( x − x2) ² sec³p + (y —Y2)² } , ( 1)which, by makingA= 1 -m² sec²p,G = m²x2sec²p- xX1,B = 1 - m²,H = m²y2 -Y₁, (2)K = m²(x2² sec²p + y2²) — xı² — yı²,may be put under the formAx² + By² + ≈² +2 Gx + 2Hу = K, ( 3)showing that the plane of xy is one of the principal planes ofthe surface, and that the planes of xx and yx are parallel toprincipal planes.Before we proceed to discuss this equation, it may bewell to observe that as it remains the same when is changedinto , or into 180° — 4, the directive plane may have twopositions equally inclined to the plane of xy, and thereforeequally inclined to the directrix. Indeed it is obviousthat, if through the point S we draw two planes makingequal angles with the directrix, and cutting it in the pointsD and D' respectively, the distances SD and SD' will beequal. Every surface described in this way has consequentlytwo directive planes; and as each of these planes is parallelto the axis of y, their intersection is always parallel to one ofthe axes of the surface . This axis may therefore be calledthe directive axis. The directive planes have a remarkablerelation to the surface, as may be shown in the followingmanner:-Suppose a section of the surface to be made by a planewhich is parallel to one of the directive planes, and whichcuts the directrix in D; then the distance ofany point S of thesection from the focus F will have a constant ratio to its distance SD from the point D; and, as the locus of a point450whose distances from the two points F and D are in a constant ratio to each other, is a plane or a sphere, according asthe ratio is one of equality or not, it follows that the sectionaforesaid will be a right line in the one case, and a circle in theother. Hence it appears that all directive sections, that is,all sections made in the surface by planes parallel to eitherofthe directive planes, are right lines when the modulus isunity, and circles when the modulus is different from unity.Since the equation (3) is not altered by changing thesign of p, or by changing into its supplement, we may suppose this angle (when it is not zero) to be always positiveand less than 90°; for the supposition = 90° is to be excluded, as it would make the secant of p infinite, and thedirective planes parallel to the directrix. In the discussionof the equation there are two leading cases to be considered,answering to two classes of surfaces. The first case, whenneither A nor B vanishes, gives the ellipsoid, the two hyperboloids, and the cone; the second, when either or each ofthese quantities is zero, includes the two paraboloids andthe different kinds of cylinders.§ 2. First Class of Surfaces. -When neither a nor в vanishes, we may make both G and н vanish, by properly assuming the origin of coordinates. Supposing this done, wehavex₁ = m² x2 sec²p,the equation of the surface being thenY₁ =m²y2,Ax² + By² + x² = K,(4)(5)in which the axes of coordinates are of course the axes of thesurface. When K is not zero, the surface is an ellipsoid or hyperboloid, having its centre at the origin of coordinates; whenK = 0, the surface is a cone having its vertex at the origin.Eliminating 2, y2 from the value of K, by means oftherelations (4) , we getK =A 2Ba₁² +A(6)451and eliminating ₁ , y₁ in like manner, we getK = A ( 1− a)x2² + B ( 1 −B)Y2²;Α(7)from which expressions it appears that, every thing else remaining, the focus and directrix may be changed withoutchanging the surface described . For in order that the surface may remain unchanged, it is only necessary that K shouldremain constant, since A and B are supposed constant. Thiscondition being fulfilled , the focus may be any point F whosecoordinates x₁, y satisfy the equation (6) , and ▲ (the foot ofthe directrix) may be any point whose coordinates x2, y2satisfy the equation (7); it being understood, however, thatwhen one of these points is chosen, the other is determined.The locus of F (supposing к not to vanish) is therefore anellipse or a hyperbola, * which may be called the focal curve,or thefocal line; and the locus of A is another ellipse orhyperbola, which may be called the dirigent curve or line:the centre of each curve is the centre of the surface, andits axes coincide with the axes of the surface which liein the plane of xy. Moreover, as the quantities 1 - A and1 - B are essentially positive, the two curves are always ofthe same kind, that is, both ellipses, or both hyperbolas;and when they are hyperbolas, their real axes have thesame direction . The directrix , remaining always parallelto the axis of ≈, describes a cylinder which may be calledthe dirigent cylinder.Since, by the relations (4) , the corresponding coordinatesof F and ▲ have always the same sign, these points eitherlie within the same right angle made by the axes of x and y,or lie on the same axis, at the same side of the centre.as these relations giveAndA BX2- xX1 = X19 - 1 = A 1 BY1,(8)

• In the Proceedings of the Academy, vol. i. p. 90, it was stated inadvertently that " if we confine ourselves to the central surfaces, the locus ofthe

foci will be an ellipse."452― -it is easy to see that the right line AF is a normal to thefocal curve; for the quantities x2 x₁ and y2 Y₁ are proportional to the cosines of the angles which that right linemakes with the axes of x and y respectively, while the valuesjust given for these quantities are, in virtue of the equation(6), proportional to the cosines of the angles which the normal to the focal curve at the point F makes with the sameaxes.It may also be shown that if the directrix prolongedthrough ▲ intersect a directive plane in a certain point, andif a right line drawn through F, parallel to the directrix,intersect the same plane in another point, the right line joining those points will be a normal to the curve described inthat plane by the first point.§ 3. To find in what way the focal and dirigent curves areconnected with the surface, let the equations (5), (6), (7)(when K does not vanish) be put under the formsها+ક།༧+R2= 1 ,x2 y² +x22 Y22= 1,+ y²² = 1 ,P2(9)(10)so that the quantities P, Q, R may represent the squares ofthesemiaxes ofthe surface, and P1, Q1, P2, Q2 the squares of thesemiaxes ofthe curves, these quantities being positive or negative, according as the corresponding semiaxes are real orimaginary. Then we haveK KPQ = R = K,A BP₁ = P ( 1 — A), Q1 = Q ( 1 — B) ,-(11)P QP₂ =Q2 AQ₂ = L_Bwhence it follows thatP₁ P₂ = p², Q1 Q2 = Q²,(12)453and also thatPIP-R, Q1 = Q- R.P2( 13)From equations ( 12) we see that P₁ and P₂ have always thesame sign, as also Q₁ and Q₂; and that, neglecting signs, thesemiaxes ofthe surface are mean proportionals between thecorresponding semiaxes of the focal and dirigent curves.These curves are therefore reciprocal polars with respect tothe section made in the surface by the plane of xy; and itwould be easy to show that the points F and ▲ are reciprocal points, or that a tangent applied at one of them to thecurve which is its locus has the other for its pole.The focal curve, when we know in which of the principalplanes it lies , is determined by the conditions ( 13) , and as itdepends on the relative magnitudes of the quantities P, Q, R,it will be convenient to distinguish the axes of the surface,with relation to these magnitudes. Supposing, therefore,the quantities P, Q, R to be taken with their proper signs,as they are in the equation (9) , that axis to which thegreatest ofthem (which is always positive) refers, shall becalled the primary axis; and that to which the quantityalgebraically least has reference, shall be termed the secondary axis; while the quantity which has an intermediatealgebraic value shall mark the middle or mean axis . Then,since both P, and Q, will be negative, if R be the greatest ofthe quantities aforesaid, the focal curve cannot lie in theplane ofthe mean and secondary axes. Its plane must therefore pass through the primary axis; it will be the plane ofthe primary and mean axes, if R be the least of the threequantities; but the plane of the primary and secondary axes,ifR be the intermediate quantity. In the former case thecurve will be an ellipse, in the latter a hyperbola; and weshall extend the name of focal curves to both the curves sodetermined, though it may happen that only one of themcan be used in the generation of the surface by the modularmethod, as the method of which we are treating may be454called, from its employment of the modulus. A focal curvewhich can be so used shall be distinguished as a modular focal; but each focal, whether modular or not, shall be supposed to have a dirigent curve and a dirigent cylinder connected with it by the relations already laid down.Since Pi -Q₁ = PQ, the foci of a focal curve are thesame as those of the principal section in the plane of whichit lies, and they are therefore on the primary axis of the surface. It will sometimes contribute to brevity of expression,if we also give the name of primary to the major axis of anellipse and to the real axis of a hyperbola. We maythen saythat the primary axes of the surface and of its two focalcurves are coincident in direction; and that ( as is evident)the foci of either curve are the extremities of the primaryaxis ofthe other.IfK be supposed to approach gradually to zero, while aand B remain constant, the focal and dirigent ellipses willgradually contract, and the focal and dirigent hyperbolas willapproach to their asymptotes, which remain fixed . When Kactually vanishes, the surface becomes a cone; the twoellipses are each reduced to a point coinciding with the vertex ofthe cone, and each hyperbola is reduced to the pair ofright lines which were previously the asymptotes. The dirigent cylinder, in the one case, is narrowed into a right line;in the other case it is converted into a pair of planes, whichwe may call the dirigent planes of the cone.§ 4. We have now to showhow the different kinds of surfaces belonging to the first class are produced, according tothe different values of the modulus and other constantsconcerned in their generation.PI. When m is less than cos o, the quantities A, B, K , P , Q , Rare all positive, and o is intermediate in value between è andThe surface is therefore an ellipsoid, and its mean axis.is the directive. As the quantities 1A and 1 - в arealways positive, the focal and dirigent curves are ellipses.R.455Here we cannot suppose K to vanish, as the surface wouldthen be reduced to a point.When = 0, that is, when the directive planes coincidewith each other, and therefore with a plane perpendicular tothe directrix, so that SD is the shortest distance ofthe pointS from the directrix , the surface is a spheroid produced bythe revolution of an ellipse round its minor axis, and thefocal and dirigent curves are circles.II. When m is greater than unity, A and B are negative;and if k be finite, it is also negative; whence P and Q are positive, and R is negative. Also, supposing not to vanish,Q is greater than P. The surface is therefore a hyperboloidofone sheet, with its real axes in the plane of xy; and thedirective axis is the primary. The focal and dirigent curvesare ellipses. But when = 0 , the surface is that producedby the revolution of a hyperbola round its imaginary axis,and the focal and dirigent* are circles.2If K = 0, which implies , since A and в have the samesign, that x1, 1 , x2, y2 are each zero, the surface is a conehaving the axis of ≈ for its internal axis; and the focal anddirigent are each reduced to a point. The focus and directrix are consequently unique; the focus can only be thevertex of the cone, the directrix can only be the internal axis;and the directrix therefore passes through the focus. Thedirective axis, which coincides with the axis of y, is one of theexternal axes; that one, namely, which is parallel to thegreater axes of the elliptic sections made in the cone byplanes perpendicular to its internal axis. This is on thesupposition that p is finite; for, when = 0, the cone becomes one ofrevolution round the axis of z.III. When m is greater than cos p, but less than unity,we have a positive and в negative, and the species of the

• When the term dirigent stands alone, it is understood to mean a dirigent line.

VOL. II. 2 R456surface depends on K. It is inconsistent with these conditions to suppose = 0, and therefore the surface cannot, inthis case, be one of revolution . The value of к may besupposed to be given by the formula1 - AK= =^ (x2 − x1) ² +1 --BB( 2 – g ) , (14)Awhich contains only the relative coordinates of the focus andthe foot of the directrix, and is a consequence of the equations (6) and (8) .1º. Ifk is a positive quantity, the surface is a hyperboloidof one sheet, with its secondary axis in the direction of x;the primary axis, as before, is the directive, but the focal anddirigent are now hyperbolas.2º. If K is a negative quantity, the surface is a hyperboloid oftwo sheets, having its primary axis coincident withthat of x. The secondary axis is the directive; the focaland dirigent are hyperbolas.3º. If K = 0, the surface is a cone, having the axis of xfor its internal axis; the directive axis being, as before, thatexternal axis to which the greater axes of the elliptic sections, made by planes perpendicular to the internal axis, areparallel. The axis of ≈ is the other external axis, whichmay be called the mean axis of the cone, because it coincideswith the mean axis of any hyperboloid to which the cone isasymptotic. As A and B have different signs, it is evident,from the equations (6) and (7) , that the focal and dirigentare each a pair of right lines passing through the vertex,each pair making equal angles with the internal axis . Twoplanes, each of which is drawn through the mean axis and adirigent line, are the dirigent planes of the cone.The corresponding focal and dirigent lines are thosewhich lie within the same right angle made by the internaland directive axes; and since by the equations (6) and (8)the value of K may be written457K = X1 (X2 — X1) + Y1 (Y2 — Y1) , (15)we see that, as K now vanishes, the right line joining corresponding points F and ▲ upon these lines is perpendicular tothe focal line. Of the two sides of the cone which are inthe plane of xy, one lies between each focal and its dirigent;and it may be inferred from the equations, that the tangentsof the angles which the internal axis makes with a focalline, with one of these sides of the cone, and with a dirigentline, are in continued proportion, the proportion being thatofthe cosine of 4 to unity. And hence it follows, that thesetwo sides of the cone, with a focal line and its dirigent, cutharmonically any right line which crosses them .§ 5. From this discussion it appears, that the ellipsoid andthe hyperboloid of two sheets can be generated modularly,each in one way only, the modular focal being the ellipsefor the former, and the hyperbola for the latter; but thatthe hyperboloid ofone sheet can be generated in two ways,each of its focals being modular, and each focal having itsproper modulus. The cone also admits two modes of generation, * in one of which, however, the focus is limited to thevertex of the cone, and the directrix to its internal axis.

• The double generation of the cone, when its vertex is the focus, may be

proved synthetically by the method indicated in the Examination Papers of theyear 1838, p. xlvi (published in the University Calendar for 1839 ) . Supposingthe cone to stand on a circular base ( one of its directive sections) , and to be circ*mscribed by a sphere, the right lines joining its vertex with the two pointswhere a diameter perpendicular to the plane of the base intersects the sphere,will be its internal and mean axes. Then if P be either of these points, V thevertex, C the point where the axis PV cuts the plane of the base, and B anypoint in the circumference of the base, the triangles PVB and PBC will be similar, since the angles at V and B are equal, and the angle at P is common toboth triangles; therefore BV will be to BC as PV to PB, that is, in a constantratio. It is not difficult to complete the demonstration, when the focus is supposed to be any point on one of the focal lines.2 R 2458But when the hyperboloid of one sheet, or the cone, is asurface of revolution, it has only one mode of modular generation. In cases of double generation, the directive planesof course remain the same, as they have a fixed relation tothe surface. A modular focal, it may be observed (and theremark applies equally to surfaces of the second class) , isdistinguished by the circ*mstance that it does not intersectthe surface. The only exception to this rule are the focallines of the cone, which pass through its vertex. A focalwhich is not modular may be called umbilicar, because itintersects the surface in the umbilics; an umbilic being apoint on the surface where the tangent plane is parallel toa directive plane. Thus the focal hyperbola of the ellipsoid,and the focal ellipse of the hyperboloid of two sheets, areumbilicar focals, and pass through the umbilics of thesesurfaces; but the hyperboloid of one sheet has no umbilics,and accordingly both its focals are modular, and neither ofthem intersects the surface. The umbilicar focals and dirigents have properties which shall be mentioned hereafter.An umbilicar focal and the principal section whose planecoincides with that of the focal are curves of different kinds,the one being an ellipse when the other is a hyperbola; buta modular focal is always of the same kind with the coincident section of the surface, being an ellipse, a hyperbola, ora pair of right lines, according as the section is an ellipse,a hyperbola, or a pair of right lines; and when the sectionis reduced to a point, so likewise is the modular focal.The plane of a modular focal always passes through thedirective axis. When the directive axis is the primary, asin the hyperboloid of one sheet, both focals are modular.But in the ellipsoid and the hyperboloid of two sheets,where the primary axis is not directive, only one of thefocals can be modular. The plane of an umbilicar focal is459always perpendicular to the directive axis; and therefore,when that axis is the primary, there is no umbilicar focal. *When the surface is doubly modular, the two modulim, m' are connected by the relationcos² фm²sin² + = 1;m/2( 16)where is the angle made by a directive plane with theplane of the focal to which the modulus m belongs. Onemodulus is greater than unity; the other is less than unity,but greater than the cosine of the angle which the plane ofthe corresponding focal makes with a directive plane. Inthe hyperboloid of one sheet, the less modulus is that whichbelongs to the focal hyperbola. In the cone, the lessmodulus belongs to the focal lines . Ofthe two moduli of acone, that which belongs to the focal lines may be termedthe linear modulus; and the other, to which only a singlefocus corresponds, may be called the singular modulus.- § 6. Second Class of Surfaces. In this class of surfaces, one of the quantities A, B vanishes, or both of themvanish .I. When m = cos p, and p is not zero, a vanishes, but в

• If the first of the equations ( 10) , when P, and Q, are both negative, be

supposed to express an imaginary focal, there will, in a central surface, be threefocals, two modular and one umbilicar; the two modular focals being in theprincipal planes which pass through the directive axis, and the umbilicar focalin the remaining principal plane. Then, when we know which of the axes isthe directive axis, we know which of the three focals is imaginary, because theplane of the imaginary focal is perpendicular to the primary axis. A modularfocal may be imaginary, and yet have a real modulus; this occurs in thehyperboloid of two sheets. In the ellipsoid, the imaginary focal has animaginary modulus. In all cases the two moduli are connected by the relation(16).It will appear hereafter, that the vertex of the cone is an umbilicar focus.The cone has therefore three focals, none of which is imaginary; but two ofthem are single points coinciding with the vertex.460does not; and the surface is either a paraboloid or a cylinder.1°. Ifthe surface is a paraboloid, we may suppose theorigin of coordinates to be at its vertex, in which case bothH and K vanish, and we have the relationsGX2- X19Y₁ = y₂ cos² 8,2 2(17)x²² + y²² cos² + − x₁² — y₁² = 0;-the equation of the surface beingy² sin² + x² + 2Gx = 0, (18)which shews that the paraboloid is elliptic , having its axisin the direction of x, and the plane of xy for that of itsgreater principal section. From the relations ( 17) we obtainthe following,y₁² tan2p + 2Gx1 + g² = 0,y22 sin² + cos² + 2Gx₂-X2 G² = 0;(19)from which we see that the focal and dirigent curves areparabolas, having their axes the same as that of the surface;and their vertices equidistant from the vertex of the surface,but at opposite sides of it. The concavity of each curve isturned in the same direction as that of the section xy. Thefocus of the focal parabola is the focus of the section xy, andits vertex is the focus of the section as of the surface; itsparameter being the difference of the parameters of thesetwo sections. The parameter of the section xy is a meanproportional between the parameters of the focal and dirigent parabolas.2º. If the surface is a cylinder, we may make G and Hvanish, by taking the origin on its axis. We then haveX2X1, Y₁ = Y2 cos²0,K = y₁² tan² = y2² sin²φ cos² p;the equation of the cylinder, which is elliptic, beingy² sin² + ² = K.(20)(21)Here the focal and dirigent are each a pair of right lines461parallel to the axis of the cylinder, and passing through thefoci and directrices of a section perpendicular to the axis.The corresponding focal and dirigent lines lie at the sameside of the axis.II. When m = 1 , and is not zero, в vanishes, but adoes not.1º. If the surface is a paraboloid, and the origin of coordinates at its vertex, the quantities G and K vanish; samethe equation ofthe surface becomes2 tan² p - 2 2нy, (22)and we have the relationsx1 = x2 sec²p,(23)K = Y2 - Y1,2x2² sec²4+ y²² — x₁² — y₁² = 0.-The paraboloid is therefore hyperbolic, its axis being thatofy, which is also the directive axis; and as the tangent ofmay have any finite value, the plane of xy, which is thatof the focal curve, may be either of the principal planespassing through the axis of the surface. The relations (23)givex² sin² - 2нy₁ — н² = 0,x2² tan²Ф sec² 4 — 2HY½ + н² = 0,-(24)for the equations of the focal and dirigent, which are therefore parabolas, having their axes the same as those of thesurface, and their concavities turned in the same directionas that of the section xy; their vertices being equidistantfrom the vertex of the surface, and at opposite sides of it.The focus ofthe focal parabola is the focus of the sectionxy, and its vertex is the focus of the section ys, its parameter being the sum ofthe parameters of these two sections.The parameter of the section xy is a mean proportionalbetween the parameters ofthe focal and dirigent parabolas.2º. If the surface is a cylinder, and the origin on itsaxis, G and H vanish, and we have462X₁ = x2 sec² 4,-K-- = x2 sin²Y₁ = Y2,= x22 tan2 sec²;(25)the equation of the cylinder, which is hyperbolic, beingx² tan² - *2 = K. (26)The focal and dirigent are each a pair of right lines parallel to the axis of the cylinder; the corresponding linespassing through a focus and the adjacent directrix of anysection perpendicular to the axis . The directive planes areparallel to the asymptotic planes of the cylinder.In this case, if K = 0, the surface is reduced to two directive planes, and the focal and dirigent to the intersectionof these planes.III. When m = 1 , and 4 = 0, both A and B vanish, andthe surface is the parabolic cylinder. If, as is allowable ,we suppose G and к to vanish, the equation of the cylinderbecomes2² + 2Hу = 0,HY2Y1-,(27)and we haveX1 X2,2 -x²² + y²² — x²² — y²² = 0;-(28)whenceY₁ = H,✔ – Y2 = H.(29)The focal and dirigent are each a right line parallel to theaxis of x, the former passing through the focus, the lattermeeting the directrix of the parabolic section made by theplane of ys. The plane of xy is the directive plane.§ 7. We learn from this discussion, that, among the surfacesof the second class, the hyperbolic paraboloid is the onlyone which admits a twofold modular generation; the modulus, however, being the same for both its focals. In theelliptic paraboloid the modular focal is restricted to the planeof that principal section which has the greater parameter;we shall therefore suppose a parabola to be described inthe plane of the other principal section, according to the463law of the modular focals; the law being, that the focus ofthe parabola shall be the focus of the principal section in theplane ofwhich the parabola lies , and its vertex the focus oftheprincipal section in the perpendicular plane. The parabolaso described will have its concavity opposed to that of thesurface; it will cut the surface in the umbilics, and will beits umbilicar focal, the only such focal to be found amongthe surfaces of the second class. We shall of course suppose further, that this focal has a dirigent parabola connectedwith it by the same law as in the other cases, the vertices ofthe focal and dirigent being equidistant from that of thesurface and at opposite sides of it, while the parameter ofthe dirigent is a third proportional to the parameters of thefocal and of the principal section in the plane of whichthe curves lie. The two focals of a paraboloid are so related, that the focus of the one is the vertex ofthe other.The cylinders have no other focals than those which occurabove.§ 8. In this, as in the first class of surfaces, the rightline FA, joining a focus F with the foot of its correspondingdirectrix, is perpendicular to the focal line; and the focaland dirigent are reciprocal polars with respect to the sectionxyof the surface. These properties are easily inferred fromthe preceding results; but, as they are general, it may bewell to prove them generally for both classes of surfaces.Supposing, therefore, the origin of coordinates to be anywhere in the plane of xy, and writing the equation of thesurface in the form- (x− x₁) ² +(y — Y₁) ² +≈² —L ( x − x2) ² + M(Y — Y2) ², (30)-which, when identified with ( 3) , gives the relationsA = 1 − L,-G = LX2 - X1,2B = 1 -M,H (31 )MY2Y1,K = Lx₂² + My₂² — x‚² — yı²,464we find, by differentiating the values of the constants G, H,and K,Ldx2 = dx1 , мdy2 = dy ,LX2 dx2 + My2 dy₂ - x₁ dx₁ — y₁ dy₁ = 0.(32)Hence we obtain(x2 - x₁) dx + (y₂ - y₁ ) dy₁ = 0; (33)an equation which expresses that the right line joining thepoints F and A is perpendicular to the line which is thelocus ofthe point F.Again, the equation of the section xy of the surface being2Ax² + By² + 2Gx + 2HY = K, (34)the equation ofthe right line which is, with respect to thissection, the polar of a point ▲ whose coordinates are x2,ya, is - -(AX2 + G) x + (BY₂ + H) y = K — GX2 — HY2; (35)but the relations ( 31 ) giveAX2 + GX2- X1 , BY2 + HY2 - Y1 ,K—GX2 — HY₂ =X₁X1 (X2 — X1) +Yı (Y2 — Yı);and hence the equation (35) becomes(36)(X2 — X1) (x − x1) +(Y2 − Yı) (Y — y₁) = 0,-(37)which, as is evident from (33), is the equation of a tangentapplied to the focal at the point F corresponding to A.This shows that the focal and dirigent are reciprocal polarswith respect to the section xy, and that in this relation, aswell as in the other, the points F and A are correspondingpoints.Supposing F and A' to be two other correspondingpoints on the focal and dirigent, if tangents applied to thefocal at F and F' intersect each other in T, the point T willbe the pole of the right line AA' with respect to the sectionxy, as well as the pole of the right line FF' with respect to465the focal; and hence if any right line be drawn through T,and if P be the pole of this right line with respect to thesection, and N its pole with respect to the focal, the pointsP and Nwill be on the right lines AA' and FF' respectively.Now it is useful to observe that the distances ▲▲' and FF'are always similarly divided (both of them internally orboth of them externally) by the points P and N, so thatwe have AP to A'P as FN to F'N. This property may beproved directly by means of the foregoing equations; or itmay be regarded as a consequence of the following theorem:-If through a fixed point in the plane of two givenconics having the same centre, or of two given parabolashaving their axes parallel, any pair of right lines be drawn,and their poles be taken with respect to each curve, the distance between the poles relative to one curve will be in aconstant ratio to the distance between the poles relative tothe other curve . * In fact, the poles of the right linesTF, TF' , with respect to the focal, are F, F'; and their poleswith respect to the section xy are ▲, A'; therefore , sincethe focal and the section xy may be taken for the givencurves, and the point T for the fixed point, the ratio ofFF' to AA' is the same as the ratio of FN to AP or of F'Nto A'P, and consequently the distances FF' and AA' are similarly divided in the points N and P.§9. In the equation ( 30), considered as equivalent tothe equation ( 1) , the constants L and м are both positive;but the properties which have been deduced from theformer equation are independent of this circ*mstance, and

• There is an analogous theorem for two surfaces of the second order which

have the same centre, or two paraboloids which have their axes parallel. Ifthrough a fixed right line any two planes be drawn, and their poles be takenwith respect to each surface, the distance between the poles relative to the onesurface will be in a constant ratio to the distance between the poles relative tothe other.466equally subsist when one of these constants is supposedto be negative (for they cannot both be negative) . Thisleads us to inquire what surfaces the equation (30) iscapable of representing when the constants L and м havedifferent signs; as also, for a given surface, what lines aretraced in the plane of xy by points F and A, of which x1 ,Y₁ and x2, y2 are the respective coordinates. After the examples already given , this question is easily discussed, andthe result is, that the only surfaces which can be so represented are the ellipsoid , the hyperboloid of two sheets, thecone, and the elliptic paraboloid-that is to say, the umbilicar surfaces together with the cone; and that, for anumbilicar surface, the locus of F is the umbilicar focal, andtherefore the locus of A is the corresponding dirigent; whilefor the cone the points F and ▲ are unique, coinciding witheach other and with the vertex of the cone. A geometricalinterpretation of this case is readily found; for as L and Mhave different signs, the right-hand member ofthe equation(30) , if м be the negative quantity, is the product of twofactors ofthe form—-f(x − x2) +gy - Y2) , f(x — X2) — g (y — Y2) ,-in which ƒ and g are constant; and these factors are evidently proportional to the distances of a point whose coordinates are x, y, z, from two planes whose equations are-ƒ(x− x2) + g (y — Y2) = 0, ƒ( x — x2) — g (Y — Y2) = 0,which planes always pass through a directrix , and are inclined at equal and constant angles to the axis of x or of y.Therefore, if F be the focus which belongs to this directrix ,the square of the distance of F from any point of this surfaceis in a constant ratio to the rectangle under the distances ofthe latter point from the two planes. And these planes are directive planes; because, if a section parallel to one of thembe made in the surface, the distance of any point of the section from the other plane will be proportional to the square467ofthe distance of the same point from the focus; and, as thelocus of a point, whose distance from a given plane is proportional to the square of its distance from a given point, isobviously a sphere, it follows that the section aforesaid is thesection of a sphere, and consequently a circle; which showsthat the plane to which the section is parallel is a directiveplane. Thus, the square of the distance of any point of *

• In attempting to find a geometrical generation for the surfaces of the second order, one of the first things which I thought of, before I fell upon the

modular method, was to try the locus of a point such that the square of its distance from a given point should be in a constant ratio to the rectangle under itsdistances from two given planes; but when I saw that this locus would notrepresent all the species of surfaces, I laid aside the discussion of it. Sometime since, however, Mr. Salmon, Fellow of Trinity College, was led independently, in studying the modular method, to consider the same locus; andhe remarked to me, what I had not previously observed, that it offers a property supplementary, in a certain sense, to the modular property; that whenthe surface is an ellipsoid, for example, the given point or focus is on the focalhyperbola, which the modular property leaves empty. This remark of Mr.Salmon served to complete the theory of the focals, by indicating a simplegeometrical relation between a non-modular focal and any point on the surfaceto which it belongs.In a memoir " On a new Method of Generation and Discussion of the Surfaces of the second Order, " presented by M. Amyot to the Academy of Sciencesof Paris, on the 26th December, 1842, the author investigates this samelocus, conceiving it to involve that property in surfaces which is analogous tothe property of the focus and directrix in the conic sections; and the importance attached to the discovery of such analogous properties induced M.Cauchy to write a very detailed report on M. Amyot's memoir, accompaniedwith notes and additions of his own (Comptes rendus des Séances de l'Académiedes Sciences, tom. xvi. pp. 783-828, 885-890; April, 1843); and also occasioned several discussions, principally between M. Poncelet and M. Chasles,relative to that Memoir ( Comptes rendus, tom. xvi. pp. 829, 938 , 947, 1105,1110). But the property involved in this locus cannot be said to afford amethod of generation of the surfaces of the second order, since it applies onlyto some of the surfaces, and gives an ambiguous result even where it doesapply. It is therefore not at all analogous to the aforesaid general property of the conic sections, and moreover it was not new when M. Amyot468the surface from an umbilicar focus bears a constant ratio tothe rectangle under the perpendicular distances of the samebrought it forward. Mr. Salmon had in fact proposed it for investigationto the students of the University of Dublin , at the ordinary examinationsin October, 1842; and it was published, towards the end of that year, inthe University Calendar for 1843 , some months before the date of M. Cauchy'sreport, by which the contents of M. Amyot's memoir were first made known.The parallelism of the two given planes to the circular sections of the surfaceis also stated in the Calendar; but this remarkable relation is not noticed byM. Amyot, nor by M. Cauchy. (See the Examination Papers of the year 1842,p. xlv, quest. 17, 18; in the Calendar for 1843. ) It is scarcely necessary toadd, that the analogue which M. Amyot and other mathematicians have beenseeking for, and which was long felt to be wanting in the theory of surfaces ofthe second order, is no other than the modular property of these surfaces, whichappears to be not yet known abroad. M. Poncelet insists much on the importance of extending the signification of the terms focus and directrix, so asto make them applicable to surfaces; and he supposes this to have been effected,for the first time, by M. Amyot. These terms however, applied in their truegeneral sense to surfaces, had been in use, several years before, among themathematical students of Dublin, as may be seen by referring to the Calendar(Examination Papers of the year 1838, p. c; 1839, p. xxxi)..The locus above-mentioned, being co- extensive with the umbilicar property,does not represent any surface which can be generated by the right line,except the cone. To remedy this want of generality, M. Cauchy proposes toconsider a surface of the second order as described by a point, the square ofwhose distance from a given point bears a constant ratio either to the rectangleunder its distances from two given planes, or to the sum of the squares of thesedistances. This enunciation, no doubt, takes in both kinds of focals, and all thespecies of surfaces; but the additional conception is not of the kind required bythe analogy in question , nor has it any of the characters of an elementary principle. For the given planes, according to M. Cauchy's idea, do not stand in anysimple or natural relation to the surface; and besides there is no reason why,instead of the sum of the squares of the distances from the given planes, weshould not take the sum after multiplying the one square by any given positivenumber, and the other square by another given positive number; nor is thereany reason why we should not take other hom*ogeneous functions of these disThis conception would therefore be found of little use in geometrical applications; while the modular principle, on the contrary, by employinga simple ratio between two right lines, both of which have a natural connexiontances.469point from two directive planes drawn through the directrix corresponding to that focus; and it is easy to see thatthis ratio, the square root of which we shall denote by μ, isequal to LM, or, neglecting signs, to the sum of the numerical values of L and M. Of course, if the distances fromthe directive planes, instead of being perpendicular, bemeasured parallel to any fixed right line, the ratio will stillbe constant, though different. For example, if the fixedright line for each plane be that which joins the corresponding umbilic with either focus ofthe section xy, the ratioof the square to the rectangle will be the square of thenumber m sec 4, where m is the modulus, and the anglewhich the primary axis makes with a directive plane.When the umbilicar property is applied to the cone, thevertex of which is , as we have seen, to be regarded as anumbilicar focus , having the directive axis for its directrix , itindicates that the product of the sines of the angles whichany side of the cone makes with its two directive planes is aconstant quantity.It is remarkable that the vertex of the cone affords theonly instance of a focal point which is at once modular andumbilicar, as well as the only instance of a focal point whichis doubly modular. This union of properties it may be conceived to owe to the circ*mstance that the cone is theasymptotic limit of the two kinds of hyperboloids. For if awith the surface, lends itself with the greatest ease to the reasonings of geometry.Indeed the whole difficulty, in extending the property of the directrix to surfacesof the second order, consisted in the discovery of such a ratio inherent in allof them; a ratio having nothing arbitrary in its nature, and for which no otherof equal simplicity can be substituted.It may be proper to mention that the term modulus, which I have used forthe first time in the present paper, with reference to surfaces of the secondorder, has been borrowed from M. Cauchy, by whom it is employed , however,in a signification entirely different. Several other new terms are also now introduced, from the necessity of the case.470series of hyperboloids have the same asymptotic cone, andtheir primary axes be indefinitely diminished, they will approach indefinitely to the cone; and, in the limit, the focalellipse and hyperbola ofthe hyperboloid of one sheet willpass into the vertex and the focal lines ofthe cone, thusmaking the vertex doubly modular, while the focal ellipseof the hyperboloid of two sheets will also be contractedinto the vertex, and will make that point umbilicar.When the two directive planes coincide, and become onedirective plane, the umbilicar property is reduced to this ,that the distances of any point in the surface from the pointF and from the directive plane are in a constant ratio toeach other; and therefore the surface becomes one of revolution round an axis passing through F at right angles tothat plane, the point F being a focus ofthe meridional section ,or the vertex if the surface be a cone. When the directiveplanes are supposed to be parallel, but separated by a finiteinterval, we get the same class of surfaces of revolution, withthe addition of the surface produced by the revolution of anellipse round its minor axis; the point F being still on theaxis of revolution , but not having any fixed relation to thesurface.§ 10. If in the equation (30) we supposed the right- handmember to have an additional term containing the productofthe quantities x — x2 and y - y2, with a constant coefficient, all the foregoing conclusions regarding the geometricalmeaning of that equation would remain unchanged, becausethe additional term could always be taken away by assigningproper directions to the axes of x and y. If, after the removal of this term, the coefficients of the squares of theaforesaid quantities were both positive, the locus of F wouldbe a modular focal of the surface expressed by the equation;but if one coefficient were positive and the other negative,the locus of F would be an umbilicar focal. The equationin its more general form is evidently that which we should471obtain for the locus of a point S, such that the square ofits distance SF from a given point F should be a given hom*ogeneous function of the second degree of its distancesfrom two given planes; the plane of xy being drawn throughF perpendicular to the intersection of these planes, andx2, y2 being the coordinates of any point on this intersection, while x , y, are the coordinates of F. The point Fmight be any point on one of the focals of the surface described by S; the intersection of the two planes (supposingthem always parallel to fixed planes) being the corresponding directrix .These considerations may be further generalised , if weremark that the equation of any given surface of the secondorder may bebe put under the form(x − x1) ² +(y — yı)² +( ≈ —≈1 ) ² =L( x— x,) ² + м(y — Y2)² +N(≈—≈2)²+L' (Y—Y2) (≈—≈2) +M′ ( x —X2) ( ≈ — ≈2) +N′ ( X — X2) (y— Y2), (38)where L, M, N, L' , M' , N' are constants, and x₁ , Y₁ , z₁ are conceived to be the coordinates of a certain point F, andX2, y2, 2 the coordinates of another point A. The constants L' , M' , N' may, if we please, be made to vanish bychanging the directions ofthe axes of coordinates; and whenthis is done, the new coordinate planes will be parallel tothe principal planes of the surface. Then, by proceeding asbefore, it may be shown that, without changing the surface,we are at liberty, under certain conditions, to make thepoints F and A move in space. The conditions are expressed geometrically by saying that the two surfaces, uponwhich these points must be always found, are reciprocalpolars with respect to the given surface, the points Fand ▲being, in this polar relation, corresponding points; and thatthe surface which is the locus of F is a surface of the secondorder, confocal with the given one, it being understood thatconfocal surfaces are those which have the same focal lines.The surface on which A lies is therefore also of the secondVOL. II. 2 s472order, and the right line AF is a normal at F to the surface which is the locus of this point. Moreover, if throughthe point A three or more planes be drawn parallel to fixedplanes , and perpendiculars be dropped upon them fromany point S whose coordinates are x, y, z, the right- handmember of the equation (38) may be conceived to representa given hom*ogeneous function of the second degree of theseperpendiculars; and the given surface may therefore beregarded as the locus of a point S, such that the squareof the distance SF is always equal to that function .§ 11. In the enumeration of the surfaces capable of beinggenerated by the modular method, we miss the five following varieties, which are contained in the general equation of the second degree, but are excluded from that method of generation by reason of the simplicity of theirforms—namely, the sphere, the right cylinder on a circular base, and the three surfaces which may be producedby the revolution of a conic section (not a circle) roundits primary axis. * These three surfaces are the prolate spheroid, the hyperboloid of two sheets, and the paraboloidof revolution; and the circ*mstance that the foci of thegenerating curves are also foci of the surfaces, renders iteasy to investigate their focal properties. In point of simplicity, the excepted surfaces are to the other surfaces ofthe second order what the circle is to the other conic sections,the circle being, in like manner, excepted from the curveswhich can be generated by the analogous method in plano; andthe geometry of the five excepted surfaces may therefore beregarded as comparatively elementary. These five surfaces.The case of two parallel planes is also excluded, but it is not here takeninto account. The case of two parallel right lines is in like manner excludedfrom the corresponding generation of lines of the second order.A paper by M. Chasles, on these surfaces of revolution , will be found inthe Memoirs of the Academy of Brussels, tom. v. ( An. 1829) .473were, in fact, studied by the Greek geometers, * and , alongwith the oblate spheroid and the cone, they make up all thesurfaces ofthe second order with which the ancients were acquainted. Except the cone, the surfaces considered bythem are all of revolution; and there is only one surfaceof revolution , the hyperboloid of one sheet, which was notnoticed until modern times. This surface is mentioned (under the name of the hyperbolic cylindroid) by Wren,† who remarks that it can be generated by the revolution of a rightline round another right line not in the same plane. Asto thegeneral conception of surfaces of the second order, the suggestion of it was reserved for the algebraic geometry ofDescartes. In that geometry the curves previously known as sections of the cone are all expressed by the general equation ofthe second degree between two coordinates; and hence itoccurred to Euler‡ about a century ago, to examine andclassify the different kinds of surfaces comprised in thegeneral equation of the second degree among three coordinates.The new and more general forms thus brought to light havesince engaged a large share of the attention of geometers;but the want of some other than an algebraic principle of connexion has prevented any great progress from being madein the investigation of such of their properties as do not immediately depend on transformations of coordinates. Thiswant the modular method of generation perfectly supplies ,by evolving the different forms from a simple geometricalconception, at the same time that it brings them within therange of ideas familiar to the ancient geometry, and placestheir relation to the conic sections in a striking point of view.

• The hyperboloid of two sheets, and the paraboloid of revolution, were

known by the name of conoids. Archimedes has left a treatise on Conoids andSpheroids, as well as a treatise on the Sphere and Cylinder.In the Philosophical Transactions for the year 1669, p. 961 .See his Introductio in Analysin Infinitorum, p. 373; Lausanne, 1748.2 s 2474It may be well to remark that the excepted surfaces arelimits of surfaces which can be generated modularly, as thecircle is the limit of the ellipse in the analogous generationof the conic sections. Thus the sphere is the limit of anoblate spheroid, one of whose axes remains constant, whileits focal circle is indefinitely diminished; and the right circular cylinder is the limit of an elliptic cylinder, whose focallines are conceived to approach indefinitely to coincidencewith each other and with the axis of the cylinder, while oneofthe axes of the principal elliptic section remains constant.In these cases the dirigent lines, along with the directrices,move off to infinity. The other three excepted surfacescorrespond to the supposition = 90°, which was excludedin the discussion of the general equation ( 1). For if wemake m sec p = n, the quantity which constitutes the righthand member of that equation may be written2n² (x − x₂) ² + n² (y — y2)² cos² p;-and if we suppose n to remain finite and constant, whileapproaches to 90°, and m indefinitely diminishes, this quantity will approach indefinitely to n² (x - 2)2, which will beits limiting value when 90°. But x - x2 is the distanceof the point S from a fixed plane intersecting the axis of xperpendicularly at the distance x2 from the origin of coordinates; and therefore, in the limit, the equation expressesthat the distances of any point S of the surface from thefocus F and from this fixed plane, are to each other as n tounity, that is , in a constant ratio; which is a common property of the three surfaces in question . This property alsobelongs to the right cone, but the right cone does not rankamong the excepted surfaces.§ 12. We have seen that, when the modulus is unity,any plane parallel to either of the directive planes intersectsthe surface in a right line; whence it follows, that throughany point on the surface of a hyperbolic paraboloid two right475lines may be drawn which shall lie entirely in the surface.The plane of these right lines is of course the tangent planeat that point, and therefore every tangent plane intersectsthe surface in two right lines. This is otherwise evidentfrom considering that the sections parallel to a given tangent plane are similar hyperbolas, whose centres are rangedon a diameter passing through the point of contact, andwhose asymptotes, having always the same directions, areparallel to two fixed right lines which we may suppose to bedrawn through that point. For as the distance between theplane of section and the tangent plane diminishes , the axesof the hyperbola diminish; and they vanish when that disstance vanishes , the hyperbola being then reduced to itsasymptotes. The tangent plane therefore intersects thesurface in the two fixed right lines aforesaid . The samereasoning, it is manifest, will apply to any other surface ofthe second order, which has hyperbolic sections parallel to itstangent planes; and therefore the hyperboloid of one sheet,which is the only other such surface, * is also intersected intwo right lines by any of its tangent planes. These rightlines are usually called the generatrices of the surface.From what has been said , it appears that the generatricesofthe hyperbolic paraboloid , and the asymptotes of its sections (all its sections, except those made by planes parallelto the axis, being hyperbolas) , are parallel to the directiveplanes. The generatrices of the hyperboloid of one sheet,and the asymptotes of its hyperbolic sections , are parallel tothe sides of the asymptotic cone; because any section ofthe

• The double generation of these two surfaces by the motion of a right line

has been long known. It appears to have been discovered and fully discussedby some of the first pupils of the Polytechnic School of Paris. This mode ofgeneration had, however, been remarked by Wren, with regard to the hypreboloid of revolution. It does not seem to have been observed, that the existenceof rectilinear generatrices is included in the idea of hyperbolic sections parallelto a tangent plane.476hyperboloid is similar to a parallel section of the asymptoticcone, and when the latter section is a hyperbola its asymptotes are parallel to two sides of the cone.PART II.- PROPERTIES OF SURFACES OF THE SECOND ORDER.§ 1. In the preceding part of this paper it has been necessary to enter into details for the purpose of communicating fundamental notions clearly. In the following part,which will contain certain properties of surfaces of the second order, we shall be as brief as possible; giving demonstrations of the more elementary theorems, but confiningourselves to a short statement of the rest.Many consequences follow from the principles alreadylaid down.Through any directrix of a surface of the second orderlet a fixed plane be drawn cutting the surface, and let S beany point ofthe section. If the directrix and its focus F bemodular, and ifa plane always parallel to the same directiveplane be conceived to pass through S and to cut the directrix in D, the directive distance SD will be always parallel toa given right line , and will therefore be in a constant ratio tothe perpendicular distance of S from the directrix . Thisperpendicular distance will consequently bear a given ratioto SF, the distance of the point S from the focus. And thesame thing will be true when the directrix and focus areumbilicar, because the perpendicular distance of the pointS from the directrix will be in a constant ratio to its distancefrom each directive plane drawn through the directrix.The fixed plane of section will in general contain anotherdirectrix parallel to the former, and belonging to the samefocal; and it is evident that the perpendicular distance of Sfrom this other directrix will be in a given ratio to its distance SF' from the corresponding focus F', the ratio beingthe same as in the former case. Hence, according as thepoint S lies between the two directrices, or at the same side477of both, the sum or difference of the distances SF and SFwill be constant.If the plane of section pass through either of the foci, asF, this focus and its directrix will manifestly be the focusand directrix of the section . In this case the plane of sectionwill be perpendicular to the focal at F. And if the surfacebe a cone, the point F being anywhere on one of its focal lines,the distance of the point S from the directrix will be in aconstant ratio to its perpendicular distance from the dirigentplane which contains the directrix, and therefore this perpendicular distance will be in a given ratio to the distanceSF. Now calling V the vertex of the cone, and taking SVfor radius, the perpendicular distance aforesaid is the sineof the angle which the side SV of the cone makes with thedirigent plane; and SF, which is perpendicular to VF, isthe sine of the angle SVF. Consequently the sines oftheangles which any side of a cone makes with a dirigentplane and the corresponding focal line are in a given ratio toeach other.§ 2. Conceive a surface of the second order to be intersected in two points S, S' by a right line which cuts twoparallel directrices in the points E, E' , and let F, F' be thefoci corresponding respectively to these directrices. Theperpendicular distances of the points S, S' from the first directrix and from the second are to each other as the lengthsSE, S'E, SE', S'E' respectively, and therefore the ratios ofFS to SE, of FS' to S'E, of F/S to SE' , and of F'S' to S'E'are all equal.Hence, the right line FE bisects one of the angles madeby the right lines FS and FS'; and the right line F'E' bisects one ofthe angles made by F'S and F'S' .When the points S, S' are at the same side of E, theangle supplemental to SFS' is that which is bisected by theright line FE. Now if the point S be fixed, and S'approach to it indefinitely, the angle SFE will approach inde-478finitely to a right angle. Therefore if a right line touching thesurface meeta directrix in a certain point, the distance betweenthis point and the point of contact will subtend a right angleat the focus which corresponds to the directrix. And if a conecirc*mscribing the surface have its vertex in a directrix, thecurve of contact will be in a plane drawn through the corresponding focus at right angles to the right line which joinsthat focus with the vertex .When the surface intersected by the right line SS' is acone, suppose this line to lie in the plane ofthe focus F andits directrix , that is , in the plane which is perpendicular atF to the focal line VF (the vertex of the cone being denoted, as before, by V); the angles made by the right linesFE, FS, FS' , are then the same as the angles made by planesdrawn through VF and each of the right lines VE, VS,VS'; and the last three right lines are the intersections ofa plane VSS' with the dirigent plane on which the point Elies, and with the surface of the cone. Therefore if a planepassing through the vertex of a cone intersect its surface intwo right lines, and one of its dirigent planes in another rightline, and if a plane be drawn through each of these rightlines respectively and the focal line which belongs to the dirigent plane, the last ofthe three planes so drawn will bisectone of the angles made by the other two. And hence, if aplane touching a cone along one of its sides intersect a dirigent plane in a certain right line, and if through this rightline and the side of contact two planes be drawn intersectingeach other in the focal line which corresponds to the dirigentplane, the two planes so drawn will be at right angles to eachother.Let a right line touching a surface of the second orderin S meet two parallel directrices in the points E, E', and letF, F' be the corresponding foci . Then the triangles FSEand F'SE' are similar, because the angles at F and F' are rightangles, and the ratio of FS to SE is the same as the ratio ofF'S479to SE'. Therefore the tangent EE' makes equal angles withthe right lines drawn from the point of contact S to the fociF, F. When the surface is a cone, let the tangent be perpendicular to the side VS which passes through the pointof contact; the angles FSE and F'SE' are then the angleswhich the tangent plane VEE' makes with the planes VSFand VSF', because the right line FE is perpendicular to theplane VSF, and the right line F'E' is perpendicular to theplane VSF'. Therefore the tangent plane of a cone makesequal angles with the planes drawn through the side of contact and each of the focal lines.Supposing a section to be made in a surface of the secondorder by a plane which cuts any directrix in the point E,if the focus F belonging to this directrix be the vertex of acone having the section for its base, the right line FE will bean axis ofthe cone. For if through FE any plane be drawncutting the base of the cone in the points S, S' , one oftheangles made by the sides FS, FS' which pass through thesepoints will always be bisected by the right line FE; and thisis the characteristic property of an axis.§ 3. Two surfaces of the second order being supposedto have the same focus, directrix, and directive planes, sothat they differ only in the value of the modulus m, or of theumbilicar ratio μ (see Part I. § 9) , let a right line passingthrough any point E of the directrix cut one surface in thepoints S, S' , and the other in the points So, S₁, and conceiveright lines to be drawn from all these points to the commonfocus F. Since, if ratios be expressed by numbers, the ratioof FS to SE (or of FS' to S'E) is to the ratio of FS。 to SE(or of FS, to S, E) as the value of m for the one surface is toits value for the other, when the focus is modular, or as thevalue of μu for the one surface is to its value for the otherwhen the focus is umbilicar, the sines of the angles EFS,and EFS ( or of the angles EFS, and EFS') are in a constant proportion to each other, because these sines are pro-4.80portional to those ratios. And since the right line FE bisects the angles SFS' and S, FS,, both internally or bothexternally, in which case the angles SFS and S'FS₁ are equal ,or else one internally and the other externally in which casethe angles SFS。 and S'FS, are supplemental, it is easy toinfer, from the constant ratio of the aforesaid sines, that inthe first case the product, in the second case the ratio of thetangents of the halves of the angles SFS, and S'FS, ( or ofthe halves ofthe angles SFS, and S'FS, ) is a constant quantity.If the point S'approximate indefinitely to S, the rightline passing through these points will approach indefinitelyto a tangent. Therefore when two surfaces are related asabove, if a right line passing through any point E of theircommon directrix intersect one surface in the points So, S1,and touch the other in the point S, the chord S。S₁ will subtend a constant angle at the common focus F, and this anglewill be bisected , either internally or externally, by the rightline FS drawn from the focus to the point of contact. Andthe angle EFS being then a right angle, the cosine of theangle SFS, or SFS, will be equal to the ratio of the less valueof m or μ tothe greater. *§ 4. Amongthe surfaces of the second order the only onewhich has a point upon itselffor a modular focus is the cone,the vertex of which is such a focus, related either to the internal or to the mean axis as directrix. In the latter relation the vertex belongs to the series of foci which areranged on the focal lines. To see the consequence of this ,let V be the vertex ofthe cone, and VW its mean axisperpendicular to the plane of the focal lines. On one ofthe focal lines and its dirigent assume any corresponding

• See Exam. Papers, An. 1839, p. xxxi . questions 9, 10. These and some

of the preceding theorems were originally stated with reference to modular focionly. They are now extended to umbilicar foci.481points F and A, and let AD be the directrix passing throughA. Then if a directive plane, drawn through any point Sof the surface, cut this directrix in D and the mean axis inW, the ratio of SF to SD will be expressed by the linearmodulus, as will also the ratio of VFto WD, since V is apoint of the surface, and WD is equal to the directive distance of V from AD. But since V is a focus to which themean axis is directrix , the ratio of SV to SW is expressedbythe same modulus. Thus the triangles SVF and SWDare similar, the sides ofthe one being proportional to those ofthe other.Therefore the angle SVF is equal to the angle SWD; thatis to say, the angle which the side VS of the cone makeswith the focal line VF is equal to the angle contained by tworight lines WD and WS, of which one is the intersection ofthe directive plane with the dirigent plane VWD corresponding to VF, and the other is the intersection of the directive plane with the plane VWS passing through the meanaxis and the side VS of the cone.Hence it appears that the sum of the angles ( properlyreckoned) which any side ofthe cone makes with its twofocal lines is constant. For if F' be a point on the otherfocal line, and D' the point where the directrix corresponding to F is intersected by the same directive plane SWD,it may be shown as above that the angle SVF' is equal to theangle SWD' , that is, to the angle made by the right lineWS with the right line WD' in which the directive plane intersects the dirigent plane corresponding to VF'. Conceiving therefore the points F, F', S, and with them the pointsD, D' , to lie all on the same side of the principal planewhich is perpendicular to the internal axis, the rightline WS will lie between the right lines WD and WD', andthe sum of the angles SVF and SVF' will be equal to theangle DWD' , which is a constant angle, being contained bythe right lines in which a directive plane intersects the twodirigent planes of the cone. This constant angle will be482found to be equal, as it ought to be, to one ofthe anglesmade by the two sides of the cone which are in the plane ofthe focal lines, namely to the angle within which the internal axis lies.If we conceive the cone to have its vertex at the centre ofa sphere, and the points F, F', S to be on the surface of thissphere, the arcs of great circles connecting the point S witheach ofthe fixed points F, F' will have a constant sum. Thecurve formed by the intersection of the sphere and the conemay therefore, from analogy, be called a spherical ellipse,or, more generally, a spherical conic, because, by removingone of its foci F, F' to the opposite extremity of the diameter of the sphere, the difference of the arcs SF and SF' willbe constant, which shows that the spherical curve is analogous to the hyperbola as well as to the ellipse. Either ofthese plane curves may, in fact, be obtained as a limit of thespherical curve when the sphere is indefinitely enlarged , according as the diameter along which the enlargement takesplace, and of which one extremity may be conceived to befixed while the other recedes indefinitely, coincides with theinternal or with the directive axis of the cone. The fixedextremity becomes the centre of the limiting curve, which isan ellipse in the first case, and a hyperbola in the second.The great circle touching a spherical conic at any pointmakes equal angles with the two arcs of great circles whichjoin that point with the foci, because the sum of these arcsis constant. This is identical with a property already demonstrated relative to the tangent planes of the cone. Indeed it is obvious that the properties of the cone may alsobe stated as properties of the spherical conic, and this isfrequently the more convenient way of stating them.§ 5. If the sides of one cone be perpendicular tothe tangent planes of another, the tangent planes of theformer will be perpendicular to the sides of the latter. Forthe plane of two sides of the first cone is perpendicu-483lar to the intersection of the two corresponding tangentplanes of the second cone; and as these two sides approach indefinitely to each other, their plane approaches toa tangent plane, while the intersection ofthe two corresponding tangent planes of the second cone approaches indefinitely to a side of the cone. Thus any given side of the onecone corresponds to a certain side of the other; and anyside of either cone is perpendicular to the plane whichtouches the other along the corresponding side . This reasoning applies to cones of any kind.Two cones so related may be called reciprocal cones.When one is of the second order, it will be found that theother is also ofthe second order, and that, in their equationsrelative to their axes , which are obviously parallel or coincident, the coefficients of the squares of the corresponding variables are reciprocally proportional, so that the equationsPx² + Qy² + Ra² = 0,x23222 ++= 0,P R(-1 )express two such cones which have a common vertex. Thesecones have the same internal axis, but the directive axis ofthe one coincides with the mean axis ofthe other, and it maybe shown from the equations that the directive planes of theone are perpendicular to the focal lines of the other. Thetwo curves in which these cones are intersected by a sphere,having its centre at their common vertex, are reciprocalspherical conics. In general, two curves traced on the surface of a sphere may be said to be reciprocal to each other,when the cones passing through them, and having a commonvertex at the centre of the sphere, are reciprocal cones. Anygiven point ofthe one curve corresponds to a certain pointof the other, and the great circle which touches either curveat any point is distant by a quadrant from the correspondingpoint of the other curve.By means of these relations any property of a cone ofthesecond order, or of a spherical conic, may be made to produce484a reciprocal property. Thus, we have seen that the tangentplane of a cone makes equal angles with two planes passingthrough the side of contact and through each of the focallines; therefore, drawing right lines perpendicular to theplanes, and planes perpendicular to the right lines here mentioned, we have, in the reciprocal cone, a side making equalangles with the right lines in which the directive planes ofthis cone are intersected by a plane touching it along thatside. It is therefore a property of the cone, that the intersections of a tangent plane with the two directive planesmake equal angles with the side of contact; a property whichit is easy to prove without the aid of the reciprocal cone.The two directive sections drawn through any point S ofa given surface of the second order may, when they are circles , be made the directive sections of a cone, and this mayobviously be done in two ways. Each ofthe two cones sodetermined will be touched by the plane which touches thegiven surface at the point S, because the right lines whichare tangents to the two circular sections at that point, aretangents to each cone as well as to the given surface; therefore the side of contact of each cone bisects one of the angles made by these two tangents; and hence the two sides ofcontact are the principal directions in the tangent plane atthe point S, that is , they are the directions ofthe greatestand least curvature of the given surface at that point; forthese directions are parallel to the axes of a section made inthe surface by a plane parallel to the tangent plane, and theaxes of any section bisect the angles contained by the rightlines in which the plane of section cuts the two directiveplanes.§ 6. It has been shown that the sum of the angles whichany side of a cone makes with its focal lines is constant.Hence we obtain the reciprocal property, that* the sum of

• This property, and that to which it is reciprocal, as well as some other

properties ofthe cone, were, together with the idea of reciprocal cones and of485the angles (properly reckoned) which any tangent plane of acone makes with its two directive planes is constant. Thisproperty may be otherwise proved as follows.Through a point assumed anywhere in the side of contact, let two directive planes be drawn. As the circles inwhich the cone is cut by these planes have a common chord,they are circles of the same sphere; and a tangent plane applied to this sphere, at the aforesaid point, coincides withthe tangent plane of the cone, because each tangent planecontains the tangents drawn to the two circles at that point.The common chord of the circles is bisected at right anglesby the principal plane which is perpendicular to the directive axis, and therefore that principal plane contains thecentres of the two circles and the centre of the sphere . Nowthe acute angle made by a tangent plane of a sphere withthe plane of any small circle passing through the point ofcontact, is evidently half the angle subtended at the centreof the sphere by a diameter of that circle; therefore theacute angles, which the common tangent plane of the coneand of the sphere above- mentioned makes with the planes ofthe directive sections , are the halves of the angles subtendedat the centre of the sphere by the diameters of the sections.But the diameters which lie in the principal plane alreadyspoken of, and are terminated by two sides of the cone, arechords ofthe great circle in which that plane intersects thespherical conics, suggested by my earliest researches connected with the mechanical theory of rotation and the laws of double refraction. I was not then aware thatthe focal lines of the cone had been previously discovered, nor that the sphericalconic had been introduced into geometry. Indeed all the properties of the conewhich are given in this paper were first presented to me in my own investigations. Its double modular property, related to the vertex as focus, was one ofthe propositions in the theory of the rotation of a solid body, and was used infinding the position of the axis of rotation within the body at a given time. Butthe modular property common to all the surfaces of the second order was notdiscovered until some years later.486sphere; and the halves of the angles which they subtendat its centre are equal to the angles in the greater segmentsofwhich they are the chords, and consequently equal to thetwo adjacent acute angles of the quadrilateral which hasthese chords for its diagonals. Hence, as two oppositeangles of the quadrilateral are together equal to two rightangles, it follows that the four angles ofthe quadrilateral represent the four angles, the obtuse as well as the acute angles,which the tangent plane of the cone makes with the planesof the directive sections; the two angles of the quadrilateralwhich lie opposite to the same diagonal being equal to theacute and obtuse angles made by the tangent plane with theplane of the section of which that diagonal is the diameter.Thus any two adjacent angles of the quadrilateral maybe taken for the angles which the tangent plane of the conemakes with the directive planes. If we take the two adjacent angles which lie in the same triangle with the angle Kcontained by the two sides of the cone that help to form thequadrilateral, the sum ofthese two angles will be equal totwo right angles diminished by к; and if we take the tworemaining angles of the quadrilateral, their sum will be equalto two right angles increased by; both which sums areconstant. But if we take either of the other pairs of adjacent angles, the difference of the pair will be constant, andequal to K.The same conclusion may be deduced as a property ofthe spherical conic. Let a great circle touching this curvebe intersected in two points, one on each side of the point ofcontact, by the two directive circles, that is, by two greatcircles whose planes are directive planes of the cone whichpasses through the conic and has its vertex at the centre ofthe sphere. Since the right lines in which the tangent planeof a cone intersects the directive planes are equally inclinedto the side of contact, the arc intercepted between the pointswhere the tangent circle of the conic intersects the directive.487circles is bisected in the point of contact; therefore, eitherof the spherical triangles whose base is the tangent arc so intercepted, and whose other two sides are the directive circles,has a constant area; because, if we suppose the tangent arcto change its position through an indefinitely small angle,and to be always terminated by the directive circles , the twolittle triangles bounded by its two positions and by the twoindefinitely small directive arcs which lie between these positions, will have their nascent ratio one of equality, so thatthe area of either of the spherical triangles mentioned above,will not be changed by the change in the position of its base.But in each of these triangles the angle opposite the baseis constant; therefore the sum of the angles at the base isconstant.From this reasoning it appears that if a spherical trianglehave a given area, and two of its sides be fixed , the thirdside will always touch a spherical conic having the fixed sidesfor its directive arcs, and will be always bisected in the pointof contact.§ 7. The intersection of any given central surface of thesecond order with a concentric sphere is a spherical conic,since the cone which passes through the curve of intersectionand has its vertex at the common centre, is of the secondorder . The cylinder also, which passes through the samecurve and has its side parallel to any ofthe arcs ofthe givensurface, is of the second order; and the cone, the cylinder,and the given surface are condirective, that is, the directiveplanes of one of them are also the directive planes of eachof the other two. This may be seen from the equations ofthe different surfaces; for, in general, two surfaces , whoseprincipal planes are parallel, will be condirective, if, whentheir equations are expressed by coordinates perpendicularto these planes, the differences of the coefficients of thesquares of the variables in the equation of the one be proVOL. II. 2 T488portional to the corresponding differences in the equation ofthe other.If any given surface ofthe second order be intersectedby a sphere whose centre is any point in one of the principalplanes, the cylinder passing through the curve of intersection ,and having its side perpendicular to that principal plane, willbe ofthe second order, and will be condirective with thegiven surface. This cylinder, when its side is parallel to thedirective axis, is hyperbolic; otherwise it is elliptic . Ifa paraboloid be cut by any plane, the cylinder which passesthrough the curve of section and has its side parallel to theaxis of the paraboloid , will be condirective with that surface;and it will be elliptic or hyperbolic, according as the paraboloid is elliptic or hyperbolic. *If two concentric surfaces of the second order be reciprocal polars with respect to a concentric sphere, the directiveaxis of the one surface will coincide with the mean axis ofthe other, and the directive planes of the one will be perpendicular to the asymptotes of the focal hyperbola of the other.When one of the surfaces is a hyperboloid, the other is ahyperboloid of the same kind; the asymptotes of the focal hyperbola of each surface are the focal lines of its asymptoticcone; and the two asymptotic cones are reciprocal .When any number of central surfaces ofthe second orderare confocal, or, more generally, when their focal hyperbolashave the same asymptotes, it is obvious that their reciprocalsurfaces, taken with respect to any sphere concentric withthem, are all condirective.§ 8. If a diameter of constant length, revolving within aI have introduced the terms directive and condirective, as more generalthan the terms cyclic and biconcyclic employed by M. Chasles . The latter termssuggest the idea of circular sections, and therefore could not properly be usedwith reference to the hyperbolic paraboloid, or to the hyperbolic or paraboliccylinder, in each of which surfaces a directive section is a right line.489given central surface, describe a cone having its vertex atthe centre, the extremities of the diameter will lie in a spherical conic. And ifthe cone be touched by any plane, theside of contact will evidently be normal to the section whichthat plane makes in the given surface, and will therefore bean axis of the section . As the axes of a section always bisect the angles made by the two right lines in which itsplane intersects the directive planes of the surface, and as thecone aforesaid has the same directive planes with the givensurface, it follows that the right lines in which a tangent planeof a cone cuts its directive planes are equally inclined to theside of contact; a theorem which has been already obtainedin another way.If a section be made in a given central surface by anyplane passing through the centre, the cone described by aconstant semidiameter equal to either semiaxis of the section will touch the plane of section; for if it could cut thatplane, a semiaxis would be equal to another radius ofthesection. Denoting by r, the semiaxes ofthe section, conceive two cones to be described by the revolution of twoconstant semidiameters equal to r and r' respectively. Thesecones are condirective with the given surface, and have theplane of section for their common tangent plane. Supposingthat surface to be expressed by the equationKx2 y² + +21 , P R(2)and the directive axis to be that of y, the axis of x will bethe internal axis of one cone, say of that described by r, andthe axis of 2 will be the internal axis of the other cone.Let be the angle made by the two sides of the first conewhich lie in the plane xx, and ' the angle made by the twosides of the second cone which lie in the same plane; theformer angle being taken so as to contain the axis of a withinit, and the latter so as to contain within it the axis of 2.2T 2490Then, considering r, r' as radii of the section xx of the surface, we have obviouslyP1+ = cos² x + sin² +K KR= + ( +1 ) + + ( -1R) CORK,(3)cos" + sin x = +-22 P (+ + 4 ) − + (P- 1R)co*k';2RKCosk';observing that when these formulæ give a negative value forr² or r²², in which case the surface expressed by the equation(2) must be a hyperboloid, the direction of r or meets, notthat surface, but the surface of the conjugate hyperboloidexpressed by the equationx² y² + +21.P R(4)Now calling and ' the angles made by the tangent planeof the cones with the directive planes of the given surface,which are also the directive planes of each cone, the anglesK, K' depend on the sum or difference of 0 and 0'. Ifthelatter angles be taken so that their sum may be equal to thesupplement of κ, their difference will be equal to x' , and theformulæ (3) will become1÷ =+ ( + )D − + (P - ) cos (0 +0')==++ ) + (P - ) cos (0-0),COS 0′) ,(5)by which the semiaxes of any central section are expressedin terms ofthe non-directive semiaxes of the surface, and ofthe angles which the plane of section makes with the directive planes. *

• See the Transactions of the Royal Irish Academy, vol. xxi. , as before

cited. The formulæ (5) were first given, for the case of the ellipsoid, byFresnel, in his Theory of Double Refraction, Mémoires de l'Institut, tom. vii. ,p. 155.491§ 9. Fromthe centre O ofthe surface expressed by equation (2) let a right line OΣ be drawn cutting perpendicularly in the plane which touches the surface at S. Let odenote the length of the perpendicular OΣ, and a, ẞ, y theangles which it makes with x, y, z. Thenσ² = P Cos²a + Q cos 23 + R cos 2y.β,(6)From this formula it is manifest, that ifthree planes touchingthe surface be at right angles to each other, the sum of thesquares oftheir perpendicular distances from the centre willbe equal to the constant quantity P + Q + R, and thereforethe point of intersection of the planes will lie in the surfaceof a given sphere. If another surface represented by theequationx2 y2 22 + + = 1 ,Po Qo Robe touched by a plane cutting OΣ perpendicularly in Zo, andif σo be the length of OZ. , thenσo² = Po cos 2a + cos 23+ Ro cos 2y;and therefore when the two surfaces are confocal, that is ,whenP ----2Po =Q Q0R=-Rok,we have o²ook, which is a constant quantity. Henceif three confocal surfaces be touched by three rectangularplanes, the sum of the squares of the perpendiculars droppedon these planes from the centre will be constant, and thelocus of the intersection of the planes will be a sphere.The focal curves of a given surface are the limits of surfaces confocal with it, when these surfaces are conceived,It was by this consideration, arising out of the theorems given in this andthe next section about confocal surfaces, that I was led to perceive the nature of the focal curves, and the analogy between their points and the foci of492by the progressive diminution of their mean or secondaryaxes, to become flattened , and to approach more and morenearly to a plane passing through the primary axis . And itwill appear hereafter, that if a bifocal right line, that is, aright line passing through both focal curves, be the intersection of two planes touching these curves, those two planeswill be at right angles to each other. Therefore the locusof the point where a tangent plane of a given central surfaceis intersected perpendicularly by a bifocal right line is asphere. The primary axis of the surface is evidently thediameter of this sphere.Hence we conclude that the locus of the point wherea tangent plane of a paraboloid is intersected perpendicularly by a bifocal right line is a plane touching the paraboloid at its vertex. For a paraboloid is the limit of a centralsurface whose primary axis is prolonged indefinitely in onedirection , and a plane is the corresponding limit of thesphere described on that axis as diameter. As this consideration is frequently of use in deducing properties of paraboloids from those of central surfaces , it may be well to stateit more particularly. It is to be observed, then, that theindefinite extension of the primary axis at one extremitymay take place according to any law which leaves the otherextremity always at a finite distance from a given point, andgives a finite limiting parameter to each of the principal sections of the surface which pass through that axis. Thesimplest supposition is, that one extremity of the axis and theadjacent foci of those two principal sections remain fixed,while the other extremity and the other foci move off, withthe centre, to distances which are conceived to increase without limit. Then, at any finite distances from the fixedconies. And I regarded that analogy as fully established when I found (in Marchor April, 1832) that the normal at any point of a surface of the second order isan axis of the cone which has that point for its vertex and a focal for its base.493points, the focal curves approach indefinitely to parabolas,as do also all sections of the surface which pass through theprimary axis, while the surface itself approaches indefinitelyto a paraboloid; so that the limit of the central surface is aparaboloid having parabolas for its focal curves. The limitof an ellipsoid, or of a hyperboloid of two sheets, is an elliptic paraboloid, having one of its focals modular and theother umbilicar, like each of the central surfaces from whichit may be derived; and the limit of a hyperboloid of onesheet is a hyperbolic paraboloid , having , like that hyberboloid, both its focals modular.§ 10. Let the plane touching at S the surface expressedby equation (2) , intersect the axis ofx in the point X, and letthe normal applied at S intersect the planes yz, xz, xy, inthe points L, M, N respectively. Since the section made inthe surface by a plane passing through OX and the point Shas one of its axes in the direction of OX, it appears, by anelementary property of conics, that the rectangle under OXand the coordinate x of the point S is equal to the quantityP; but that coordinate is to LS as O2 or σ is to OX, andtherefore the rectangle under σ☛ and LS is equal to p. Similarly the rectangle under o and MS is equal to q, and therectangle under ☛ and NS is equal to R. Thus theparts of the normal intercepted between the point S andeach of the principal planes, are to each other as thesquares ofthe semiaxes respectively perpendicular to theseplanes; the square of an imaginary semiaxis being regardedas negative, and the corresponding intercept being measuredfrom S in a direction opposite to that which corresponds to areal semiaxis.The rectangle under σ and the part of the normal intercepted between two principalplanes, is equal to the differenceof the squares of the semiaxes which are perpendicular tothese planes . This rectangle is therefore constant, not only494for a given surface, but for all surfaces which are confocalwith it.Hence the part of the normal intercepted between twoprincipal planes bears a given ratio to the part of it intercepted between one ofthese and the third principal plane,whether the normal be applied at any point of a given surface, or at any point of a surface confocal with it.If therefore normals to a series of confocal surfaces be allparallel to a given right line , they must all lie in the sameplane passing through the common centre ofthe surfaces,because otherwise the parts of any such normal, which areintercepted between each pair of principal planes, would notbe in a constant ratio to each other.The point S being the point at which any of these parallel normals is applied, the plane touching the surface at S isparallel to a given plane, the perpendicular OΣ droppedupon it from the centre has a given direction , the planeOSE is fixed, and the directions of the lines OL, OM, ONin which this plane intersects the principal planes are alsofixed . And as the angle OZS is always a right angle, andthe normal at S is always parallel to OZ, the distance Sbears a given ratio to each of the distances OL, OM, ON,and therefore also to each ofthe intercepts MN, LN, LM.Hence, since the rectangle under O and any one of theseintercepts is constant, the rectangle under O and SΣ isconstant.Therefore if a series of confocal central surfaces betouched by parallel planes, the points of contact will all liein one plane, and their locus , in that plane, will be an equilateral hyperbola, having its centre at the centre of the surfaces, and having one of its asymptotes perpendicular to thetangent planes. This hyperbola evidently passes through twopoints on each of the focal curves, namely the points wherethe tangent to each curve is parallel to the tangent planes.If a series of confocal paraboloids be touched by parallel495planes, it will be found that the points of contact all lie in abifocal right line, and that the normals at these points lie ina plane parallel to the axis ofthe surfaces; so that the partof any normal which is intercepted by the two principal planesis constant. This theorem may be proved from the two following properties of the paraboloid: —1 . A normal being applied to the surface at the point S, the segments of thenormal, measured from S to the points where it intersectsthe planes of the two principal sections , are to each other inversely as the parameters of these sections. 2. Supposingthe axis of x to be that of the surface, the difference betweenthe coordinates x of the point S and of the point where thenormal meets the plane of one of the principal sections, isequal to the semiparameter of the other principal section .§ 11. Let a tangent plane, applied at any point S of1 asurface of the second order, intersect the plane of one of itsfocals in the right line e, and let P be the foot of the perpendicular dropped from S upon the latter plane. The poleof the right line →, with respect to the principal sectionlying in this plane, is the point P. Let N be its pole withrespect to the focal. Then if T be any point of the rightline , the polar of this point with respect to the sectionwill pass through P, and its polar with respect to the focalwill pass through N; and if the former polar intersect thedirigent curve in A, A' , and the latter intersect the focal inF, F , the points F, F' will correspond respectively to thepoints A, A' , and the distances AA' and FF' will be similarlydivided by the points P and N ( See Part I. § 8) . But sincethe point S is in the plane of the two directrices which passthrough ▲ and A' , the lengths AP and A'P, which are theperpendicular distances of S from the directrices, are proportional to the lengths FS and F'S. Therefore FN is toF'N as FS is to F'S . and the right line NS bisects one oftheangles made by the right lines FS and F'S . And as this holdswherever the point T is taken on the right line , that is ,

496in whatever direction the right line FF' passes through thepoint N, it follows that the right line NS is an axis of thecone which has the point S for its vertex and the focal forits base. Further, if FF' intersect in the point Q, wehave FN to F'N as FQ is to F'Q, because N is the pole of→ with respect to the focal; therefore FQ is to F'Q asFS is to F'S, and hence the right line QS also bisects one ofthe angles made by FS and F'S. The right lines NS andQS are therefore at right angles to each other, and as thelatter always lies in the tangent plane , the former must beperpendicular to that plane.Consequently the normal at any point of a surface ofthesecond order is an axis of the cone which has that point forits vertex and either of the focals for its base.It is known that when two confocal surfaces intersecteach other, they intersect everywhere at right angles; andthat through any given point three surfaces may in generalbe described, which shall have the same focal curves. If threeconfocal surfaces pass through the point S, the normal toeach ofthem at S is an axis of each ofthe cones which standon the focals and have S for their common vertex. Thenormals to the three surfaces are therefore the three axes ofeach cone.If the points at which a series of confocal surfaces aretouched by parallel planes be the vertices of cones havingone of the focals for their common base, each of these coneswill have one of its axes perpendicular to the tangent planes.Therefore when an axis of a cone which stands on a givenbase is always parallel to a given right line, the locus of thevertex is an equilateral hyperbola or a right line, accordingas the base is a central conic or a parabola.§ 12. A system of three confocal surfaces intersectingeach other consists of an ellipsoid, a hyperboloid of onesheet, and a hyperboloid of two sheets, if the focals becentral conics; but it consists of two elliptic paraboloids497and a hyperbolic paraboloid , if the focals be parabolas. Inthe central system, the ellipsoid has the greatest primaryaxis, and the hyperboloid of two sheets the least; and thefocal which is modular in one ofthese surfaces is umbilicarin the other. The asymptotic cones of the hyperboloidsare confocal, the focal lines of each cone being the asymptotesofthe focal hyperbola. In the system of paraboloids, thetwo elliptic paraboloids are distinguished by the circ*mstance that the modular focal of the one is the umbilicarfocal ofthe other.The curve in which two confocal surfaces intersect eachother is a line of curvature of each, as is well known; * anda series of lines of curvature on a given surface are found bymaking a series of confocal surfaces intersect it.Nowifa series of the lines of curvature of a given surfacebe projected on one ofits directive planes by right lines parallel to either of its non-directive axes, the projections will bea series of confocal conics; and when the surface is umbilicar, the foci of all these conics will be the correspondingprojections of the umbilics. When the surface is not umbilicar, its directive axis will be parallel to the primary axisofthe projections.The same line of curvature has two projections, according as it is projected by right lines parallel to the one or tothe other non- directive axis. In the ellipsoid these projections are always curves of different kinds, the one being anellipse when the other is a hyperbola; but in a hyperboloidthe projections are either both ellipses or both hyperbolas. In the hyperbolic paraboloid the projections areparabolas. In the elliptic paraboloid , one of the projectionsis always a parabola, and the other is either an ellipse or ahyperbola.

• See Dupin's Développements de Géométrie.

Exam. Papers, An. 1838, p. xlvi . , quest. 4; p. xcix. , quest. 70.498The corresponding projections of two lines of curvaturewhich pass through a given point of the surface, are confocal conics intersecting each other in the projection of thatpoint, and of course intersecting at right angles.§ 13. Abifocal chord is a bifocal right line terminatedboth ways by the surface. In a central surface, the lengthof a bifocal chord is proportional to the square of the diameter which is parallel to it; the square of the diameterbeing equal to the rectangle under the chord and the primary axis.More generally, if a chord of a given central surface touchtwo other given surfaces confocal with it, the length of thechord will be proportional to the square of the parallel diameter ofthe first surface, the square of the diameter beingequal to the rectangle under the chord and a certain rightline 27, determined by the formula12 =PQR(P— P′) ( P — P') '-(7)wherein it is supposed that the equation (2) represents thefirst surface, and that P', p" are the quantities correspondingto P in the equations of the other two surfaces.In any surface of the second order, the lengths of twobifocal chords are proportional to the rectangles under thesegments of any two intersecting chords to which they areparallel.χIn the paraboloid expressed by the equationy2 2+Ρ q= x,if x be the length of a bifocal chord making the angles Band γ with the axes of y and z respectively, we have1=cos 232B+cos 27Χ Ρ q

• The theorems in § 13 are now stated for the first time.

(8)4.99§ 14. At the point S on a given central surface expressedby the equation (2) , let a tangent plane be applied, andlet k, k' be the squares of the semiaxes of a central sectionmade in the surface by a plane parallel to the tangent plane;each ofthe quantities k, k' being positive or negative according as the corresponding semiaxis of the section is real orimaginary, that is, according as it meets the given surface ornot. Then the equations of two other surfaces confocalwith the given one, and passing through the point S, arex² y² +P- k --k R - k

y2 + 2 =121, + 12 + 2 = 1 . (9) P -k' Q- k' R-k'The given surface is intersected by these two surfaces respectively in the two lines of curvature which pass throughthe point S; the tangent drawn to the first line of curvatureat S is parallel to the second semiaxis of the section , and thetangent drawn to the second line of curvature at S is parallelto the first semiaxis of the section.When two confocal surfaces intersect, the normal appliedto one of them at any point S of the line of curvature formedby their intersection lies in the tangent plane of the other,and is parallel to an axis of any section made in thelatter by a plane parallel to the tangent plane . Supposing the surfaces to be central, if two normals be appliedat the point S , and a diameter of each surface be drawn parallel to the normal of the other, the two diameters sodrawn will be equal and of a constant length, wherever thepoint S is taken on the line of curvature; the square ofthatlength being equal to the difference of the squares oftheprimary axes of the surfaces, and the diameter of the surface which has the greater primary axis being real, whilethat of the other surface is imaginary. As the pointS moves along the line of curvature, each constant diameter

• Exam. Papers, An. 1837, p. c . , quests. 4 , 5, 6; An. 1838, p. c. , quests. 71 , 72.

500describes a cone condirective with the surface to which itbelongs; the two cones so described are reciprocal, and thefocal lines of the cone which belongs to one surface areperpendicular to the directive planes of the other surface.When two confocal paraboloids intersect, if normals beapplied to them at any point S of their intersection, and abifocal chord of each surface be drawn parallel to the normal ofthe other, the two chords so drawn will be equal andof a constant length, wherever the point S is taken in theline of intersection of the surfaces; that constant lengthbeing equal to the difference between the parameters ofeither pair of coincident principal sections.§ 15. The point S being the common intersection of agiven system of confocal surfaces, of which the equationsare+y²+1 ,x² y²+ 1 , R R(10)Z + 2 + R2" = 1,suppose that another surface A confocal with these, and expressed by the equationx2 y2 22 + + 1 , (11)Po Qo Rois circ*mscribed by a cone having its vertex at S. Ifthenormals applied at S to the given surfaces, taken in the orderof the equations ( 10), be the axes of new rectangular coordinates § , n, S, the equation of the cone, referred to thesecoordinates, will be*

• The equation ( 12 ) was obtained in the year 1832, and was given at my

lectures in Hilary Term, 1836. The most remarkable properties of conescirc*mscribing confocal surfaces, are immediate consequences of this equation.That such cones, when they have a common vertex, are confocal, their focal linesbeing the generatrices of the hyperboloid of one sheet passing through the ver-501ફ્ n² +P Ро P' Ро p" Ро =0.(12)The surfaces of the given system, in the order of theirequations, may be supposed to be an ellipsoid, a hyperboloid ofone sheet, and a hyperboloid of two sheets; the axesofx, y, z being respectively the primary, the mean, and thesecondary axes of each surface. Then P is greater than r' ,and P' greater than p".The normals to the given surfaces are the axes of the coneexpressed by the equation ( 12); and if the surface A bechanged, but still remain confocal with the given system, itis obvious from that equation that the focal lines of the circ*mscribing cone will remain unchanged, since the differencesofthe quantities by which the squares of E , n , & are dividedare independent of the surface A. As P' is intermediatein value between P and P", the normal to the hyperboloid of one sheet is always the mean axis of the cone; thefocal lines lie in the plane E , and their equation isP'-€2P+P'ૐ--- 0,P( 13)which shows that they are parallel to the asymptotes of acentral section made in the hyperboloid of one sheet by aplane parallel to the plane E , since the quantities p' — P andP′ – p" are (including the proper signs) the squares ofthesemiaxes of the section which are parallel to and-retex, was first stated by Professor C. G. J. Jacobi, of Königsberg, in 1834.See Crelle's Journal, vol. xii . , p. 137. See also the excellent work of M.Chasles, published in 1837 , and entitled " Aperçu historique sur l'Origineet le Développement des Méthodes en Géométrie; " p. 387. The analogy whichexists between the focals of surfaces and the foci of curves of the second orderwas supposed by M. Chasles to have been pointed out in that work for the firsttime ( Comptes rendus, tom. xvi . , pp. 833 , 1106); but that analogy had beenpreviously taught and developed in the lectures just alluded to.502spectively. The focal lines are therefore the generatricesof that hyperboloid at the point S.When R = 0, the equation ( 12 ) becomes{2R2n² L2 + + = 0,R R( 14)which is that of the cone standing on the focal ellipse andhaving its vertex at S. When Q, 0, the same equationbecomes2n²+ + =0,( 15)which is that of the cone standing on the focal hyperbola ,and having its vertex at S. The normal to the hyperboloidofone sheet at the point S is the mean axis of both cones;the normal to the ellipsoid is the internal axis of the firstcone and the directive axis of the second, while the normal to the hyperboloid of two sheets is the directive axis ofthe first and the internal axis of the second.The three surfaces expressed by the equations12 ²n ع2+ + = 1 ,E2 n²R€22+ + 2 = 1 ,(16)+1/ +1 = 1,Rare a confocal system, having their centre at S, and beingrespectively an ellipsoid , a hyperboloid of one sheet, and ahyperboloid oftwo sheets. They intersect each other in thecentre ofthe system expressed by the equations ( 10) , andtheir normals at that point are the axes ofx, y, z respectively.The relations between the two systems of surfaces are therefore perfectly reciprocal. From the equations ( 14) and ( 15)it is manifest that the asymptotic cones of the hyperboloidsof one system pass through the focals of the other.§ 16. The point S being the intersection of a given system ofconfocal paraboloids whose equations are503y² ༧°+P 9= x + h,32p"≈2y/2Zp'+ = = = + W+1,(17)+ = x + h",where p - p'q- q' = 4 (h — h') , and p - p" = q- q″= 4(hh'); suppose that another paraboloid A confocalwith these, and expressed by the equationy2 +Ро १०.x + ho, (18)is circ*mscribed by a cone having its vertex at S. Then ifthe normals applied at S to the given system of surfaces ,taken in the order of their equations , be the axes ofthe coordinates , n, respectively, the equation of the circ*mscribingcone will be૬22 n+ +P -Po p' -po =0;p" - Po (19)showing that those normals are the axes of the cone, andthat the focal lines of the cone are independent of the surface A, provided it be confocal with the given surfaces. Ifthe hyperbolic paraboloid be the second surface of the givensystem, the parameter p' will be intermediate in value between p and p", and the equation of the focal lines of thecone will be€2 L2 +p' -p p' —-p"= 0, (20)-which is the equation of a pair of right lines parallel to theasymptotes of a section made in the hyperbolic paraboloid bya plane parallel to the plane E , since the quantities p' —pand p' — p' are proportional to the squares of the semiaxesofthe section which are parallel to & and respectively. Thefocal lines are therefore the generatrices of the hyperbolicparaboloid at the point S.-VOL. II. 2 U504Putting po and go alternately equal to zero in the equation ( 19) , we getРn² ૐ+ + = 0,pp"₤2 n² + +q q' q"=0, (21)the equations oftwo cones which have a common vertex atS, the first of them standing on the focal which lies in theplane xx, the second on the focal which lies in the plane xy.The mean axis of each of these cones is the normal at S tothe hyperbolic paraboloid; the internal axis of either coneis the normal to the elliptic paraboloid which has the baseof that cone for its modular focal.As the cones which have a common vertex, and stand onthe focals of any surface of the second order, are confocal,they intersect at right angles. Therefore when two planespassing through a bifocal right line touch the focals , theseplanes are at right angles to each other. And as cones.which have a common vertex, and circ*mscribe confocalsurfaces, are confocal, two such cones, when they intersecteach other, intersect at right angles. Therefore when aright line touches two confocal surfaces, the tangent planespassing through this right line are at right angles to eachother.§ 17. When two surfaces are reciprocal polars* with respect to any sphere, and one of them is ofthe second order,the other is also ofthe second order. Let the surface B bereciprocal to the surface A before mentioned , with respect toa sphere of which the centre is S; and suppose R' and R tobe any corresponding points on these surfaces. Then theplane which touches the surface A at the point R, intersectsthe right line SR' perpendicularly in a point K, such that therectangle under SR' and SK is constant, being equal to the.

• Transactions of the Royal Irish Academy, vol. xvii. , p. 241; Exam. Papers,

An. 1841 , p. cxxvi. , quest. 4.505square of the radius of the sphere. Now if the point Kapproach indefinitely to S, the distance SR' will increasewithout limit, the surface B being of course a hyperboloid;and if through S any plane be drawn touching the surfaceA, a right line perpendicular to this plane will evidently beparallel to a side of the asymptotic cone of the hyperboloid.The asymptotic cone of B is therefore reciprocal to thecone which, having its vertex at S, circ*mscribes the surfaceA. Hence, as the directive planes of a hyperboloid are thesame as those of its asymptotic cone, it follows that the directive planes of the surface B are perpendicular to the generatrices of the hyperboloid of one sheet, or the hyperbolicparaboloid, which passes through S, and is confocal withthe surface A. And this relation between two reciprocalsurfaces ought to be general, whatever be the position of thepoint S with respect to them; for though it has been deduced by the aid of the circ*mscribing cone aforesaid, itdoes not, in its enunciation, imply the existence of such acone. This conclusion may be verified by investigating theequation of the surface B in terms of the coordinates E, n, S.Suppose p to be the radius of the sphere with respect to whichthe surfaces A and B are reciprocal. Then if A be a central surface expressed by the equation ( 11 ) , and havingEo, no, So for the coordinates of its centre, the surface B willbe represented by the equation-Po) 2(22)(P — Po) ¿² + (P′ — Po) n² + (P″= 2p² (Eo & + non + 5% 5) — p¹;but if A be a paraboloid expressed by the equation ( 18) , theequation of B will be-(p − po) ¿² + (p' — Po) n² + ( p" — Po) 5²= 4p² (§ cos a + n cos ß + cos y),(23)where a, ẞ, y are the angles which the axis of a makes with

• This relation was first noticed by Mr. Salmon.

506the axes of E, 11, respectively. In the first case, the equation(22) shows that the directive planes of B are perpendicularto the right lines expressed by the equation ( 13); in thesecond case, the equation (23) shows that the directiveplanes of B are perpendicular to the right lines expressedby the equation (20) .When the surface A is a paraboloid , and the distance ofthe point R from its vertex is indefinitely increased , theplane touching the surface at R approaches indefinitely toparallelism with its axis, and the right line SK, perpendicular to that plane, increases without limit. Therefore thesurface B passes through the point S, and is touched in thatpoint by a plane perpendicular to the axis of A.When the point S lies upon the surface A, the coefficientof the square of one of the variables, in the equation (22) or(23) , is reduced to zero , and the surface B is a paraboloid having its axis parallel to the normal applied at S to the surfaceA. This also appears from considering that when S is apoint of the surface A, the normal at that point is the onlyright line passing through S, which meets the surface B atan infinite distance .If a series of surfaces be confocal, their reciprocal surfaces, taken with respect to any given sphere, will be condirective.When the equations of any two condirective surfaces areexpressed by coordinates perpendicular to their principalplanes, the constants in the equations may be always so takenthat the differences of the coefficients of the squares of thevariables in one equation shall be equal to the correspondingdifferences in the other. Then by subtracting the one equation from the other, we get the equation of a sphere. Therefore when two condirective surfaces intersect each other,their intersection is , in general, a spherical curve. But whenthe surfaces are two paraboloids of the same species, theirintersection is a plane curve.507§ 18. Through any point S of a given surface four bifocal right lines may in general be drawn. Supposing thesurface to be central, let a plane drawn through the centre,parallel to the plane which touches the surface at S , intersectany one of these right lines. Then the distance ofthe pointof intersection from the point S will always be equal to theprimary semiaxis of the surface. *If through any point S of a given central surface a rightline be drawn touching two other given surfaces confocalwith it, and if this right line be intersected by a plane drawnthrough the centre parallel to the plane which touches thefirst surface at S, the distance of the point of intersectionfrom the point S will be constant, wherever the point S istaken on the first surface. If this constant distance be called7, and the other denominations be the same as in the formula(7) , the value of 7 will be given by that formula. †Professor Mac Cullagh communicated the following noterelative to the comparison of arcs of curves, particularly ofplane and spherical conics.The first Lemma given in my paper on the rectificationof the conic sections (Transactions of the Royal Irish Academy, vol. xvi. , p. 79) is obviously true for curves describedon any given surface, provided the tangents drawn to thesecurves be shortest lines on the surface. The demonstrationremains exactly the same; and the Lemma, in this generalform, may be stated as follows.Understanding a tangent to be a shortest line, and supposing two given curves E and F to be described on a given

• Exam. Papers, An. 1838, p. xlvii. , quest. 9.

In the notes to the last mentioned work of M. Chasles, on the History ofMethods in Geometry, will be found many theorems relative to surfaces of thesecond order. Among them are some of the theorems which are given in thepresent paper; but it is needless to specify these, as M. Chasles's work is sowell known.508surface, let tangents drawn to the first curve at two pointsT, t, indefinitely near each other, meet the second curve inthe points P, p. Then taking a fixed point A on the curveE, if we puts to denote (according to the position of thispoint with respect to T) the sum (or difference) of the arcAT and the tangent TP, and s + ds to denote the sum(or difference) of the arc At and the tangent tp, we shallhave ds equal to the projection of the infinitesimal arc Ppupon the tangent; that is, if a be the angle which the tangent TP makes with the curve F at the point P, we shallhave ds equal to Pp multiplied by the cosine of a.Now through the points P, p conceive other tangentsT'P, t'p to be drawn, touching the curve E in the pointsT', '; and let s' and ds' have for these tangents the samesignification which s and ds have for the former tangents.Supposing the nature of the curve F to be such that it always bisects, either internally or externally, the angle madeat the point Pby the tangents TP and T'P, it is evident thatdsds', and therefore either s + s' or s s' is a constant quantity.-A simple example of this theorem is afforded by theplane and spherical conics. If the curves E and F be twoconfocal conics, either plane or spherical, and tangentsTP, T'P be drawn to F from any point P of E (the tangentsbeing of course right lines when the curves are plane, andarcs of great circles when they are spherical; in both casesshortest lines) it is well known that the angle TPT' madeby the tangents is always bisected by the conic E. Theangle is bisected internally or externally according as theconics intersect or not. Hence we have the two followingproperties of confocal conics:-

• The first of these properties was originally given for spherical conics by

the Rev. Charles Graves, Fellow of Trinity College, in the " notes and additions" to histranslation ofM. Chasles's Memoirs on Cones and Spherical Conics,509"1. When two confocal conics do not intersect, if one ofthem be touched in the points T, T' by tangents drawn fromany point P of the other, the sum of the tangents TP, T'Pwill exceed the convex arc TT' lying between the points ofcontact, by a constant quantity.2. When two confocal conics intersect in the point A, ifone of them be touched in the points T, T' by tangentsdrawn from any point P of the other, the difference betweenthe tangents TP, T'P will be equal to the difference bethe arcs AT, AT'.These properties give the readiest and most elegant solution of problems concerning the comparison of differentarcs of a plane or spherical conic. Any arc being given ona conic, we may find another arc beginning from a given point,which shall differ from the given arc by a right line iftheconic be plane, or by a circular arc if the conic be spherical.DONATIONS.Memoires de la Société Géologique de France. Tom. 5.Parts 1 , 2. Presented by the Society.The Tenth Annual Report of the Royal Cornwall Polytechnic Society. ( 1842.) Parts 1 and 2. Presented bytheSociety.Bulletin de l'Academie Royale de Bruxelles, from 5th ofNovember, 1842, to 8th of July, 1843.p. 77 ( Dublin, 1841 ) . Mr. Graves obtained it as the reciprocal of the proposition, that when two spherical conics have the same directive circles, anytangent arc of the inner conic divides the outer one into two segments, each ofwhich has a constant area. Both properties, with the general theorem relativeto curves described on any surface and touched by shortest lines, were afterwards given in the University Calendar. See Exam. Papers, An. 1841 , p. xli. ,quests. 3-6; An. 1842, p. lxxxiii . , quests. 30-34.conics were communicated, in October 1843 , to theParis, by M. Chasles , who supposed them to be new.tom. xvii. p. 838.These two properties ofAcademy of Sciences ofSee the Comptes rendus,510Ordnance Survey of Tipperary, in 93 Sheets, includingTitle and Index. Presented by His Excellency the LordLieutenant.Oberon's Vision in the Midsummer Night's Dream. Illustrated by the Rev. N. J. Halpin. Presented by the Author.Oversight over det Kongelige Danske VidenskabernesSelskabs Forhandlinger og dets Medlemmers Arbeider, 1Aaret, 1841. By Professor Oersted. Presented by theAuthor.The Numismatic Chronicle and Journal ofthe Numismatic Society of London for July, 1843. ( No. 21 ) . Presentedby the Society.PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1844.January 8.No. 43.SIR WM. R. HAMILTON, LL.D. , President, in the Chair.William Henry and John Neville, Esquires, were electedMembers of the Academy.The President read a letter from the Rev. James Kennedy Bailie, D.D., presenting his " Fasciculus InscriptionumGræcarum."The special thanks of the Academy were given to Dr.Bailie for his donation.Robert Ball, Esq. , read a notice of the Means used bythe Ancients for attaching Handles to the Stone and MetaImplements called Celts .Mr. Ball stated that many years since, the lamented DeanDawson proposed to him to put handles to the four most remarkableforms of celts , with a view of discovering the probablemanner in which these instruments were used. He accordingly did affix the handles (exhibited to the Academy), andthey appeared satisfactorily to answer the question: but recent observation has convinced him that in two at least ofthese hypothetical mountings he was incorrect, as proved,he thought, by a stone celt mounted, which was a short timesince brought from a mine in Mexico, and an iron one-awar weapon-brought a few weeks since from Little FishBay in Africa. As he deemed the subject one of interest toVOL. II. 2 x512antiquarians, he described as follows the mounting oftherecent implements alluded to, which, he conceived, may fairlybe assumed as the manner used in olden time for celts ofsimilar form.N:15INCHESbogdeno tropos BThe Mexican stone celt (No. 1) (which is the property ofMrs.Lyle) was mounted by placing a slender rod at each side Nº23 INCHES.513ofit, in the direction of its length, so that the larger ends ofthe rods would have overlapped each other about two inches,had they not been separated by the body of the instrument;a small cord was then loosely wound round the ends of therod and the included celt: when thus arranged, the smallerends of the rods were brought together and tied, formingwhat sailors call a Spanish Windlass. The elasticity of therods keeping a constant strain , makes a more effective handlethan it would appear possible to form by ordinary tying, andwith much less expense of time and trouble. The iron celt(No. 2) kindly given to Mr. Ball by Captain Adams, R.N., isfixed in the bend of a club formed like a Scotch golf stick;by this arrangement, while the iron is so fixed that a strokeserves to make it only the faster, the effectiveness of theweapon is much increased by the weight of the knob at itsend. The accompanying figures illustrate the foregoing.Mr. Ball observed that these were, he thought, proofs ofthe value of seeking explanation of antiquarian difficulties ,by observing the analogies afforded by the less civilized portions of the human race, rather than by indulging in hypothetical fancies.Mr. Oldham read a brief notice of a stone with Oghamcharacters in the County of Waterford.The stone referred to (fig 1 ) is well known throughout thatportion ofthe country, by the name of Ballyquin stone. Itstands on the road to Curraghmore from Carrick- on- Suir,about three miles and a half from that town. This road iscomparatively a new one, and the stone has been left standingabout three feet from the ditch on the south side. It is asingle block of the hard and coarse red conglomerate, soabundant in the neighbourhood, and in the adjoining rangeofthe Commeragh mountains. In height it is eight feet, andtapers gradually but irregularly from about four feet at thebase, to about one foot three inches at the top, and is about2x2514one foot or a little more in average thickness. The sides ofthe stone are rough, and do not exhibit any trace of chiselling or tooling, further than possibly a rude dressing withFig. 1 . tulhas had oftthe hammer; but along the south east corner of the stone(as it now stands), and extending from the summit to nearthe base, are a series of Ogham characters of peculiarinterest. These have been carefully worked, the bottom ofM515the cuts or grooves which form them being quite smooth andeven, notwithstanding the very unfavourable texture of thestone, composed as it is of pebbles varying in size, composition, and hardness. Some of these markings or letters areimperfect, from injuries which the stone has received , orfrom wear by exposure, but the drawing (fig. 1 ) gives atolerably accurate idea of its present state.This Ogham differs in some respects from any with whichMr. Oldham was acquainted. There is no combination ofmore than four letters or grooves in it, and if the corner ofthe stone be considered the centre line , to which these letters should be referred, several of them do not come up tothat line, and in one case two appear interrupted or discontinued in the centre; that is , there are portions ofthe cutor groove corresponding to each other at both ends, but theydo not pass over the corner or central line. Mr. Oldham'sobject was, however, more particularly to add another to thecollection of Ogham inscriptions, and thus increase the datafrom which some clue to these now unknown quantities mightperhaps be obtained . He was the more anxious to do this,as this stone had been altogether omitted on the OrdnanceMaps of the County of Waterford recently published.This stone is mentioned by Ryland in his History of Waterford, who merely notices the existence of some defacedmarkings. He alludes to the occurrence of caves in thefields adjoining. Ballyquin is also the name of the townland in which the stone stands.Mr. Oldham also presented drawings ofsome Oghams nowin the Cork Institution, and remarked how very desirable itwas that they should be published at once , the originalsbeing so liable to injury, either from accident or design.Fig. 2, is a block of sandstone, very rough and unhewn, thesurface on which the letters or marks are cut being the onlyflat one on the stone. It is about four feet six inches in516length, ofwhich the letters extend two feet; one foot teninches broad at the top, and tapers rudely to the base.Fig. 2.Fig. 3.66 Fig. 3 was dug out of an ancient fort or rath at Burntfort, near Mallow, in the County of Cork, on the property ofH. Purcell, Esq." It is of talcose mica slate, coarse-grained;the broad face is exceedingly rough and uneven; the narrow one more smooth and regular, being the natural cleavageof the rock. It is nearly seven inches wide on the narrowside, and fifteen on the broad, and about five feet high along,being nearly a parallelogram. The cuttings are nearlysimilar throughout in depth and care of execution.Fig. 4 was found at Glounaglough, parish of Aghabolloge.The entire stone is five feet seven inches long; eleven inchesand a-half broad at top, and nearly nine at the bottom.It is of a clayey-slate rock. The letters do not extend furtherdown the stone than one foot ten inches; it is nearly ofthesame thickness all through, forming a thin slab. On the faceof the stone there are scrapings, and the lower letters are517not formed by a regular groove, as the upper are, but haveall the characters of such scratches as would be formed on astone by sharpening knives or other edged tools.Fig. 4.TWITFig 5 .0000 100%000000000900//༥༽བརྟ::|リFig. 5 is of sandstone, rudely chiselled on the faces andsides, and roughly rounded on the corners of the back, theback itself being flat. It is two feet eight inches high; eleveninches and a-half at the broadest part, and about seven inchesthick. In shape it has a rude resemblance to the ordinaryform of a coffin. The letters are distinct grooves, but theydo not appear to be all of the same age, as some are veryevidently new or recent, and, as in Fig. 3, very similar to thescratches formed by sharpening tools.The Cork Institution is indebted to the zeal of Messrs.Windele and Abel for these valuable Ogham stones.Dr. Apjohn read a notice, by the Rev. Thomas Knox, onCyanogen, as a Food for Plants.518Liebig having proved in his work on Agricultural Chemistry that the nitrogenous compounds of vegetables are derived principally from the decomposition of ammonia, andthat the carbon is derived from the carbonic acid of the atmosphere, it occurred to me to try (while experimenting onsome manures) whether a source of each might not be foundin some salt of cyanogen (C₂ n) . This, I think, the followingfacts will make probable. The salt I used for this purposewas the ferro-cyanuret of potassium,(K2 Cfy = C6 N3 + Fe + K2.EXPERIMENTS.A piece ofgrass was selected in the garden, as being aseven and equal as possible, and five plots were marked outon it, side by side, each containing exactly ten square yards;they were marked out by pegs in the corners, and a line putround each while the salts were putting on, and during thecutting of the grass. They were then manured as follows,on the 17th of June last:No. 1 . Muriate of Ammonia, 3 oz.2. Aqua Ammonia of the shops, a pint; with Linseed3.Oil, 4 pints.Nothing.4. Yellow Prussiate of Potash, 3 oz. In the usual state,5.as sold by druggists , in crystals.Phosphate of Soda, 1 oz.Pearl Ash, 3 oz.Sulphate of Magnesia, 1 oz.Carbonate of Ammonia, 3 oz.The salts on these two last plots were not laid on till the26th of June, which gave them a slight disadvantage. Theywere all mown on the 25th of September, and weighed freshthe moment they were cut, when the weights were as follows:519No. 1 . 23 lbs.2. 193. 214. 325. 28when dry 7 lbs.9915/1/199 6199 9/1/2099 83I cannot depend on the dry weight, nor draw any conclusions from it, though it follows nearly the same proportion asthe fresh grass; the weather had been very wet, and it hadbeen left too long exposed to it.The great advantage of the plot manured with the prussiate ofpotash over the others is very remarkable; for abouta month it seemed rather inferior to that manured with themuriate of ammonia; but after that time the difference became very perceptible to the eye or foot.The final advantage of No. 4 above No. 1 is at the rate of38 cwt. of fresh grass, or 8 cwt. of dry grass to the acre.The reason of this superiority cannot arise from the nitrogenalone, as the quantity of it in the three ounces of muriate ofammonia (applied to No. 1 ) actually exceeds that in the threeounces of ferro-cyanuret of potassium, in the proportion of13 to 11. It must, therefore, be sought for in the other elements of the salt.Supposing this salt to be absorbed by the plant, anddecomposed in the same manner as the ammoniacal salts ,the plant will then obtain carbon and potash, as well as thenitrogen, in the nascent state, which seems to be the onlyway in which carbon can be assimilated. In fact almost everyelement required by the plant is contained in this one compound, and obtained by one and the same decomposition.I beg leave to lay these facts before the Academy, as theymay prove interesting to those engaged in the subject ofmanures, and may tend to throw a little further light on thesubject of the food of plants, should they be confirmed onrepetition; but I fear they can be of no service to the practical agri-520culturist, from the high price of all the compounds ofcyanogen.Mr. George Yeates read a paper containing the results ofa Meteorological Journal for the year 1843.- See Appendix V.The Rev. H. Lloyd communicated a letter written manyyears ago to his father, the late Dr. Lloyd, Provost ofTrinity College, by Mr. Mac Cullagh, who was then aFellowship-Candidate in the College. It relates principallyto a mechanical theory (that of the rotation of a solid body)which Mr. Mac Cullagh was occupied with at that period,and which he had occasion to allude to at the last meetingof the Academy. The following is an extract from the letter.The beginning and the date are wanting." THEOREM I.—If a rigid body, not acted on by any extraneousforces, revolve round a fixed point O, and if an ellipsoid be describedhaving its semiaxes in the direction of the principal axes passingthrough O, and equal to the radii of gyration round them; then aperpendicular to the invariable plane being raised from Oto meet thesurface of the ellipsoid in I, the line OI ( which is fixed in space, asthe ellipsoid revolves with the body) will be of a constant lengthduring the motion; and a perpendicular from O upon the plane whichtouches the surface at I , will always be the axis of rotation, and willvary inversely as the angular velocity." Corollaries."1. Since every radius which is nearly equal to the greatest orleast semiaxis of an ellipsoid must lie near that semiaxis, it appearsthat if, inthe beginning of the motion, the point I be near the vertexof either of these semiaxes, it will always be near it, since OI remainsconstant; and therefore, by the preceding construction, the axis ofrotation will always remain near the same semiaxis. Hence the rotation about the axes of greatest and least moment in any body isstable. The rotation about the axis of mean moment is unstable,because the radii of an ellipsoid, which are nearly equal to the meansemiaxis, do not all lie near that semiaxis.521"These things are evident from considering the trace of the constant line OI on the surface of the ellipsoid, and observing that, ingeneral, its projection on the plane of the greatest and least axes is ahyperbola, and its projections on the other two planes ellipses."2. But if OI be equal to the mean semiaxis b ( a and c being thegreatest and least) it will always intersect the body in the same plane,and the ellipsoid in a circle. For there are two circular sectionsthrough the mean axis; and therefore ifthe point I be at any instantin either of them, it will remain in it during the motion. It wouldbe easy to show also, that the axis of rotation, connected with OI bythe construction in the proposition, will in this case always remain ina given plane within the body." 3. If two axes (or moments) of the ellipsoid are equal, OI willdescribe in the body a conical surface round the third, and theaxis of rotation will always be in the same plane with OI and thatthird axis, and these three lines will make constant angles with eachother; also the perpendicular on the tangent plane, and therefore theangular velocity, will be constant. These things are evident merelyfrom considering that the ellipsoid becomes one of revolution."4. Whatever be the forces applied to the body, the varying planeof the maximum of areas and the axis of rotation are always connected by the construction in the proposition. But the angularvelocity is no longer inversely as the perpendicular.“ To find the axis about which a body restrained by a fixed pointO, and acted on by given forces, will begin to revolve, is usuallyconsidered a problem of great complexity. But it may be elegantlysolved by means of the ellipsoid described above. Reduce the givenforces to a single one through the fixed point O, and a pair; raise aperpendicular to the plane of the pair from O to meet the ellipsoidin I; a perpendicular from O to the tangent plane at I will be theinitial axis of rotation." The construction is true whether the forces that set the bodyin motion be impulses or pressures. If they be impulses, and noexternal forces subsequently act on the body, the axis of rotationwill vary its position both in the body and in space; its course in thebody is determined by the preceding theorem, as well as the variationof the angular velocity. The motion of the body in space dependsmainly on the two following theorems and the rectification ofthe ellipse.522Let the principal axes of the ellipsoid (ora, b, c) be OA, OB, OC." THEOREM II.-If a perpendicular IPbe let fall from I on any of the principalplanes (as AOC), the areolar velocity of Pround O will be proportional to the perpendicular IP.Q"By areolar velocity I mean the increment of the area (as POp)divided by the increment of the time when taken indefinitelysmall."Since IP = √ ( OI - OP²), the position of OI, and therefore ofthe axis of rotation at any given time, may be determined from thistheorem by the method of quadratures; and it may be reducedto the rectification of the ellipse." THEOREM III.—Let a plane passing through the fixed line OIand any of the principal axes (as OB) , intersect the plane AOC inOQ, and the invariable plane (to which OI is perpendicular) in astraight line which may be called OR; the angular velocity of ORis inversely as the square of OQ; and hence if OR be always takenequal to OQ, the point R will describe in the invariable plane areasproportional to the times."Since OQ is known at any time by the preceding proposition,the position of OR at any time will be known from this by the method of quadratures. Also the inclination of the plane AOC to theinvariable plane is known, since it is equal to the angle OIP.Hence the position of the body at any instant is completely determined."For an application ofthe theorems let us take the following problem:--The body revolving round a line indefinitely near the greatestor least of the principal axes, to find the time of an oscillation. Bythe time of an oscillation I mean that in which OI, and consequentlythe axis of rotation , returns to the same position within the body." Let the axis of rotation be indefinitelynear OA. Then x, y, z being the coordinates of I, we have x² +y² + z² = 0I² = k²,x2 y2 22be and + + = 1 . ThereforeCB Y5232² ( -1) + ( - 1 ) = 1- ya²k2aHence the locus of P is an ellipse whose semiaxes a' and b' areb√ (a² - k²)√(a² — b²)and -c√(a² - k²)√(a² - c²)-

and therefore its areaza'b' =xbc (a² - k²)√(a² — b²) (a² — c²³)"But I oughtto have mentioned, as part of Theorem II., the method of determining in general the areolar velocity of P. Let theangular velocity multiplied by the cosines of the angles which theaxis of rotation makes with OA, OB, OC be denoted (as is usual) byp, q, r. These have constant ratios to the perpendiculars, as IP,drawn in that proposition; and in that case the areolar velocity of Pisequal to (b² - k²)q: and similarly when AOC is any of the otherprincipal planes. Hence, in the present instance, the areolar velocity= (a² - k²) p; and therefore the time of an oscillation=27bcp√(a² — b²) (a² — aº)from the above value of the area of the ellipse, and observing that,since OI is indefinitely near OA, IP and therefore p may be regarded as constant.2πp'"If T denote the time of one revolution of the body round itsaxis, then ultimately T =tion is to thetime of a revolution as the rectangle under the semiaxesof the section BOC is to the rectangle under the eccentricities ofthe other two sections. A similar theorem holds when the body revolves round a line indefinitely near the least principal axis. Thetimes of small oscillations of different magnitudes are equal, as in thependulum.and therefore the time of an oscilla66 Many particular consequences might be deduced from what hasbeen said; but it will be better to mention some new theoremsabout moments of inertia and centrifugal forces.524"The forces resulting from the centrifugal forces of a body of anyfigure, revolving round an axis passing through a fixed point O, maybe found elegantly by the ellipsoid of which we have already madeso much use. Let a plane at right angles to the given axis OK,and cutting it in K, touch the ellipsoidin I; the centrifugal forces will be reduced to a pair whose moment is OK XKIX 2* (w being the angular velocity),whose plane is OKI, and direction asmarked in the figure; and a single forceequal to Mpa², p being the distance ofthe centre of gravity from OK.0"If OK pass through the centre of gravity, there remains only thepair. The perpendicular OK is the radius of gyration for the axisOK. Particular consequences of these things are numerous.66 Any line, taken at random in a body, may not be a principal axis.All the principal axes parallel to a given line lie in the same plane;and the points of their lengths which must be fixed, in order that theymay be principal axes, will lie in a hyperbola. Suppose in this casethe point O (preceding fig. ) to be the centre of gravity, and OK tobe parallel to the given line, and describe through I an equilateralhyperbola whose asymptotes are OK and OL; then all theprincipal axes, as O'K' , O" K" , parallel to OK, lie in the planeOKI, and the points O' , O" of their lengths, which must be fixed,are at their intersections with the hyperbola."By means of theorems of this nature, all of which are provedgeometrically, without any calculation, I have been able to give acomplete geometrical solution of the problem of the motion of a solidbody not acted on by any forces. If it be acted on by given forces,the differential equations in A, B, C and p, q, r, which are given byall the writers on mechanics, are direct consequences of the firstprinciples, without the intervention of any calculation.

"Another thing with which I had occupied myself is the attrac-

• Multiplied by the mass of the body, or by M.

525tion of ellipsoids. Having written out a simple demonstration of avery elegant known theorem relating thereto, I shall subjoin it separately."Theproposition above alluded to depends on the following theorem, which may be very simply proved:—If from the extremitiesA, B, C of the semiaxes of an ellipsoid whose centre is O, there bedrawn three parallel chords Aa, BB, Cy, meeting the surface of theellipsoid in a, ß, y; and if a perpendicular from a on OA meet it in r,a perpendicular from ẞ on OB meet OB in s, and a third from y onOC meet OC in t; then willAr Bs Ct + + = 1 .AA' BB' CCAA', BB' , CC' are the whole axes." Theproposition itself is this:-Ifthe particles of a hom*ogeneousellipsoid attract inversely as the square of the distance, and if a, b, сbe the semiaxes, and A , B , C, its attractions on points placed attheir vertices, then willBo + b+= 4π.с" The attractions are here, as is usual, represented by lines; theattraction of an indefinitely small part of the solid being representedby its volume divided by the square of its distance from the attractedpoint." The attraction being thus measured, it is evident that if from thevertex of a pyramid, whose transverse sections are indefinitely small,as a centre, with any radius, a sphere be described whose surface ispenetrated by that of the pyramid, the attraction of the pyramid ona point at its vertex will be to its length, as the intercepted surfaceof the sphere is to the square of its radius."Let A, B, C be the three vertices ofthe axes, and from them letparallel chords Aa, Bß, Cy be drawn; from whose extremities a, ß, ylet perpendiculars be let fall on the respective axes, meeting themin r, s, t; then by the preceding theoremn526Ar Bs Ct + + = 1 .AA' BB' CCpyLet now two other chords be drawn from A making with Aa verysmall angles, so as to form with it the edges of a very small pyramid,and let other chords parallel to them be drawn from B and C, formingalso with B and Cy the edges of two other small pyramids. Imagine a sphere fixed in space, from whose centre are drawn three linesparallel to the three chords drawn from A, or from B, or from C, andconceive the surface of the pyramid, of which they are the edges, topenetrate that of the sphere; then will the attractions ofthe threeramids, reduced each to the direction of the axis passing through itsvertex, be to Ar, Bs, Ct as the intercepted surface of the sphere tothe square of its radius; and therefore the sum of each of those attractions, divided respectively by AA' , BB' , CC' , will be to unity inthe same ratio. Conceive pyramids thus related to be multiplied indefinitely, and the spheroid will be exhausted at once from each ofthethree points A, B, C, while half the surface ofthe sphere is exhaustedby the parallels drawn from its centre. Hence it appears that thesum of the whole attractions at A, B, C, divided respectively byAA' , BB' , CC', is to unity as the surface of a hemisphere to thesquare of its radius, or as 27 to 1; and thereforeaBo + + = 4%.January 22.REV. JAMES H. TODD, D. D. , Vice-President, in the Chair.Mr. W. H. Hudson exhibited specimens of Irish books,now in the course of publication in Cork, which are lithographed. He described the advantages which that processpresents over types, for composition in the Irish character.Dr. Kane read a paper on the Chemical Composition ofthe different kinds of fuel found in Ireland .527Although this country is recognized as destitute of thegreat development of the coal strata , which has proved soimportant an element in the industrial progress of GreatBritain, yet there are known to exist several coal districts ,some bituminous and some anthracitous, as well as depositsofwood coal, which, with the great extent of turf-bog occupying the surface in many places , may be considered as storesof fuel, available and sufficient for the supply of the interiorof the country for a very long time. In order, however, tobe able to calculate the economic value, or calorific power ofany of these Irish fuels, and so to compare them with thecorresponding fuels in other countries, it was necessary toknow their elementary composition; and hence, in order tolay the basis of a true estimate of the worth of our nativefuels, Dr. Kane commenced the series of analyses whichformed the present communication.In order to exhibit all the relations of the composition ofthese fuels, that might be useful in drawing practical conclusions, Dr. Kane adopted two distinct modes of analysis:one, exhibiting the real elementary composition; the other,which he terms the practical analysis, representing the relation of the ashes, and of the fixed and volatile constituentsof the fuel. He also in each case ascertained the quantityof oxygen which the fuel was capable of taking up, in orderto be perfectly consumed. As the analysis of fuels is knownto present some difficulty, it is necessary to mention brieflythe precautions taken in order to secure accurate results.The point first determined was in each case the quantityof ashes present. To effect this a certain weight of the fuelwas burned in a current of hot air, until all traces of organicmaterial disappeared . The residual ash was then weighed.To conduct the determination of the carbon and thehydrogen of the fuels, the methods were varied according tothe nature of the substance, with turf, lignite, and the bituminous coals . The proper weight of the material havingVOL. II. 2Y528been dried at 212° F., was in some cases mixed withchromate of lead, and the analysis conducted in the ordinarymanner; in other cases, the substance was mixed with blackoxide of copper, and some chlorate of potash having beenplaced in the end of the analysis tube, the operation wasconducted in the usual way to near the termination, whenthe chlorate of potash being heated , a stream of oxygen gaspassed through the apparatus, and burned out the last tracesof the organic substances.These two modes gave almost identical results with thesame fuel, and there is no necessity for distinguishingamongst the analyses, of which the results follow, those thatwere done in the one way or in the other.It was found, however, that the anthracite could not beperfectly analysed by either of these modes: the difficultyof burning away the last portions of the carbon was so great.Hence a totally different plan was adopted for that varietyof fuel. An analysis tube of Bohemian glass having beentaken about a foot long, the substance to be analysed wasplaced in a little boat of platina foil, and introduced into thetube near one end. To this end was fitted a tube containingdry chloride of calcium to collect the water; then the potashabsorbing apparatus, then another potash absorbing apparatus, and finally a tube containing dry potash. These threewere for the purpose of separating the carbonic acid perfectlyfrom the excess of oxygen, and also to prevent the oxygenfrom carrying away any moisture from the potash liquor.The other end ofthe tube was connected with a gazometerfull of pure oxygen gas, which, streaming over a large surface of fused chloride of calcium, was rendered perfectlydry. The apparatus being so adjusted, the analysis tubewas heated to redness by charcoal, so that the oxygen gaspassed through five or six inches of red hot tube beforecoming to the ignited anthracite . The analysis was thusconducted, as it were, with the hot blast, and the combustionwas in all cases quite perfect. This kind of process would529only answer with such fuels as anthracite, which containsvery little hydrogen, but with those it succeeded perfectly.Such were the means taken for the organic elementaryanalysis. The nitrogen was not separately determined, asthe results were only required for economic calculations,and the minute trace of nitrogen does not there become important. Its weight (in all cases very small) is included in thenumber assigned to oxygen in the results of the analyses.The practical analysis was conducted by very stronglyigniting a weighed portion of the fuel in a platinum cruciblethe cover of which fitted so closely as to prevent any sensible combustion of the residual co*ke. The weight of ashesbeing known, the pure co*ke was then found.The determination of the reducing power of the fuel bymeans of litharge, requires very considerable care in practice in order to get satisfactory results. The principal pointto be attended to, is to use a roomy crucible, and to apply aquick and strong heat, so that the litharge shall at once runthin. When this is done, the results with the same fuel arevery uniform, and with different fuels are fully comparable;although in no case is so much lead got as should be intheory obtained from the conversion of the carbon andhydrogen ofthe fuel, minus its oxygen, into carbonic acidand water. The deficiency is usually proportional to thequantity of volatile matter in the fuel, and is not in any caselarge, provided proper care be taken. Hence Dr. Kaneconsiders, and the opinion is also held by Berthier, that theresult is so near the truth as to be quite available as a practical and ready measure of the heating power of the fuel.The general nature of the inquiry, and the methods employed, having been thus described , it is only necessary toadd the numerical results of the analysis.In order that the results might represent as far as practicable the average composition of the fuel, in each caserather a large mass was broken up, and its coarse powder2Y2530well mixed. Some ounces of this were then reduced toimpalpable powder, and from this all the portions to beoperated upon were taken.I. ANTHRACITES OF THE SOUTH OF IRELAND.Three specimens of this kind of coal were analysed:1 , from the Rushes Colliery, Queen's County;2, 99 the Pollough Vein, Castlecomer, Co. Kilkenny;3, 99 the Sweet Vein, Kanturk, County Cork.The anthracites have no tendency to froth or cake inco*keing. They give off little or no inflammable gas on beingignited, but usually the masses break up quite small, especially if the heat be suddenly applied . The ashes are almostalways red, owing to peroxide of iron remaining after thecombustion of the iron pyrites, which the anthracite generally contains.Rushes anthracite-0.375 grammes gave:Water •Carbonic acid .Light red ashes· 0.1181.2380.014The Pollough anthracite. 0.364 grammes gave:Water • • 0.079Carbonic acid • • • • 1.086Brown ashes • · 0.036The Sweet Vein anthracite-0.293 grammes gave:Water .Carbonic acid .0.305 gave0.098• 0.9280.026 ashes, white.These coals consisted , therefore, of:Rushes. Pollough. Sweet Vein.CarbonHydrogen· 90.04 81.36 86.373.50 2.41 3.71Oxygen • 2.73 6.34 1.40Ashes 3.73 9.89 8.52100.00 100.00 100.00531Of these coals the Sweet Vein was perfectly free fromsulphur; the Rushes coal contained but a minute trace;but the Pollough coal contained a good deal, and as thesulphurous acid produced during its combustion should beabsorbed by the potash, and counted as carbonic acid in theanalysis, it was necessary to correct the above result by adirect determination of the sulphur. For this purpose 3.526grammes of the coal were boiled with aqua regia, and theliquor precipitated by chloride of barium. The sulphate ofbarytes obtained weighed 1.589 grammes, corresponding to45.07 per cent. , containing 6.18 of sulphur.Now, 6.18 sulphur give 12.36 sulphurous acid, and subtracting that from the carbonic acid obtained in the elementary analysis, then converting the sulphur into bisulphuret of iron, and subtracting the pyrites from the ash,there comes out, as the true composition of the Polloughcoal:Ash, free from ironBi- sulphuret of ironCarbonHydrogenOxygen2.19· 11.58• • 75.42• 2.41 giving of pure an- •thracite 86.23.• 8.40100.00It is interesting to contrast the composition of the reallyorganic part of these three varieties of coal.Rushes. Pollough. Sweet Vein.Carbon .Hydrogen• · 93.53 87.46 94.39• · 3.63 2.79 4.05Oxygen · 2.84 9.75 1.56100.00 100.00 100.00By the practical mode of analysis these coals were foundto give, per cent.:532Rushes. Pollough. Sweet Vein.Volatile matter • •. 9.85 10.40 10.35Pure co*keAshes· · · 86.42 79.71 81.133.73 9.89 8.52100.00 100.00 100.00Hence they correspond respectively.The result of ignition with litharge was, thatOne part of Rushes coal gave 31.8 oflead .PolloughSweet Vein100 parts of Rushes to .•• 26.7 9929.0 ""· 93.5 of pure carbon.100 99100PolloughSweet Vein• • 73.5 9999 • 85.3 99And in average 100 parts of Irish anthracite may be considered to possess a calorific power equal to 84 parts of purecarbon.II. COAL OF THE CONNAUGHT BASIN.The coals examined were all from the collieries of Brahlieve mountain, forming the western division of the LoughAllen coal field . The specimens were furnished throughthe kindness of Colonel Jones, member of the Shannon Commission. The results were as follow:AUGHABEHY COAL.A rich, black coal, easily broken. Sp. gr. 1.274. Whenheated, it gives off a good deal of inflammable gas , and leavesa light grey, porous, coherent co*ke.Its elementary analysis was effected:0.472 grammes gave:Carbonic acidWater · ·· · • 1.379 grammes.• 0.2650.921 grammes gave of white ashes, 0.099, or 10.75per cent.533Hence it contained:CarbonHydrogenOxygenAshes .ROVER COAL.· 79.696.24· 3.3210.75100.00This coal is rather brown in aspect, and splits casily intocubical fragments. On ignition it gives out gas, but doesnot froth. Its co*ke is porous, slightly coherent.Its elementary analysis was:3.196 grammes gaveequivalent to 7.41 per cent.0.489 gramme gave:Water •Carbonic acid .Hence it contained:CarbonHydrogenOxygenAshes• 0.237 of ashes ,0.2161.45381.044.91· 6.647.41100.00The practical analysis of these two coals gave the following results:Aughabehy Coal. - 13.418 grammes gave on ignition10.340 of co*ke.Rover Coal. -14.300 gave on ignition 11.770 of co*ke.Hence they consisted of:Volatile matterPure co*keAshes·• •Aughabehy.23.10Rover.· • 17.7066.15 • 74.8910.75 7.41100.00 100.00534Specimens of coal from the Celtnaveena and the Meenashama collieries were also examined in this manner, withthe following results:Celtnaveena Coal.-14.772 grammes gave by ignition11.960 of co*ke.1.091 gramme gave 0.164 of white ashes.Meenashama Coal. -6.280 grammes gave 5.095 co*ke.3.778 gave 0.742 of ashes.Hence they consist ofVolatile matterPure co*keAshes••Celtnaveena. Meenashama.19.10 • . 18.90• 65.87 • · 61.4615.03 • · 19.64100.00 100.00Each of these varieties of coal was examined as to thequantity of oxygen it absorbed by reducing litharge.1 part of Aughabehy coal produced 26 parts of lead .1 part of Rover coal produced 28 parts of lead.1 part of Celtnaveena coal gave 26 of lead.1 part Meenashama coal gave 25 of lead .100 parts are therefore equivalentOf Aughabehy to • 77 parts of pure carbon.RoverCeltnaveenaMeenashama99 84• 77 2973 ""These coals are similar in appearance to the Aughabehy,but are more slaty. When ignited they give off inflammablegas, but do not froth. Their co*ke is dense.It is thus seen that the Aughabehy is the most bituminous of these coals, whilst the Rover is the least so, andthat in fact the latter approaches closely in its compositionto the anthracite of the Munster coal field .535III. COAL ON THE TYRONE BASIN.Of this locality two kinds of coal were examined, fromopposite sides of the field , the new Drumglass Colliery, andthe colliery at Coal Island.COAL ISLAND COAL.It is slaty in structure, dull coloured; sp. gr. 1.267 .On ignition it gives off much gas, froths, and leaves a veryporous co*ke.2.814 gave 0.328 of ashes almost white.8.830 grammes gave after ignition 5.390 of co*ke.It hence consisted ofVolatile matterPure co*keAshes . ••· 38.9649.3911.66100.00In its elementary analysis, 0.563 gramme gave:WaterCarbonic acidWhence results the compositionCarbon •HydrogenOxygenAshes ••• 0.297· 1.42669.085.86• 13.4111.65100.00On ignition with litharge, one part of this coal gave 261of lead, hence 100 parts correspond to 78 of pure carbon.NEW DRUMGLASS COLLIERY .This coal is brilliant, black, friable, frequently mixedwith pyrites, which oxidize on exposure to the air . Itsashes are consequently reddish . On ignition it gives offmuch gas, froths, and produces a light porous co*ke. Itspractical analysis was as follows:5361.977 grammes gave of brown ash 0.342.11.540 gave on ignition 5.920 of co*ke. It consistedhence ofVolatile matterPure co*ke1 Ashes· 48.7034.0017.30100.00.When ignited with litharge, one part produced 22 partsof lead. 100 parts of it are therefore equivalent to 65 partsof pure carbon.IV. COAL OF THE ANTRIM DISTRICT.The coal of Ballycastle is dull, black; sp. gr. 1.279.On ignition it gave out much gas, frothed , and left a porousco*ke. On its practical analysis it gave in 100 partsVolatile matterPure co*keAshes • ·•· • · 36.96• 45.94• • • 17.10One part ofit produced 25 of lead, and 100 are thereforeequivalent to 71 parts of pure carbon.V. LIGNITES OF LOUGH NEAGH.Having thus determined the composition, and more important practical relations of the coals from the several coaldistricts of Ireland, Dr. Kane proceeded to examine thenature of the deposit of lignite which is found among thetertiary beds along the southern extremity of Lough Neagh.As these investigations had solely a technical object, thesilicified wood of that district did not require any notice,but only such wood- coals as were capable of use as fuel,Two specimens were examined. They retained all thestructure of wood, and were of a deep brown colour. Whenignited they gave off gas, which burned brilliantly, and left adense black charcoal.On elementary analysis, they gave the following results:537No. 1. - 1.887 gave 0.163 of a reddish ash containingmuch iron.0.489 grammes gave:Water . •Carbonic acid ·· 0.2621.050No. 2. -3.393 grammes gave of slightly reddish ashes0.550.0.648 gramme gaveWater . • 0.429Carbonic acid · • 1.220These lignites consequently consisted ofNo. 1 . No. 2.CarbonHydrogen58.56 51.36• 5.95 7.35OxygenAshes· 26.85 25.08• 8.64 16.21100.00 100.00The results of the practical analyses were as follows:Volatile matterPure charcoal ·AshesNo. 1. No. 2.• 57.70 53.7033.66 30.098.64 16.21By ignition with litharge, No. 1 gave 193 parts of lead ,and No. 2 gave 16.7 parts. They hence were equivalent in100 parts.No. 1.-To 58 parts of pure carbon.99 50 وو 2.- .NoVI. TURF.The specimens of turf were selected from Cappoge, inKildare, and Kilbeggan, in Westmeath, on different sidesof the great Bog of Allen, and from Kilbaha, in Clare.When ignited, turf gives off inflammable gas, and leaves alight, easily combustible charcoal .The elementary analyses were as follows:KILBEGGAN TURF..383 grammes gave:538WaterCarbonic acid ·AshesKILBAHA TURF.• 0.2300.8570.0073.435 grammes gave 0.277 of a light reddish ash.0.663 gramme gave:Water .Carbonic acid · •0.3781.243CAPPOGE TURF.10.566 grammes gave 0.270 of ashes.0.500 gramme gave:WaterCarbonic acid ·• 0.3080.935From these results follow the composition:Kilbeggan. Kilbaha. Cappoge.CarbonHydrogenOxygenAshes .• 61.04 51.13 51.05• 6.67 6.33 6.85· • 30.46 34.48 39.55· · 1.83 8.06 2.55100.00 100.90 100.0In the practical analysis of turf it is necessary to attendto the physical constitution of the fuel, as, even with the samechemical elements, the heating power, and the proportion offixed and volatile parts, will vary with the denseness of texture of the fuel. Important differences exist also in thecharacters of the turf taken at different depths below thesurface of a bog. These circ*mstances require to be carefully attended to in practice.When ignited, there were obtained from specimens oflight surface turf:Volatile matterPure charcoalAshes ·• ·Cappoge. Kilbeggan.• · 73.63 75,5023.82 22.672.55 1.83100.00 100.00539and from deep- seated turf,Volatile matterPure charcoalAshes •Kilbaha. Cappoge.72.80 70.10• 19.14 23.668.06 6.24100.00 100.00Of these varieties of turf it was found that on ignitionwith litharge,1 part light Cappoge turf gave 13.0 of lead ,1 291 99Kilbeggan turfKilbaha turf99 14.2 ""29 13.8 39and hence that 100 parts corresponded, ofCappoge turf to 37 of pure carbon.Kilbeggan ,, 41 ""Kilbaha ""402999 ""By means ofthese investigations Dr. Kane trusted thatthe chemical nature, and economic value of the fuels of Ireland might be considered as established, and thus one stepmade towards a correct knowledge of the circ*mstances under which this country is placed as to those important materials of industry. The question as to the extent of thosedeposits, the real quantity of each fuel available in practice,as well as the mode in which those deposits have had theirorigin, pass from the domain of chemical inquiry, and hencehave been left by Dr. Kane to those geological philosopherswhom the Academy proudly enumerates amongst its members.Dr. Apjohn and Mr. R. Mallet made some observations.

PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1844.February 12.No. 44.REV. JAMES H. TODD, D. D., Vice- President, in the Chair.Henry Clare, Esq. , was elected a member of the Academy, and the Rev. Charles Graves was elected a member ofthe Committee of Polite Literature.Mr. Ball made a communication on a collection of theIrish names of animals, which he had been for many yearscollecting from ancient manuscripts, dictionaries, personsspeaking the Irish language at present, &c. He stated thatfor one important addition he was indebted to Mr. Curry,who pointed out in a manuscript poem, said to be of the fifthcentury, ascribed to Caoilte , one of Finn Mac Coole's heroes,and which is certainly older than the year 1000, a portion,in which the names of one hundred animals are recorded ina list of the ransom paid for the celebrated Finn Mac Coole,when a prisoner. Some of the names mentioned have not yetbeen translated . Mr. Ball observed on the value of such acollection as a means ofthrowing light on the names of placesin Ireland, and urged the interest that naturalists of othercountries felt, in preserving the names by which animalswere known in their native places, as a sufficient reason fordesiring to preserve those of Ireland. He stated his intention of having the collection he had made properly digested542and arranged by a competent person, and that he wouldthen offer it tothe Academy for publication.Professor Mac Cullagh made some remarks, of which thefollowing is the substance, concerning the letter communicated by Mr. Lloyd at a former meeting (see Proceedings,p. 520).The letter read by Mr. Lloyd at a late meeting of theAcademy, was written by me immediately after the examination for Fellowships, which was held in Trinity College, inthe year 1831. I had been a candidate on that occasion;and Dr. Bartholomew Lloyd, to whom the letter was addressed, had been one of the examiners. The letter contains, among other things, several theorems taken from a geometrical theory of Rotation, with which I had been previouslyoccupied. Soon after it was written, I returned to thattheory, for the purpose of improving it in one part where Ifelt it to be defective, and where, indeed , I experienced thechief difficulty; I mean the part which relates to finding theposition ofthe body at any given time. The method given inmy letter for doing this by quadratures, had occurred to mein 1829; but I was, of course, not satisfied with it, and Ihad in the interval made some attempts to find a methodmore elegant, and , as far as possible, really geometrical. Inthe autumn of 1831 I succeeded completely in this, and nofurther additions of any consequence were made to thetheory. The position of the line OI within the body, at anygiven time, was found by an elliptic function of the first kind,the modulus and amplitude of which are given immediatelyby geometrical considerations; the modulus of the functionbeing in fact the ratio of the two moduli of the cone whichthat line , stationary in space, describes within the body.This result was deduced from Theorems I. and II . of the letter. The cone reciprocal to that just mentioned was used tofind the position of the body in space. This reciprocal cone,543carried about with the body, always touches the invariableplane; the side of contact, at any instant, being that whichcorresponds to OI, and which therefore lies in the planepassing through OI and the axis of rotation. The angle described in the invariable plane by the side of contact is thesum or difference of two angles , one of which is proportionalto the time, and the other is the angle described by that sidein the surface of the cone. As the latter angle is measuredby the arc of a spherical conic, it followed , on comparingthis result with the integral given by Legendre in his discussion ofthe question of rotation, that the arc of a spherical conic represents an elliptic function of the third kindwith a circular parameter.The curve described by the point I on the surface of theellipsoid, is a spherical conic; and it now appears in whatway the consideration of this mechanical question led to thestudy ofthe properties of cones and spherical conics. Fromtheorems relating to centrifugal forces and principal axes ofrotation, I was further led to consider systems of ellipsoidsand hyperboloids having the foci of their principal sectionsthe same; and then the focal curves presented themselvesas the limits of these surfaces. The properties of the focalcurves and of confocal surfaces occupied me, at intervals, inthe year 1832; but in the latter part of that year my attention was diverted from these subjects, and it was not until1834 that I began to think of writing down and publishingthe results of my inquiries respecting them. In doing so, Iwished to be able to assign a geometrical origin to the surfaces ofthe second order, the theory of these surfaces beingintended to precede that of rotation; and in seeking forsuch an origin, I found the modular property. But not longafter (in the summer of 1834) happening to look into a Frenchscientific journal, I learned that M. Poinsot had just readto the Academy of Sciences of Paris a memoir in which hetreated the question of rotation geometrically, by a methodVOL. II. 2 z544substantially the same as mine. This caused me to give upthe design of writing on that subject; and , my thoughtsthen turning to the theory of light, the subject of surfaces ofthe second order was also dropped.Another form of Theorem I. is given by the property ofreciprocal ellipsoids. If a second ellipsoid be constructed ,having its centre at O, and its semiaxes coincident with, andinversely proportional to those ofthe first, and if this ellipsoidbe touched by a plane parallel to the invariable plane, it isobvious, from the relations of reciprocal ellipsoids, that thetangent plane will be fixed in space, and that the right linewhich joins the point of contact with the point O, will alwaysbe the axis of rotation, and will be proportional to the angular velocity. This form of the theorem, though not mentioned in the letter, was nevertheless employed in my theoryof rotation. It is the form given by M. Poinsot, who usesonly the second ellipsoid; and it has the advantage of determining geometrically (as M. Poinsot has remarked) thesuccessive positions of the body in space, independently ofthe consideration of time; for the ellipsoid evidently rollsupon the fixed plane which it always touches. This advantage, however, though evident when stated, I do not recollect that I had distinctly perceived .The theorem mentioned in my letter, for finding the moment ofthe centrifugal forces, is the same (making allowancefor the difference of the ellipsoids) with one given byM. Poinsot, which he speaks of as " a simple and remarkabletheorem, containing in itselfthe whole theory ofthe rotation.of bodies;" and ofwhich he further observes, as I have done,that " translated into analysis, it gives immediately the threeelegant equations which are due to Euler, and which areusually demonstrated by long circuits of analysis. " It was,in fact, from this theorem, by means of the principle ofthe composition and resolution of rotatory motions , that mytheory, as well as that of M. Poinsot, was deduced. I may545add, that I also employed M. Poinsot's beautiful theory ofcouples, which has introduced so much clearness into thefundamental doctrines of mechanics.Mr. G. Wilkinson read a paper on the existence ofthepointed arch in the early buildings of Ireland, prior to theintroduction of Gothic architecture.Mr. Petrie offered some remarks on Mr. Wilkinson's communication.Dr. Allman noticed the occurrence in Ireland ofFredericella Sultana, and entered into certain details of its zoologicaland anatomical characters. This zoophyte has been veryimperfectly described , and is moreover burthened with a discordant synonomy which has involved its history in no smallobscurity. The difficulty which is thus necessarily connected with the attempt to determine the true FredericellaSultana, Dr. Allman endeavoured to remove, by reducing tosome sort of order the mass of synonymes in which it is involved. It would appear to be the Tubularia Sultana ofBlumenbach, its original discoverer; the Plumatella Gelatinosa of Dr. Fleming; the Plumatella Sultana of Sir J. G.Dalyell; and the Fredericella Sultana of Gervais. It wouldappear also that the zoophyte described by Mr. Varley, in alate number of the London Physiological Journal, is thesame as the present.By some singular oversight, Dr. Fleming, in the description of his Plumatella Gelatinosa, refers to the TubulariaGelatinosa of Pallas, described in the " Elenchus Zoophytarum." The Tubularia Gelatinosa of the Elenchus, however, is quite a different animal; it belongs to the group withcrescentic disks, and is identical with the free variation ofPlumatella repens.The author, in entering into the details of its anatomicalstructure, drew attention to the high ascidiform type which2 z 2546it presented. He also noticed a hyaloid membrane of greattenuity which surrounds the base of the tentacular plume,and extends upwards for about the fourth of the length ofthe plume, being adherent to the tentacula, and constitutinga kind of calyciform appendage to the base of the crown.He mentioned the existence of this calyciform membranein Plumatella and Cristatella, but would not speak positivelyas to its presence in Alcyonella; from Paludicella it is certainly absent, a fact which, along with several others, tends toapproach this elegant zoophyte to the marine Ciliobrachiates.Dr. Allman also alluded to a singular valve- like organwith which the mouth is furnished , exactly similar to thatfound in Plumatella , and described by the Author at the latemeeting of the British Association. This organ he has alsodetected in Cristatella.Through the external tunic of the polypidom will befound scattered , numerous silicious particles of no definitefigure, and the Author considered himself justified , from theobservations which he had made upon the fresh-waterzoophytes, to come to the general conclusion that in thecorneous polypidom of these animals, silica replaces the calcareous deposits of the marine species.February 26.ROBERT BALL, Esq. , Treasurer, in the Chair.The Secretary read a paper by the Rev. Dr. Hincks," On the Defacement of Divine and Royal Names on Egyptian Monuments."An attempt is made in this paper to specify the severaloccasions, on which the principal defacements of Egyptian547monuments took place; mentioning the principal ones whichsuffered on each occasion. The occasions specified arefour.I. The dethronement or death of Q. Amuneth (circa1325, B. C.) , when her monuments were defaced by herbrother Thothmos III. The propylon at Elassassif is theprincipal one defaced on this occasion.II. The change in the religious views of Amenothph IV.(the sun-worshipper of El Tell) (circa 1250, B. C. ) , which ledhim to deface all the figures and titles ofthe God Amoun, andall names of which his name formed a part. The monumentsdefaced on this occasion are referred to three classes.1. Those which were never restored, as the lesser obelisksat Karnac.2. Those in which the sun- worshipper substituted anothername for what he defaced; as in a cartouche of his own citedby M. Prisse, and in those of his supposed grandfatherAmenothph III. , where he substituted a repetition of theprænomen for the defaced phonetic name.3. Those in which the names and figures that were defaced have been restored by subsequent kings. Instances ofthis are the Lateran Obelisk at Rome, the great obelisks atKarnac, and those cartouches in which the name of Amenothph III. appears cut over the repetition of his prænomen; the latter having been previously substituted for theoriginal name.III. The overthrow ofthe sun-worshippers and restoration ofthe worship of Amoun, on which occasion all themonuments of the intrusive worship were destroyed, as atKarnac, Gebel Tounh, and Ell Tell (a few years after thepreceding occasion). The tomb of the king called Skhai,the father ofthe sun- worshipper, was violated at this time;and this was probably the occasion on which the royal nameon the lion, presented by Lord Prudhoe to the BritishMuseum, was obliterated. It was that of Amenothph IV.548IV. The hostility to the god Seth, Nahas, or Noubti,which arose in the minds ofthe Egyptian priests, and whichled to the defacement of all monuments in which he appearsas a beneficent god, and of his name when forming a part ofnames of kings. The time when this hostility arose, and thecause of it, are yet unexplained; but it could not have led tothis defacement sooner than 1100, B. C. This defacement isconspicuous on the statues of Menephthah III. at Turin andLondon, and the Flaminian Obelisk of Menephthah I. atRome, and frequently at Karnac.It is incidentally mentioned that Pone, or Penne, is LowerEgypt; its extremities being mentioned in a papyrus in theBritish Museum in connexion with Ebo, or Elephantine, asthe limits of Egypt. And the titles " King of Penne,""King ofthe Pure Country," which occur in the second cartouches ofmany Egyptian kings , are shewn to imply that thekings bearing those titles were only kings of parts of Egypt;a King of Penne, or Lower Egypt, like Horus, always implying a King of Keme, or the pure country, i. e. of UpperEgypt, as Skhai and Amenothph IV. were.Mr. E. Clibborn made a communication respecting theHycsos, or Shepherd Kings, tending to shew that they weredescendants ofIsaac.March 16. (Stated Meeting. )SIR WM. R. HAMILTON, LL. D., President, in theChair.RESOLVED, That the Rev. J. D'A. Sirr's collection ofIrish Antiquities be purchased on the terms recommendedby Council. The terms being a payment of £350, the549cancelling of his arrears, and his being made a Life Memberof the Academy.The Secretary of Council read the following Report:In presenting to the Academy the Report of Proceedings duringthe past year, the Council does not find it necessary to enter intomuch detail, as the events of that period have not been of any considerable importance or unusual character.The Second Part of the 19th Volume of our Transactions hasbeen published and distributed to the members of the Academy.The 20th volume, which will be altogether occupied by Mr. Petrie'sEssay on the Round Towers, is still at press . The delay in its publication arises mainly from the number and importance of the artisticillustrations; and it is expected that the retarded progress of thiswork will be fully compensated for, in the opinion of the Academy,by its excellence, when brought out.Several Memoirs are already prepared and printed for the 21stVolume of the Transactions, and the Proceedings of last Session,which compose Part VII. , have been lately distributed to the members.Since the date of the last Report the attention of the Councilhas been given to the means of providing for the exhibition andguarding of the collection of Irish Antiquities. The plans proposedfor this object have been already submitted to the Academy, but arenot as yet in any way carried into effect; the Council being, on theone hand, restricted by want of funds, and, on the other, as it wasfound that the duration of tenure of the Academy House becomesuncertain after a few years, it was thought advisable not to expendmuch money on alterations in the building, until some definite arrangement had been made concerning its future tenure. For thispurpose the Council have been in communication with the lawagents of the Academy, but no decisive result has been as yet arrivedat. It is a question of great importance to the Academy, for, atpresent, from the want ofplace for exhibition, the antiquarian treasureswhich we possess, and to which, we trust, each year will make largeadditions, are practically inaccessible to the public. Some of the550best evidences of the activity and utility of this Institution are hiddenfrom the public eye, and thus the influence of the Academy, and itsclaims for public sympathy, are narrowed, and deprived of force.The Donations to the Antiquarian Museum during the pastyear have been few in number, most probably owing to the circ*mstances just now described.The work of cataloguing the Irish Manuscripts in the libraryof the Academy is still in progress, but is expected to be terminatedin a few weeks. The time occupied in this work, and the extent,three vols. folio, to which the Catalogue has gone, will be understoodwhen it is considered that, not merely the name, but also an abstractof the contents of each MS. are inserted in the Catalogue, which willthus in itself become a very valuable addition to our library.About a year ago the Council received a communication fromthe Booksellers to the Academy, Messrs. Hodges and Smith, regarding the purchase of a collection of Irish Manuscripts in their possession. A Committee of Council, appointed for the purpose, reported that the Manuscripts were of much interest, and worth theprice which Messrs. Hodges and Smith had set on them. The funds ofthe Academy did not, however, admit of the Council taking any directsteps for their purchase, but an application has been made, throughhis Excellency the Lord Lieutenant, for some assistance towardstheir purchase from the Government. His Excellency has expressedon this, as on all occasions, the greatest anxiety to advance the objects of the Academy, but as yet no final answer has been receivedfrom the heads of the Government in England.The Library of the Academy has been increased during thepast year, by numerous donations of scientific and literary works, forwhich, at the several meetings, thanks have been voted to the donors.An interchange of Transactions has been kept up with most of theeminent scientific institutions of Europe and America, there havingbeen added during the past year:The Academy of Sciences of Metz, the Royal Academy ofAmsterdam, with whom we did not previously correspond, and theMuseumn du Jardin des Plantes, at Paris, the correspondence withwhich had been accidentally interrupted.551During the past year seventeen new members have been electedinto the Academy. Their names are as follows, viz .:George J. Allman, M.D.Rev. Francis Crawford.Henry Lindsay, Esq.John M'Mullen, Esq.Hon. and Very Rev. Henry Pakenham, Dean of St. Patrick's.Goddard Richards, Esq.John Wynne, Esq.I. George Abeltshauser, A.B.Rt. Hon. The Earl of Dunraven.Matthew Dease, Esq.William M'Dougall, Esq.Sir Montague L. Chapman, Bart.James H. Pickford, M.D.Edward Bewley, M.D.James S. Eiffe, Esq.William Henry, Esq.John Neville, Esq.Out of our list of members we have to deplore the loss ofseveral since the date of our last Report; most of them, certainly,persons whose energies, being devoted to other spheres, renderedtheir connexion with this Academy only nominal: but some, andespecially one, whose connexion with us was of the closest and mostendearing kind, whose scientific labours in various climates were ofan extent and diversity which, while they created for him a distinguished reputation, unfortunately sapped the foundations of hishealth.List of Members ofthe Royal Irish Academy deceased since the16th ofMarch, 1843.Robert Bateson, Esq. Major- General Sir Joseph O'Halloran, K.C.B.Right Hon. William Vesey Lord Rev. Thomas Prior , D.D.Thomas Coulter, M.D.Fitzgerald and Vesci.Arthur Hume, Esq.Rt. Hon. John Radcliffe, LL.D.Honorary Members deceased:His Royal Highness the Duke ofSussex.Professor Wallace.Amongst the honorary members had been reckoned his RoyalHighness the Duke of Sussex. His exalted rank removed him fromin any way personally contributing to the advancement of knowledge,but he favoured its cultivation by his august patronage, and filled formany years the office of President of the Society of Arts, having adecided taste for practical mechanics, and leaving behind him, at his552death, a very valuable and numerous collection of clocks and watches.In the year 1830 he was elected to the Presidency of the RoyalSociety of London, and was present at the meetings of that illustriousassemblage, whenever his health, which, unfortunately, was delicate, orthe other demands upon his time, unavoidable from his exalted rank,admitted of his so doing. He was nominated an honorary memberof this Academy, of course not for any special scientific merits, butthat we might show some consonance of feeling with the scientific menof London who elected his Royal Highness to the most exalted scientific position of the British Empire, the chair of Newton.Professor Wallace, of Edinburgh, was known to the mathematical world for various memoirs, into the details of which it is notnecessary to enter. His works were not of a character to influencethe progress of general science in any material degree, although theymanifested powers of inquiry and analysis of a very creditableamount.Of the ordinary members of the Academy whom we have lostduring the past year, the Lord Fitzgerald and Vesci, the Right Hon.Judge Radcliffe, Arthur Hume, Esq. , the Rev. Thomas Prior, D.D.,and Major- General Sir Joseph O'Halloran, do not require specialnotice. They were all men publicly known, and recognized as ofeminent ability in the various professional pursuits to which they haddevoted themselves. Success of no ordinary kind was the result oftheir exertions, and has connected the names of some permanentlywith history. It can hence be understood that, except by a generaldesire to promote the objects of this Academy, by which, we trust,every member is actuated, they were not able to take any part inour proceedings.We cannot, however, pass so briefly from the name of RobertBateson, late M.P. for Derry. Separating himself from the whirl ofmerely trivial and political pursuits, to which young men of his ageand station are unfortunately in this country almost exclusively devoted, he engaged in the cultivation of literature and antiquities witha zeal and ability which promised to bear the best fruit. Theancient monuments and history of his native country specially occupied his attention, but not exclusively; and whilst travelling inPalestine, for purposes of literary inquiry, amongst those scenes in553which the most important acts of human history have been performed, he was seized with fever, and expired in Jerusalem.The position which Dr. Coulter occupied in this Academy, inour University, and in science generally, rendered it the duty oftheCouncil to prepare, with more than ordinary care, a sketch of his lifeand labours, such as might not be derogatory to his fame; and, happily, the task was undertaken by one who, from long acquaintanceand intimate friendship with the deceased, was enabled to speak minutely of his personal career; and whose own extensive and profoundacquaintance with almost every department of knowledge , which thisAcademy has had so often occasion to admire, enabled him to judgecorrectly of the aspects in which the labours of Doctor Coultershould be placed . The following biography of Doctor Coulter hasbeen drawn up for this Report by the Rev. Dr. Robinson."It is an old saying, that science has its martyrs as well as religion; we may add that it has its Forlorn-hope as well as war, urgedto the adventure by loftier and nobler impulses, encountering in itspursuit even a greater amount of suffering and danger; but too oftenunnoticed and unrewarded. Its heroism is of too high an order tobe appreciated by vulgar minds; the wise and good, who alone valueit, are comparatively few and powerless, and the triumphs which itachieves are not in unison with the evil tendencies and passionswhich unhappily predominate among mankind. Therefore it finds,in the Present, neglect, perhaps scorn or contemptuous pity of thefolly which wasted on such unprofitable pursuits the powers that, ifotherwise directed, might have commanded wealth, rank, and power.But the Present ere long becomes the Past; all of its glittering array which is not based on the eternal and immutable principles ofvirtue and truth moulders to dust; the stream of time in its flowwashes all that is earthy from the ruin, and leaves in imperishablebrightness the grains of gold and gem which it contained, the treasure of the Future. In this sacrifice of self to science, few have surpassed the associate, whose loss, during the last year, it is my painfulduty to announce to you; and a brief notice of his history maytherefore be permitted." Thomas Coulter was born in 1793, near Dundalk. His parentsdied during his childhood, but the loss was in part supplied by the554guardianship of a good and intelligent uncle. From an early age hewas devoted to field sports, which he followed with a minute attention to the habits of his game, that belonged more to the naturalist than to the sportsman. Bees were another favourite object;and he possessed that remarkable power of handling these irritableinsects with impunity, which attracted so much notice in Wildmanand others. He had in after-life the same privilege as to serpents;of which some members may recollect an amusing exhibition in thisroom; his secret being the union of gentleness and courage."He was prepared for college by Dr. Neilson, the author of awell-known Irish Grammar, from whom, perhaps, he derived thatintense interest in the antiquities of our native land, which characterized him to the last. One proof of it deserves to be recorded forexample's sake. There stood on his property an ancient building,described in Wright's Louthiana, as a Ship Temple, which the tenant was converting into lime. The young landlord had him prosecuted and punished for the trespass, to the surprise of many whowere in the practice of similar misdeeds. In the University he hadthe good fortune to be placed under the care of the late Dr. Lloyd,whose esteem and regard he possessed in a high degree; though theprevailing bias of his mind prevented him from equalling in mathematical attainments some of his fellow-pupils. He pursued thatscience only so far as it ministered to other objects. But in practical mechanics, in Chemistry, Physiology, and above all, in Entomology and Botany, he far outstripped his college contemporaries, andwhile yet an undergraduate, his collections of Irish insects andmosses were such as might have been owned with credit by a veteran.But his success made him only the more conscious of his deficiencies,and determined him to seek abroad the means of supplying them .Having spent one or two summers in Paris, where he made very extensive dried collections of the plants of the Jardin des Plantes,he established himself in 18-, at Geneva, where, under the auspicesof De Candolle, he found all that he could desire. How well thethree or four years which he spent there were employed, appearsfrom the memoir on the Dipsacea, which he then published, and stillmore from his Herbarium, of which the European part was then formed,and compared with De Candolle's own collection; a work, which when555considered as the result ofalmost unaided individual exertion, may wellbe called gigantic. * The consciousness of power excited him to enterprize, and on his return from the Continent, in 1824, he arrangedan expedition to explore a considerable portion of America. Hisintention was to commence at Buenos Ayres, cross the great plainsto Mendoza and Chili, to explore the western side of the Cordilleras,and the Lake of Titicaca; thence to California, and to return byMexico, or by the Columbia river and Canada. For this he hadactually made arrangements, and it is to be regretted that he did notexecute it. He had every requisite for success among half civilizedor savage races: a noble and commanding person; great stature,strength, and dexterity in the use of arms; good temper, courage, andpresence of mind: a combination of qualities, which Bruce only, ofmodern travellers, possessed in the same degree, while he was farbehind him in practical science."He was, however, induced to change part of his plan, and commence with Mexico, engaging as medical attendant to the establishment of the Real del Montè Mining Company for three years, duringwhich time he hoped to complete the Mexican Flora, and afterwardsto resume his original design.†" But in that unhappy country, there was found neither probitynor peace. The English companies were regarded as legitimate objects ofplunder, and several of those whom they employed retired insickness or despair from their posts." Under such circ*mstances he felt himself called to go beyondhis peculiar duty, and undertook the charge of one of the company'sprincipal mines, the Veta Grande, though such work was entirely new

• His Herbarium (including the Mexican and Californian plants) , contains

about 150,000 specimens."While in Mexico he collected, at a very great expense, plants of seventyspecies and varieties of Cacti, and sent them to the late Provost, the Rev. Dr.Lloyd, then Bursar, to be presented to the College for their botanic garden.He sent, at the same time, a similar collection to his friend, the late ProfessorDe Candolle, for the Geneva Botanic Garden. Many of them were then veryvaluable, and unknown in European collections. One of them, a fine tall- growing species, has been named Cereus Coulteri, and may now be seen, as well asother interesting species, in the College Botanic Garden.556to him; he, however, soon acquired the necessary knowledge, andunder his management the concern became productive. This measure was fortunate for his employers, but not for himself. It distracted his attention from his primary object, detained him for morethan a year in a district barren and uninteresting to the botanist,and, above all, mixed him up with the cabals and personal feelingswhich seem inseparable from such corporate bodies, and in which thehigh-minded and open-hearted always have the worst. At the closeof his engagement he passed to California, where, and in Sonora, hespent four years, always actively employed on his primary objects, *and involved in spirit-stirring adventure; at times exposed to theIndian arrows, or compelled to defend his countrymen from the attacks of revolutionary patriots; exploring a burning waste of sand,when the thermometer reached 140, or nearly perishing by the bitesof poisonous but almost invisible insects. At one time his metallurgic skill had acquired for him considerable wealth, which, during abotanical excursion, was plundered in some political convulsion." The industry and energy with which he carried on his botanicalinquiries, is abundantly shewn by the fact, that the herbarium which hecollected under such circ*mstances contains upwards of 50,000 specimeus of 10,000 to 11,000 species, the far greater proportion of whichwas collected and preserved by himself; and that in connexion withthe herbarium he had gathered specimens about the size of a 16mo.book of nearly 1,000 descriptions of woods, most, if not all of whichare accompanied by dried specimens of the foliage and inflorescence

• "One of his most interesting discoveries in California is a tall-growing

pine, having cones a foot or more in length, and six inches in diameter. Thishas been named by the late Professor Don, at the desire of Mr. Lambert, PinusCoulteri. It is quite hardy, and plants of it may now be seen in various collections in England and Ireland. It was found in the mountains of Santa Lucia,near the mission of San Antonio, in lat. 36°, within sight of the sea, and at anelevation of 3,000 or 4,000 feet above its level, growing intermixed withanother fine species, Pinus Lambertiana, also introduced, and rising to theheight of from 80 to 100 feet, with large permanent spreading branches, anda trunk three or four feet in diameter. There are two small plants of itin the College Botanic Garden, and the cones may be seen in the College Herbarium. "557of the trees from which they were taken; the whole gathered by himself, and being, perhaps, the largest collection of this particular kindever made by any unaided individual." At the end of this period he returned to Europe with an immense increase to his collection, but with a constitution irreparablyinjured by the hardships which he had encountered; and even athome he was destined to meet a severe loss. In the transport fromLondon to Dublin, a case containing his botanical manuscripts, andthe materials ofa personal narrative, disappeared, and could never betraced; so that of the latter, nothing remains except a brief accountof Upper California, published in the 5th volume of the Journal ofthe Geographical Society, and the former are totally lost, except somecommunications to De Candolle and Lambert. After this his chiefanxiety was to secure the herbarium, which had cost him so much,from dispersion or neglect; and in this at least he was not disappointed. It has become the property of our University, and thetask of arranging it was the employment of his few remaining years,which were devoted to that work with a concentrated energy thatshewedhis consciousness of his days being numbered. It was completedfor the European part, and about 8,000 ofthe American specimens;but the remaining packages are well furnished with memoranda, sothat for them also the arrangement is practicable. That the possession of this invaluable treasure must give a powerful impulse to thestudy of Botany among us is sufficiently obvious; but it is doublyinteresting to a scientific body like this, as an evidence of the increasing importance attached to the study of Natural History in thehighest and most influential quarter. That important branch ofknowledge has hitherto been too much neglected in university education; but better prospects are opening; and to this the influenceof one so good and highly gifted as Dr. Coulter seems mainly to havecontributed. Should our hopes be realised, there is no doubt thathe would have regarded it as an ample compensation for all his sufferings."The ballot for the annual election having closed, theScrutineers reported that the following gentlemen wereelected Officers and Council for the ensuing year:1558President-Sir William Rowan Hamilton, LL. D.Treasurer-James Pim, Jun. , Esq.Secretary to the Academy-James Mac Cullagh, LL. D.Secretary to the Council-Robert Kane, M. D.Secretary of Foreign Correspondence-Rev. HumphreyLloyd, D. D.Librarian-Rev. W. H. Drummond, D. D.Clerk and Assistant Librarian- Edward Clibborn.Committee of Science.Rev. Franc Sadleir, D. D., Provost of Trinity College;Rev. Humphrey Lloyd, D. D.; James Apjohn, M. D.;James Mac Cullagh, LL. D.; Robert Ball, Esq.; RobertKane, M. D.; G. J. Allman, M. B.Committee of Polite Literature.His Grace the Archbishop of Dublin; Samuel Litton,M. D.; Rev. William Hamilton Drummond, D. D.; Rev.Charles Graves, A. M.; Rev. Charles W. Wall, D. D;John Anster, LL. D.; Rev. S. Butcher, A. M.Committee ofAntiquities.George Petrie, Esq.; Rev. James H. Todd, D. D.;Henry J. Monck Mason, LL. D; Samuel Ferguson, Esq.;J. Huband Smith , A. M.; James Pim, Jun. , Esq.; CaptainLarcom, R. E.The President then appointed, under his hand and seal,the following Vice- Presidents:The Rev. James Henthorn Todd, D. D.; James Apjohn, M. D.; the Rev. Charles W. Wall, D. D.; and GeorgePetrie, Esq.The Auditors appointed by Council to examine theTreasurer's accounts reported as follows:559"We have examined the above Account, * with the vouchersproduced, and have found it to be correct; and we find that thereis a balance in bank, amounting to £203 18s. 3d. , sterling, and inthe Treasurer's hands, 6s. 1d.""(Signed, )" JOSEPH CARSON." THOMAS A. LARCOM."“March 15th, 1844."" The Treasurer reports, that there is £ 1117 10s. 10d. in 3 perCent. Consols, and £ 1643 19s. 6d. in 3 per Cent. Stock, thelatter known as the Cunningham Fund. He also reports that thereare due this 16th March, 1844:2 Entrance fees, at £5 5s. per • •6 Arrears of two years, at £4 4s. per25 Do. one year, £2 2s. per£ 10 10 025 4 052 10 0357 0 0£203 18 3170 Subscriptions for the past year, now due, at£2 2s. per .Balance unappropriated in the Bank of Ireland,Balance in Treasurer's hands,6606 1 £204 4 4£ 649 8 4Signed for JAMES PIM, Jun . , Treasurer." EDWARD CLIBBORN, Clerk, &c."April 8.JAMES APJOHN, M. D. , Vice- President, in the Chair.The Marquis of Kildare and William Smith O'Brien,Esq. , M. P., were elected Members of the Academy; andVOL. II.

• Entered in Treasurer's book.

3 A560Robert Ball, Esq. , was elected Treasurer of the Academy,in the room of James Pim, Jun. , Esq. , who resigned .Dr. Apjohn read a paper by Mr. Thomas Knox, " Onthe Purification and Ventilation of Vessels from bad Air. "In reperusing lately Professor Daniell's interesting researches " on the spontaneous evolution of sulphurettedhydrogen in the waters of the western coast of Africa andofother localities," a method occurred to me ofpurifying thecabins of vessels, and the sleeping apartments in houses,which would be as efficacious as Professor Daniell's , without being liable to the objection of having free chlorinealways present producing its enervating effects.The method I propose is this: to have air pumpedthrough tubes extending from the steam engine to the cabins.The extremities of the tubes should dip into vessels containing solutions of chlorine or metallic solutions; the last solution, being of lead , would indicate when the solutions were tobe renewed, by the black precipitate of sulphuret of lead .Atthe further end or top of the cabins there should be corresponding tubes to allow the foul air to be removed; theselatter would be unnecessary when there was a fire, the draftbeing sufficient to remove the foul air.As we can absorb or destroy all vapours, miasma, &c. ,this method would apply to all unhealthy regions of theworld , and would render habitable parts of the world whichat present lie deserted and waste. Sierra Leone would ceaseto be the grave of Europeans, and the Pontine Marsheswould no longer exhibit a ghostlike peasantry.EXPERIMENTS.Chambers made ofwood, with air- tight windows, havingapertures in the sides, into which the tubes would fit , could

• Phil. Mag. , July, 1841 .

561be made at little expense, and sent to Sierra Leone and thePontine Marshes; in the latter place the pumps might beworked by water conveyed from the mountains or othercheap motive power.66 Dr. Apjohn read a paper On the hygrometric Correction in barometric Formulæ for the Measurements ofHeights.If the atmosphere were of one uniform temperaturethroughout, destitute of moisture, or in a constant hygrometric condition, and ifthe intensity of gravity were also constant, it is well known that the difference of the altitude ofany two points in the atmosphere would be represented correctly by the formula d = m × log. 2, m being a constantquantity, and p and p' being the respective pressures at thelower and upper stations , as measured by the barometer, orin any other way. A correction for temperature has beenlong applied by augmenting or diminishing the approximateheight, or m × log. 2, by the amount that a column of airof this length would expand or contract if its temperaturet + 0were changed from 32° to 9 t being the temperature of 2the lower, and that of the upper extremity of the serialcolumn, by which the expression becomesD = m × log. 2 X× ( 1+t+0 32 2-493Such is, I believe, a correct account ofthe present formof the barometric formula, at least when we neglect the correction for variations of gravity, which is , however, in general so small as to be safely negligible. The presence ofmoisture in the air, or rather its varying amount, must obviously exercise some disturbing effect on this formula; but3 A 2562though this has been generally admitted by those who haveturned their attention to the subject, I am not aware thatany attempt at estimating its exact amount has been as yetmade; and as the correction for moisture is frequently ofconsiderable magnitude, and may, in my opinion, be appliedwith as much accuracy as that for temperature, I have takenthe liberty of occupying, for a few moments, the time of theAcademy with an explanation of the method which it has occurred to me to devise, and with which, from some trials Ihave made ofit , I have every reason to be satisfied .Let p be the pressure, and t the temperature of the air atthe lower station, t" the dew point of the air, andf" the forceof the included vapour; and let p' , 0, 0″ and F" represent thecorresponding quantities at the upper station. This beingunderstood , a little consideration will suffice to shew thatthe presence of the aqueous vapour produces on the formula a twofold deranging effect. It augments the values ofp and p' beyond what they would be in dry air, and it produces an alteration in the length of the column of air betweenthe two stations additional to that which results from the difference between its mean temperature and 32°, or the freezing point. The first ofthese is obviated , or, in other words,the correction for it is made, by substituting for p and p' inthe approximate formula, pƒ" and p' - F", by which itbecomesD = mxlog.p-f"p' — F *Having thus eliminated the effects of the tension ofaqueous vapour upon the pressures, we have next to estimate the conjoint influence of it and temperature, in elongating the pillar of air between the two stations. The theoryofmixed gases and vapours enables us to do this, providedwe can assign proper mean values to the temperature, thepressure, and the force of vapour ofthe aerial column in ques-563tion. The mean temperature its usually taken as t + 02• andthis must be very nearly its true value. For the same reason,the mean force ofvapours may be set down asƒ" + F"2

and

let us assume the mean value belonging to the pressure as√(p −ƒ'"') × (p′ — F″) .Nowa volume v of dry air at 32° under a pressure π, if raisedto a temperature t", becomesv x461 + t"493and if saturated with vapour at this temperature, the tensionofsuch vapour being s" , it will becomevх 461 + t"493 П -πS"This is the volume of the air when raised to t" and saturated with vapour at this temperature; and if this volumeof air have its temperature further changed, we shall say to t,then its bulk will be represented by the expression461 + t" πυ Χ X X493 " π461 t461 + t"= vx 461t.493ПXπ-Ssubstituting, then, in this expression instead of v the valueof the length of the column of air between the two stations supposed dry, and at 32° , viz.:m x log. P-f"p' —Fand for π, t, and s" their proper mean values as already explained, the barometric formula finally becomesD = mx log.p -f"461 ±(t+-0)X2Xp -- ' F"/ 493I√(p<ƒ) × (p' —F″)√(p−ƒ) × (p' —F″) − } (ƒ" +F" )may add here, that the correction for moisture is farfrom being insignificant in its amount, as may be seen by564the following example. Let us suppose, that when the approximate height, corrected for temperature, amounts to2700 feet (a height reached by several of our Irish mountains) , the mean value of π, or the pressure to be used in thefinal factor of the formula, is 27.3, and of the force of vapour, 0.3 of an inch , its value when the dew point is 43.6,then the elongation of the aerial column resulting from moisture is th of 2700 30 feet. It will, of course ,have been observed that the correction for aqueous vapourdiffers from that for temperature in the circ*mstance of beingalways positive; and this coincides perfectly with the observation I have had frequent occasion of making, namely, thatin damp states of the atmosphere heights calculated by theformulæ in general use are all appreciably less than the truth .And here I may be permitted to observe, that the greatLaplace, in discussing the barometric formula, in his " Système du Monde, " has fallen into a slight oversight; for as arude method of compensating for the effect of the aqueousvapour present in the atmosphere, he proposes, that in applying the correction for temperature the coefficient of theexpansion of gases should be augmented from .00375 , itsvalue for one degree Centigrade, to .004. Now this wouldcertainly produce the desired effect at all temperatures above32°; but as below 32° this equation is subtractive, the augmentation of the coefficient, instead of diminishing, wouldincrease the error. The following is the passage referred to:" Les vapeurs aqueuses répandues dans l'atmosphère,etant moins denses que l'air, à la même pression et a lamême temperature, elles diminuent la densité de l'atmosphère; et comme, tout étant égal d'ailleurs , elles sont plusabondantes dans les grandes chaleurs; on y aura égard enpartie, en augmentant un peu le nombre .00375 qui exprimela dilatation de l'air pour chaque degré du thermomètre.Je trouve que l'on satisfait assez bien a l'ensemble des observations, en le portant a 0,004; on pourra donc fair usage565de ce dernier nombre, du moins jusq'à ce que l'on soit parvenu par une longue suite d'observations sur l'hygromètre, àintroduire cet instrument dans la mesure des hauteurs par lebaromètre. "*

I may in conclusion observe, that in assuming, with theview of calculating the expansion produced by moisture, thatthe pressure to be employed is the geometric mean ofthecorrected pressures given by the barometer at the two stations, I am quite aware that I am assigning to it but an approximate value. An exact expression for the pressure tobe employed admits of being investigated; but its introduction into the formula, while it would give the latter comcomplexity of form, and thus render it less suited for practical use, would conduct to results not appreciably differentfrom those given by the more simple methods just explained.Mr. Clibborn presented to the Academy an ancient stoneimage, called in some places a Shela-na-gig; and read thefollowing extract from a letter from Dr. Charles Halpin:

" About two years ago, as I drove past the old graveyard of Lavey Church, I discovered this curious figure, laidloosely, in a half reclining position, on the top of a gate pierthat had been built recently, to hang a gate upon, at the ancient entrance of the old church-yard . I believe the stonesused in building those piers were taken from the ruins ofSysteme du Monde, p . 89.† Let= P.Mlog.PM being the modulus of the common system of logarithms,Then if v be the column of dry air, and that, when saturated with moisture whose force is f, it becomes v' , we will havev =v XPP- fFor the very elegant expression for P I amindebted to my friend, ProfessorRenny.566the old church of Lavey ( there is scarcely a trace of theold church on the site it occupied); and I think probable,that this figure was found amongst them, and laid in theposition in which I found it, by the masons employed at thework. I was not aware of its real value, until apprised of itby my brother, the Rev. N. J. Halpin . He immediately recognized it as a ' Sheela-na-gig,' and the most perfect ofany he had seen. I thought it my duty to protect this precious relic from the hammer.66' Lavey church lies about fifty miles north- west of Dublin, on the mail- coach road. There is a neat new churchnear the site of the old one."Mr. Petrie having expressed a desire that some furtherinformation should be given about this figure , and others,of the same kind , of which, he understood , there were two inthe museum ofthe Academy, which had belonged to the lateDean Dawson:Mr. Clibborn explained that he had received notices oroutlines of ten other figures, of the same kind, which hadbeen found in old churches and castles, and from their position in the walls, sometimes hid in the course, and from thedifference of the stone, it was probable they had been usedin older buildings, so that their actual antiquity could not bedetermined by the age of the buildings in which they hadbeen found. From the form of the stones on which severalof these figures were carved, it was surmised that someof them had been originally used as grave- stones, and probably intended to act as charms to avert the evil eye, or itsinfluence, from the place . These figures have a great similitude to others used elsewhere for this purpose formerly, aswell as at present, by the natives ofthe east coast of Africa.He also explained that, about five years ago, when, incompany with several advocates of the O'Brien theory of theRound Towers of Ireland, he was led to express an opinionthat, possibly, these buildings, though erected subsequently567to the introduction of nominal Christianity into Ireland ,might still have, to a certain extent, some analogies to viewsentertained by the African and Asiatic ascetics, and whichmight have been imported into Ireland by the first Christians, in the third century; who, if from Africa or Spain, mayhave brought with them more or less of Gnosticism (orviews analogous to it) , and with it notions and practices notvery unlike, apparently the same originally with those, bywhich the author above-mentioned endeavoured to explainthe nature and origin of the Round Towers. The first nominal Christians, if he had been correctly informed, whocame to Ireland, were lay ascetics; and, like the ascetics ofEgypt and the East, they selected secluded valleys in themountains, or islands in lakes, where they gave themselvesup to those penitential observances calculated , according totheir views, to destroy the " Hylic, or material," to humbleandconquer the " psychic, or animal, " and to elevate and cultivate the " pneumatic, or spiritual," principle of their natures.

It was argued that, if the tower was the residence ofthe Irish ascetics during their lives, it may have been considered the type of the plus, male, " pneumatic," or spiritualprinciple; and so the earth, grave, crypt, or church near it,in which were deposited the bodies, or material principles ofthe deceased, originally derived from mother earth, mayhave been considered the type of the negative female, hylic,or material principle, and have been considered analogousto Ge, or De-meter, to whomthe body of the dead returned ,by interment; and, hence, it was argued that, if O'Brien'stheory were true in this qualified sense, it should apply tothe churches or graves near the towers or residences of theascetics, where we should find types or indications of thenegative principle. Mr. R. P. Collis, who was present, im-

• See Moore's Hist. p. 221. The extract from St. Patrick's letter: " ubi nunquam pervenerat qui baptizaret, aut clericos ordinaret, aut populos consummaret. "

568mediately mentioned the female figure at Rochestown, andstated that he had heard ofseveral others in the same neighbourhood, and he recommended an inquiry into the subject,which led to the discovery of several more figures of thesame kind in different places.The " hylic principle, " including the materials composingthe body, was little more than the locus, where the battle ofthe two other principles was fought during the life ofthe ascetic; and if he persevered to death in the practices prescribed for the evolution of the pneumatic principle, and losthis life in these observances, or in the fulfilment ofthe dutieswhich belonged to this system, his victory over the hylic orpsychic principles was complete, and he was said to havearrived at " perfect virtue," and consequently became, according to Asiatic views, an inferior , or little Bauddha, whichmay, possibly, give us an original of the name of Monasterboyse; in Irish, the monastery of Boaithin, or the littleBauddha. The legend of St. Colum Cille, who struck hiscrosier against the glass ladder, by which he went to heaven,which belongs to this place, and which strongly corroboratesa Ceylonese legend, increases the suspicion , that the systemwhich was called here Christian, originally may have beenanalogous to that ascetic system which existed under thesame name in Egypt and the East, and was closely allied toBauddhism, which was, and is, a system of Asceticism,† and

• This doctrine is the same, or nearly the same, as that which is called

Dualism, which attributes creation and life to the action and reaction of twoprinciples, plus and minus, or positive and negative, which were personified bythe ancients under every species of antagonism. The fighting dogs and serpentsof the Irish are, apparently, manifestations of it, applied specially to the dailystrife, or " cross, " of these two principles in the body of the ascetic.When O'Brien's book was written our knowledge of the Bauddist systemwas very limited. Now its antiquity, history, principles, and corruptions, arebetter understood , through the labours of Mr. Princep, Fa-hian's Travels,The Mahavansa, &c.569mixed up with more or less pure Gnosticism; for, " thegreatest part of the Gnostics adopted very austere rules oflife, recommended rigorous abstinence, and prescribed severebodily mortifications, with the view of purifying and exalting the mind," like the Irish ascetics. " These tenets wererevived in Spain, in the fourth century, by a sect calledPriscillianists," where they may have been, to a certain degree, suppressed by the instrumentality of missionaries andseculars from Rome. The same system which existed inSpain previously, and which planted those views there afterwards, may have also planted them here; and the samemeans which suppressed them there for a time, may havehere suppressed them; or there may have been, to a certaindegree, for several centuries, a compromise between the advocates of both systems , and that which was finally adoptedhere, and called Christianity, may have, in a covert way,contained much Gnosticism , particularly that branch of itwhich was adopted by the ascetics, or Culdees, and smallreligious communities, and by whom the first towers mayhave been originally built. * It is a curious circ*mstance,not hitherto noticed by any writer on the Round Towers,that the technical term for a Bauddist monastery in the East,is a tower; no matter whether it be a cave in the earth, ora cabin or palace on its surface.We may add to these notices another notion of the

• The following extract, from the very old Irish MS. called the Speckled

Book, in the Academy, will explain and confirm what I have stated concerningIrish asceticism: "When, then, said St. Bartholomew, the Son of God wasborn, he was tempted by the Devil, but Christ overcame, by fastings in the wilderness, him who overcame Adam, in Paradise, through gluttony; for it wasmeet that Christ, the son of the Virgin, should overpower him who overpoweredAdam, the son of the virgin, i.e. the son of holy earth; for the ( mother) earthof which Adam was formed was virgin, because it had not then been pollutedby iron, nor by the blood of man, nor had it been opened for the interment ofman in it at that time. "570Gnostics, which was, "that malevolent genii presided innature, and occasioned diseases and calamities, wars , anddesolations; induced them to apply themselves to the studyof magic, in order to weaken the powers, or suspend the influence, of these malignant agents. " This doctrine of their'swas, no doubt, extended and carried out fully in every modeand form, and led them to consider themselves, and all thingsliving on the earth, to be under the influence and subject tothe evils caused by the instrumentality of these evil genii, who,in some cases , attached themselves to individuals , who werethen said to have the evil eye, or who became afflicted withwhat is termed " covetousness, " which blasted everythingwhich they desired , and made it unlucky; and its possessorwas shunned and avoided , as he was subject to that maligninfluence which is technically termed the " evil eye . " Thisinfluence was greatly dreaded by the living, for themselves,their children, cattle, and goods, and their houses; and inmany places, even now, people put up over their doors, overtheir hearths, and in many other places, talismans, to givethem good luck, or to take away or neutralize the evil look,which brings them bad luck, by averting the evil eye , also considered to be a distinct individuality, or genius . The term 66 good look," or " luck ," is incorporated into the English language, though the belief of the evil eye is nearly lost in England, where it was universal. It still exists in Scotland , andwe find it also in Ireland, where various methods are stillpractised to avert its influence from children, cattle, churnsof milk, houses, &c.One ofthe most efficacious is the horse shoe, which iscalled " the lucky horse-shoe" for this reason, and it isnailed to doors and gateways for luck, by people who have nonotion that they are, probably, putting up equivalents forthose hideous figures which the people call shela- na-gigs ,one of which was lately discovered at Kiltynan Castle, by571Mr. Thomas Oldham, which held the lucky horse- shoe inone hand, and a cross, or dagger, in the other.The horse-shoe, and the triangle, A, or n, &c. , and thetrefoil, are all, apparently, emblems for the same antidote,which the evil eye abhors, and by which the mechanic's wifewas not only able to identify the evil genius himself, but toeject him from her house, and save her husband's body andsoul, the stake which he proposed to play for. In this country the peasantry are said to entertain similar notions ofthe great efficacy of the same means, which is said to becapable of driving the Devil away, " the use for which, it issurmised, these figures were intended.66Mr. William Hackett, the moment he saw a drawing ofone of the figures, declared it was a " fetish; " the Africanname of a figure which closely resembles the shela-na-gigs,and is commonly used for the purpose of averting the evileye, and giving good luck. On the north coast of Africacertain emblems, carved in stone, are placed over the doorsfor this purpose; and formerly it would appear that certainparts of animals were used instead . In Italy the peasantry ,in the neighbourhood of Naples, have a complete system" of magic" for averting the evil- eye, which consists, toa great extent, of exposures and practices, which are compared to the ancient orgies, and calculated to eject or avertthe evil eye, or genius, from a place, and drive him and hiscolleagues, and their influence, beyond certain limits.These figures were, probably, intended as fetishes, orcharms, to keep off the evil eye, or its influence; and, consequently, they are found placed over doors of churches andcastles, &c. In many instances they are evidently mucholder, and of a totally different material and style of art, tothe building in which they are found . The workmanship isquite unequal, and the style of the figures differ very much.They are not copies of a common original, but, generally,572the most hideous and frightful- looking female figure whichthe stonecutter could devise. There is, however, in thebest sculptured figures a certain expression of countenancewhich resembles that of death. In these the hair is verylong, and there is no appearance of the tonsure, which occursin others. The former have a strong resemblance to a Mithraic figure, published in the Archæologia, XIX. p. 74, andalso to another figure, in Ingrami " Monumenti Etruschi,"T. 3, Tav. XXIII. Both of these, it is thought, were alsoused as fetishes, or figures intended to drive away the evilinfluence, and obtain good luck instead.The hair of some of the figures appears to be intended torepresent a peculiar tonsure, and the persons ofwomen represented are apparently attenuated by fasting and that course oflife whichthe Gnostics and ascetics so strongly insisted on, asthe means of gaining the victory over the hylic or psychic(together, the evil principle) in themselves, and what St.Bridget so ably contended for in herself, and those whoplaced themselves under her rules. In these almost skeletonfigures we have an analogy between the rule of abstinenceof the Gnostics, and also their notion about amulets, abraxes,fetishes, and the evil genius; and hence the probability,that the use to which they have been assigned is thecorrect one, independent of any other considerations whicharise from the practices now said to be efficacious in Ireland ,&c. , in ejecting the evil genius, or averting the evil eye; andwhich formerly, as well as at present, were common in Africa,Italy, Spain, Ireland , &c .With the ancient Egyptians the crux ansata appears tohave been the great emblem of good luck, prosperity, andsoforth. It appears to have been the antidote to the evileye which we find mentioned in Prov. xxiii. 6 , and xxviii. 22,and the Gnostics and early Egyptian Christians appear tohave adopted it, without any alteration or change in its formfrom that used by the old Egyptians . The crux ansata ap-573pears to have been a substitute for the gesture called thefico of the ancient Romans and modern Neapolitans , whichcombined the Dualism, or positive and negative principle.It is still used , according to the Canon De Jorio, when a layNeapolitan wishes another good luck, when he is going onan expedition, &c. And we find the fico, combined withother emblems into the form of the crux ansata, in the museum at Naples, where there are many examples analogousto many Gnostic emblems, which are well known; some ofwhich have been published by the Rev. Dr. Walsh. Onefound in the baggage of Prince Charles Edward, after thebattle of Culloden, has on it a woman, in a better style ofart than that of the shela-na-gigs; but, probably, intendedfor the same purpose, 66 as a charm" to avert the evil eye,and gain the good luck instead .The crosses which are placed round certain enclosuresin Ireland, and act as termini, or boundary marks, had probably the same use formerly, to keep off the evil eye and itsinfluence from the enclosure, so that the sleep of the deadmight not be disturbed; hence the request to pray for the repose of the soul of Bran, on the tombstone in the museum,and the usual " may he rest in peace"; terms calculated toneutralise the disturbing influence of the evil- eye principle.In Asia and Africa things owned by individuals are frequentlytabooed, or marked with the cross, or circle, crescent, orboth combined, which, it is believed, protects them from theevil-eye, and consequently from being coveted by people,or rendered unlucky. This practice, or the notions whichcaused it, appears to be almost as old as man himself,and is found incorporated into the language, and occupying agreater or less proportion of the popular belief in everycountry. The pattern which composes the tracery on ourcross of Cong, and other old Irish shrines, reliquaries, andthe tomb at Cashel, which represents an animal like a dogor serpent always worrying itself, or another creature of the574same kind, may probably be a type of the doctrine of abstinence or mortification of the flesh, * which to the ascetic washis daily cross, and antidote to the hylic or evil principle,which he considered himself bound to bear, and which hismaster before him had borne victorious to death, and bywhich he became exalted to the highest rank in heaven, consistent with our extract from the Irish MS. , in which we findat least one of the doctrines mentioned, which the asceticsmagnified into a constant rule of life, and made it the meansofconquering the evil principle in themselves, to which thesefigures, it is thought, may have been charms or external antidotes, like the cross and bells, &c. , which they ornament,which are covered with dog and knotted serpent patterns,crossing each other continually, and supposed to be emblematic of the ascetic principle, or daily cross , and antidotesof the evil eye or principle. By this rule the stone in themuseum presented by Mr. Webber, which apparently represents two dogs fighting, may have been an ingeniousdevice to hide from common eyes, but to exhibit this principle where it would be understood , instead of a shela-na-gigof the common form, and so it may have been intendedoriginally as a fetish or charm to the house or castle fromwhence it was removed. Besides the three figures now inthe Museum, I have been informed of the existence ofmany

• The emblem, or device, for Christianity on the Roman medals , given by

the Rev. Dr. Walsh, is analogous to the monstrous figures of the double dogand serpent patterns referred to, which, it is surmised, may be emblems of theascetic principle. He observes: " It may be that Dioclesian wished to represent only the depraved and corrupt sectarians, of which this figure (in his plate)is the emblem; and that his more atrocious colleague, careless of distinction,exhibited the genius of Christianity, under any form, as equally the object of hispersecution. " There is a figure called the Idol, at Cashel, with fish- tail extremities, with a face like the shela- na-gig presented by Mr. Halpin. It appears to connect, or identify, the designs on the Roman medals with those Irishfigures.575Shela-na-gigs in different parts of Ireland; but have receiveddrawings and exact descriptions of five others only.1. The first discovered and described by Mr. R. P.Collis. It is in the gable of an old church at Rochestown,County Tipperary. This figure is called a Shela-na-gig, bythe country people, and as it was the first found it has supplied the name to all the others.2. In the church at Dowth there is a Shela-na-gig,carved in stone quite different to that which composes thewalls of the church. This figure appears to have beenoriginally a head or foot- stone of a grave. It was said to bea figure of St. Shanahan, by the person who shewed me theplace. At Lusk there was a figure called the Idol, whichwas buried by the late Rev. Mr. Tyrrell. It appears to havebeen a Shela-na-gig also.3. Found over the door of the keep of BallinahinchCastle, near Cashel. In this figure there is an appearanceofthe tonsure. It was the opinion of the person who examined it, that it had been inserted in the wall, and mighthave been taken from the ruins of the church, which arequite near the Castle.4. Found in the south front of Moykarkey Castle, CountyTipperary. This figure has a more finished and modernair than any other of which I have drawings. The countrypeople have a legend, and call it Cathleen Owen. * It alsoappears inserted into the wall, and there is a ruin of a churchquite near, from whence it might have been procured, tobring luck about the house."5. Found in the wall of the old church on the WhiteIsland, Lough Erne, in the demesne of Colonel Archdall.This figure occurs lying on its side, and is in the course lowdown near the door, and appears to have been a part of the

• This legend may be equally authentic as that about the dog and wolf stone,

presented by Mr. Webber.VOL. II. 3 B576materials of an older building, which were used in the building ofthe church now in ruins. In the same way one of thefigures in the Museum, from the Dawson collection, appearsto have been built into the wall of the church where it wasfound. Under such circ*mstances, the actual antiquity ofthese curious figures is quite problematical. The subjectis a new one, and well deserving of the attention of antiquaries, to whom this notice is submitted more as a suggestionfor consideration than as an opinion. The number of factsknown are few, and probably it may be premature to attempta generalization.April 22.SIR WM. R. HAMILTON, LL. D., President, in the Chair.READ, —a letter from the Secretary of the Lord Lieutenant, presenting to the Academy the stones containingthe inscription from the old bridge of Athlone.—RESOLVED, That the thanks of the Academy be givento His Excellency the Lord Lieutenant for his donation.The Rev. Professor Graves read a paper on the Algebraic Geometry of Curves traced upon given Surfaces.Let u = (x, y, z) = 0 be the equation of a surface referred to ordinary rectangular coordinates. Its completedifferential will bePdx + Qdy + Rdx = 0.MakingPX = and y =Mr. Graves denominates x and y the normal coordinates ofa point on the surface. When they are known, the x, y, ≈of the point are determined by the three equations577u = 0, 2 = x, and == Yx.Ꭱ ᎡAs P, Q, R, are proportional to the cosines of the angleswhich the normal at the point (x, y) makes with the axes; itis easy to shew that if we describe a sphere with its centreat the origin and radius = 1 , x and y will be at the same timethe rectangular spherical coordinates of that point on thesphere at which the tangent plane is parallel to the planetouching the surface U= 0 at the point (x, y) . Thus, toevery point on the latter corresponds a point on the former:and a succession of points, or a line of any kind , on the surface uois in general represented by a succession of points,or a line upon the auxiliary sphere.As plane curves have been classed according to the degrees of the equations by which they are represented, socurves traced on any given surface may be advantageouslydistinguished by the degrees of the equations in x and ywhich define them. For the properties of a curve, tracedon the surface U=o, and characterized by an equation ofthe nth degree between x and Y, are, so far as we regardonly the relations of normals or tangent planes along it,identically the same as those of the spherical curve whichhas the same equation . But the analogy between sphericaland plane curves of the nth degree has been already established. Instead, then , of looking upon the shortest lines on asurface as analogous to the right line, Mr. Graves directshis attention to the line defined by the equationax + by + 1 = 0, (A)the geometrical character of which is , that the normal at anypoint on it is always parallel to a fixed plane. Systems ofsuch lines upon any surface possess, in general, those properties of right lines which have been termed projective.Thus, for instance: " If four lines of the first degree, diverging from the same point on a given surface, be cut in578four points, a, b, c, d, by another line ofthe same kind, weshall havesin [a, d]. sin [ b, c]sin [a, b]. sin [ c, d]=a constant,"[a, b] being used to denote the angle between the normals tothe surface at the points a and b.The normals along the line (A) are all parallel to thetangent plane at the point whose normal coordinates are aand b. Mr. Graves designates this point the pole of the line.And if a and b be connected by an equation, so that the poledescribes some curve of the nth degree, the line ( A) willalways touch another curve to which n tangent lines ofthefirst degree may in general be drawn from the same point.This relation between the curves being obviously reciprocal,Mr. Graves calls them reciprocal curves. Here is laid thefoundation of a theory of polar reciprocals for curves tracedupon any given surface.Amongst other exemplifications of this method, Mr.Graves employs it to discuss the lines of greatest and leastcurvature on the surface of an ellipsoid . Their equation innormal coordinates isa²(a² — k²)b2c² x² +(b² — k²) c² - k² = 0,k2where a², b², c² are the squares of the semi-axes of theellipsoid, and k² is indeterminate.Now, from the mere fact of this equation being of thesecond degree, it follows that the sum or difference of theangles between the tangent plane at any point on a line ofcurvature and two fixed planes is constant.But further, all the spherical curves of the second degree represented by the preceding equation are biconfocal:and it is easy to shew that their common foci are the pointson the sphere which correspond to the umbilici of the ellipsoid. Hence, the sum or difference of the angles between579the tangent plane at any point on a line of curvature, andthe tangent planes at two umbilici, is constant; or, as thetangent planes at the umbilici are parallel to the planes ofcircular section , we have the following elegant theorem:"The sum or difference of the angles between the tangent plane at any point along a line of curvature on an ellipsoid, and the two planes of circular section, is constant. "The proposition just mentioned was, it is believed , firstpublished by Sir William Hamilton, in the Dublin UniversityReview, part (3); the short article which contains it beingdated June, 1833. It has also been published by Dr.Joachimsthal, in a paper printed in the 26th vol . of Crelle'sJournal, and dated January, 1842, where that geometerclaims it as " novum neque inelegans."The reciprocal of the line of curvature has for its equationa² --- k²a²-x²+b2 k2b2 x² +c² ―― k2 = 0,in which if we makex = 2, and y =2==>20ywe shall get the equation of the cone, whose generatricesare parallel to the normals along the reciprocal of the line ofcurvature, and whose vertex is at the centre of the ellipsoid .After this substitution the last equation becomesy262 x² + y² + x² - k² ( 2²² + 1/2 + 1/2) = 0,from the form of which it is evident that the cone passesthrough the intersection of the given ellipsoid , and a concentric sphere having k for its radius. The properties ofthis cone, and its relation to the lines of curvature, were firstnoticed by Professor Mac Cullagh . *

• Proceedings of the Academy, vol. ii. p. 499.

580For the quadrature of areas on the surface of the ellipsoid Mr. Graves gives the following formula:area = a²b³c² SS (1 + x² + y²)³ dx d v(c² + a²x² + b² y²)²The President made some observations on the communication of Professor Graves.Mr. Clibborn read a notice of certain points in EgyptianHistory.READ, -The following Report from the Council:" That the Council do recommend to the Academy, at its nextmeeting, to carry into effect the following recommendations of theCommittee of Antiquities, and to request a vote of the Academyof £ 100 for the fitting-up of the Museum." 1. That the resolution of the Academy, of the 30th of November, 1842, for making a new Board Room in the lower part of thehouse, be carried into effect." 2. That the present Board Room be converted into a Museum ." 3. That, for this purpose, two tables be provided, to stand acrossthe new Museum, opposite the piers. The present glass cases, except that containing the Cross of Cong, to be placed on those tables,and flat glazed cases to be added; the Cross of Cong to stand on aseparate pedestal between the tables, i. e. in the centre of the room." The Council having taken into consideration the best meansof exhibiting the antiquarian treasures contained in the Museum ofthe Academy, and thus giving proper importance and utility to thatdepartment, appointed a Committee, which recommended the adoption of the resolutions of the Committee of Antiquities. Thesehave been adopted by the Council, and are now proposed for theadoption ofthe Academy."RESOLVED, That this Report and Recommendation ofthe Council be adopted , and that £100 be placed at the disposal ofthe Council for the purpose specified .581DONATIONS.Annuaire de l'Académie Royale de Bruxelles. NéuviemeAnnée 1843.-Annuaire de l'Observatoire Royalde Bruxelles,1843. Dixiéme Année. —Rapport sur l'Etat et les Travauxde l'Observatoire Royal, pendant l'Année 1841 et 1842.—Résumé des Observations magnetiques et meteorologiquesfaites a des Epoques determinees. (Extrait du tome XVI.des Memoires. - Observations des Phenomenes periodiques(Extrait des tomes XV. , XVI. des Memoires).—Instructionspour l'Observation des Phenomenes periodiques. — MemoiresCouronnés et Memoires des Savans Etrangers. Publiés parl'Academie Royale. Tome XV. partie 2. -Nouveaux Memoires de l'Academie Royale de Bruxelles. Tome XVI. Presented by the Academy of Brussels.Memoires de la Société Geologique de France. Tom. V.Parts 1 , 2. Presented by the Society.Memoires de l'Academie Imperiale des Sciences de St.Petersbourg. Sixth Series. -Sciences Mathematiques et Physiques. Tom. XIII. Livraisons 1 , 2, 3.-Sciences Politiques.Tom. VI. Livraisons 1 , 3. -Sciences Naturelles. Tom. V.Livraisons 1 , 2.-Recueil des Actes des Seances Publiques,tenues le 31 Decembre, 1841 , et le 30 Decembre, 1842.-Memoires presentes a l'Académie. Par divers Savans. Tom.XVI. Livraison 5. Presented by the Academy of St. Petersburgh.Sur l'Emploi de la Boussole dans les Mines. Par A Quetelet . Presented by the Author.ErsterZusatz, zu der Schrift Ueberden Galvanismus. VonGustav. Crusell. Presented by the Author.Ninth Annual Report of the Poor Law Commissioners,for 1843. Presented by the Commissioners.Catalogue of the Museum of the School of Medicine,Park-street, Dublin. By John Houston, M.D. Presentedby the Author.582Faune Ornithologique de la Sicile. Par Alfred Malherbe.Presented by the Anthor.Annales des Sciences Physiques et Naturelles, &c. Parla Société Royale d'Agriculture, &c. , de Lyon. Tom. IV.1841. Presented by the Society.Proceedings ofthe American Philosophical Society, May25-30, 1843. Presented by the Society.Transactions of the American Philosophical Society. Vol.VIII. , new Series, Parts 2, 3. Presented by the Society.PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1844.May 13.No. 45.SIR WM. R.HAMILTON, LL. D., President, in the Chair.Wm. H. Harvey, M. D. , was elected a Member of theAcademy.READ, A recommendation of Council to the Academy,to open a subscription list for the fund required to completethe sum necessary for the purchase of Hodges and Smith'sIrish MSS. , and that the Academy be recommended to headthe list by a subscription of £100.READ — , Aletter from Lord Adare to Mr. Petrie, regarding a Grant from Government to the Academy, for the saidpurchase; and also a letter from Sir Robert Peel to LordAdare, in which he stated that he was " willing to recommend to the Treasury to grant £600 for the purchase of theMSS. ," " on the condition that the whole collection shall bepurchased, and that the sum required to complete the purchase of the whole shall be raised from other sources."RESOLVED, on the recommendation of Council, -Thatthe Academy do open a Subscription list for the fund abovementioned, and that it do head the list by a donation of£100.Wm. R. Wilde, Esq. , read a paper on the Pharos ofCorunna.VOL. II. 3 c584Mr. Wilde prefaced his observations by stating that hehad already published an account of this celebrated building,which is situated at the extremity of the peninsula, on whichthe town of Corunna stands , wherein he had cursorily mentioned, that independent of the architectural beauty of itsstructure, its inestimable value as a beacon to marinerscrossing this portion of the Bay of Biscay, and its markingthe common entrance to the harbours of Corunna and Ferrol, what added " still greater interest to it in the eye ofthetraveller, was the fact of its enclosing within its massivewalls one of the most interesting monuments of antiquitythe Pharos of Hercules-the oldest existing specimen of thiskind in Europe, and amongst the very few now anywhereto be found.'""*These observations were those of an ordinary traveller,who had no particular theory to support, and no peculiarobject in view, save that of eliciting truth, and recording,with fidelity, what passed under his notice. Since then SirWilliam Betham having, in his " Etruria Celtica," questionedsome of the statements put forth in this quotation, and finding, as he states , some incongruity between the accountsgiven by Mr. Wilde and Laborde, appears to have come tothe conclusion that the ancient Pharos is not included, as isstated, within the walls of the modern Tower.Mr. Wilde went on to say, that " being about to republish the original notice of this building, and feeling somewhatpiqued at the assertion of Sir William Betham, who, neverhaving seenthe locality, laboured, I conceive, under such disadvantages as hardly entitled him to criticise, although, itmust be said, in the most kindly spirit, the descriptionwhich I had given from a personal examination on the spot,

• Narrative of a Voyage to Madeira and the Mediterranean, 2 vols. 8vo.

1st edition, 1840, pp. 12-14.585I have, however, to thank him for having noticed the subject,even in the manner which he did, for it has led to the discovery of a most interesting manuscript and two drawings, theonly ones, I believed , in existence, of the ancient and modernTowers, which I beg leave to lay before the Academy, andwhich I procured in the following manner:"When Sir William's book appeared I wrote to theBritish Consul at Corunna, requesting him to procure mesome information upon the subject of the ' Hercules Light, ' aswell as plans or drawings of the ancient and modern tower;and also to have made for me a copy of, or extracts from,any work or archive, either in manuscript or print, whichmight be still extant at Corunna, Betanzos, or Brigantia, orany ofthe towns bordering the splendid harbour of Ferrol,and where such a record would be most likely to have beenpreserved; at the same time, from the present unsettled stateof Spain, and the various revolutions with which that unhappy country has been visited , I hoped for, more than anticipated, a favourable answer to my communication . Afterthe lapse of a considerable length of time I have received themost confirmatory proof of my original position in these twodrawings, together with the Spanish manuscript, which I nowexhibit to the Academy, and which were discovered in thebureau of an old architect in Corunna. This document, entitled , ' Copia de la representacion y mas documentos queconfha de 16 de Marzo de 1786, dirigio, esta Junta de Gobierno condor Planos al Ecmo Sr. Marques de la Sonora,'appears to be a Report presented to the Marquis De La Sonora by a Government Commission, empowered to inquireinto and report upon certain improvements destined to beput in force in the harbours of Corunna and Ferrol, in 1786.In this ' Memoria Sobre la antiquedad de la Torre de Hercules, ' it is recommended to repair the ancient Tower orPharos standing at the extremity of the peninsula, the •3 c 2586only notice of which, ' says the writer of this Report, ' is,that it was in existence at the beginning of the fifth century,'and was originally intended for the same purpose, namely, asignal for the ships going to England. It may be remarked,that so advantageous was the post considered , that in 1684the Consuls of England, Holland, and Flanders, entreated ofthe Spanish authorities to have the building repaired, andstated that their Governments would, at their own expense,defray the cost of keeping up a light on it.WOW" The preceding representations faithfully exhibit thecondition of the original Tower, as it stood in 1786, andalso that ofthe present modern casing ofgranite with whichit is surrounded." The wood- engraving to the left represents the originalancient Pharos, a square, hollow tower, surmounted by arotundo, which was crowned by a large flag, bearing evident587marks ofthe long- continued action of fire upon its surface.At each of the corners there was a small square turret; oneof these is represented as still existing when this drawingwas made, but evidently of a much more modern construction than the rest of the building . At foot of the drawingwe find the following inscription: Fecit Trueva AlumnusAcademiæ ex Civitate portus Brigantini, anno 1797.'"" An external winding staircase led to the top , and permitted ingress to its internal apartments, through the smallapertures still existing in the tower. A small square buttress at each corner, portions of which were in existencewhen this drawing was made, seems to have supported thestair or external winding passage at the angles; and thegroove in the masonry still shews the position which suchoriginally occupied. We read of a similar mode of accessbeing employed on the exterior of the celebrated Pharos atAlexandria, probably for the purpose of carrying up thefuel, which was used to light the beacon that was placed attop."The mode ofconstruction of this Tower is decidedly antique, although the general architecture and stone-work doesnot point out a period older than that of the Romans; andthe masonry, composed of stones of comparatively small size ,is cemented together by a lime- concrete, similar to that knownto have been employed, if not introduced , by this people.The height of the Tower, from the base to the rotunda atthe top, was 82 royal Spanish feet, and the rotundo itselfwas 11 more, making in all about 132 feet English . It was31 feet broad on each side, and in the interior were twowalls crossing in the centre, each 4 feet in thickness . TheTower was divided into chambers or compartments by threestone floors, originally without any apertures in them, so thatthese apartments could only have been entered from without.The outer winding stair having been removed at some period long prior to the date to which we now refer, apertures588were made in these stone floors , and ladders leading fromone flight to another, enabled persons to ascend to the topfrom within. It is stated in this Spanish document that theouter staircase was pulled down to build a convent in theneighbourhood, but at what precise period history does notrecord. The small Towers at the top are believed to havebeen erected subsequent to the removal of the outer stair,perhaps in 1684, when the British, Dutch, and FlemishConsuls relighted this wide-spreading beacon."Withregard to the precise date ofits destruction, all thatwe can learn from Spanish authorities is, that when MolinaDe Malaga wrote his description of Galicia, in 1549, thisstaircase did not exist; for in this old poetic work we findsome rhymes referring to it, thus:• Pues la Coruna tampoco la deso,Gran Puerto do numa fortuna le corre.Yhablo de aquerte por sola una TorreAntiquo Castillo que llaman el Vieso;Aquerte es do dicen que estaba el eyrep,Mas es fabuloso sabido lo que eraEstaba cereada de grand escaleraQue quien la deshiro no tubo consep.'Of which the following exceedingly rough, but literal translation, may afford the English reader some idea:But Corunna I do not like,A Great Port where no fortune runs.I speak of this only on account of a Tower,An ancient Castle, which was called le Vieso (the old);This is where they say lived the witch,But it is a fabulous saying-whatever it wasway down.Was surrounded by a large staircase,Which whatever mounted could not find its"The origin of the original Tower, and its name, areinvolved in much obscurity. Galician tradition assigns it tothe workmanship of Hercules himself. Some characters,scarcely legible , on one ofthe stones, says the writer of this589Spanish manuscript, states that it was erected in honour ofsome of the Cæsars. Near its base was discovered a stonebearing the following inscription: the translation of which isattended with someMARTI .AVG. SACR .G.SEVIVS .LVPVSdifficulty from defacement, as wellas the number ofcontractions ofthetext. In any attempt at doing soit should be compared with the inARCHITECTVS . scription at p. 593.AF⠀⠀⠀⠀⠀ SISBaron Humboldtstates thatLaborde,LVSITANVS EXV who furnished himwith a copy oftheselines, likewise informed him, I suppose from the inscription, that thisPharos was constructed by Caius Sevius Lupus, architect ofthe city of Aqua Flavia (Cheves) , and that it was dedicatedto Mars.'66' Strabo, indeed , affirms that Galicia had been peopledby Greek colonies, and according to an extract from theGeographies of Spain, by Asclepiades, the Myrlean, anancient tradition, stated that the companions of Herculessettled in these countries. Very few Spanish authoritiesmention this ancient Torre del Pharo,' or, as it is sometimes called , The Iron Tower; and the appearance which itmust have presented when originally built, accords preciselywith the descriptions which we read of the ancient Pharos atMessina, and also that at Alexandria, around which we knowthere wound an external spiral staircase, so broad and sogentle in ascent that it is recorded a car and oxen couldwith facility pass to the top. The Spanish manuscript, which590I now lay before theAcademy, refers its construction (in alllikelihood) to the time of Trajan, because none of the geographers who lived before this emperor mention it, not eventhe accurate Mela, who alludes to other particularities onthis coast. This, however, is but a negative proof; andeven among later geographers the same silence is preserved.There is, however, one record extant in a stanza to befound in the old Spanish geographer Ororio, or Orosirus,who lived in the beginning of the fifth century, to thiseffect:'Ubi Brigantia Calletce Civitas SitaAltissimum pharum & inter paucaMemorandi operis ad speculam BritaniceErigit . . . .'" Here we have the first notice of one of the purposes forwhich this Tower was supposed to be erected, and also ofthe ancient tradition , existing both in this country and inSpain, of the British Isles being seen from the Pharos ofHercules. Without, however, attaching any weight to thestory of our island being seen from this Tower, it may beremarked, that if the ancients sailed directly northward fromit they would, owing to the concavity in the Bay of Biscayin which the harbour of Corunna is placed, arrive at CapeClear, instead of Cornwall."The early writers upon Irish history and Irish traditions have made frequent allusions to this ancient structure, as the ' Tuir Breoghan.' It is mentioned underthis head in the Leabhar Gabhaltas, or Book of the Conquests, a translation of which was made by Henry O'Hartabout theyear 1686, and the original, which is now in the possession of Sir William Betham, contains this notice of it:' Then Lughaigh, the son of Ith, went to Tuir Breoghan,or Corunna, and shewed his father's dead body unto theposterity of Breoghian, ' &c.; and from this Breoghain is, in591all probability derived the name of Brigantia, one of theoldest cities in this part of Europe.·" Sir William Betham has, with great labour and ingenuity, searched out and recorded , in his Etruria Celtica,' thevarious Irish authorities that refer to this building, and says,that he has discovered references made to it in the EugubianTables, which, he believes, speak of the early navigatorssteering by the fire set up on the land when the ship left thecoast of Spain for the Turn or Carne; and in the same passage the triple- pointed hill of Cape Ortugal, the next mostprominent headland, appears to him to be referred to." In another place Sir William Betham says: ' The nameof Corunna and the Groyne are both derived from theriver upon which the town stands, -Garonne, the roughor boisterous river, as the Garonne of France. ' On thispassage, however, I may remark, that I cannot agree withmy brother Academician, for Corunna does not stand on anyriver, and the only one in its neighbourhood, and that tooat a considerable distance across the harbour, is not theGroyne or Garonne, but the Rio Burgo. The term Groyne,however, is constantly applied by the early Spanish writersto the Bay itself."The term Corunna, or Colonna, may have been appliedin after- times by the Romans, from the circ*mstance of finding the Tower or Column upon this headland, in the sameway that the appellation of Cape Colunna has been appliedto the island in the Grecian Archipelago on which waserected the celebrated Suniam temple, the remarkable columns or pillars of which are still standing.66 6Again: There is,' says Sir William, some incongruity between the accounts of Mr. Wilde and Laborde. Thelatter says, the lighthouse is situated " upon a very highmountain, a league from the harbour;" and Mr. Wilde hasstated its position to be " about a mile to the S. W. ofthetown, on a rock by the water's edge. " Any one, however,592at all acquainted with the locality, knows that there is nosuch mountain in this vicinity as that described by Laborde,and the position of the Hercules Tower can easily be ascertained by those who have not seen it by referring to any ofthe Admiralty's charts of the coast; and, moreover, a lighton a very high mountain a league from the harbour" wouldbe oflittle service for nautical purposes."669“ I find, however, on again referring to the work of Laborde, that it consists of two parts—an itinerary, or journal,which appears to have been written from personal observation, and a running comment, in the form of notes, andprinted in a smaller type, on the population, commerce, administration, natural history, &c. &c. of the countries visited ,and which is evidently derived from other sources, and compiled from different authorities. It happens that this latter isthe part quoted by Sir William, and not the text of the Journal, where, at p. 435, speaking of the harbour, he sharbour is in the form of a crescent; at the two points arethe castles of Sainte-Clare and Saint Martin, which defendit,says: ' Theand a little island which shelters it from the north wind.Alltravellershavementionedtheancienttowerwhichexcitesadmirationfromits height, and its strongandsolidwalls. TheGaliciansdeclarethatit wasbuiltby Hercules,whosenameit still bears

this

is to attributeit to thePhonicianmerchantswhofrequentedthiscoast

but

a Romaninscriptionhasbeenfoundnearthistower, whichascribesittothegodMars. If it is reallythe workof the Phoenicians,asitsantiquityandthetraditionleadus to believe, thisaccountmaybe reconciledbysupposingthattheRomans,wishingto preservet monument, and in gratitude for their victoryoverthe Carthaginians, whosprungfromthePhoenicians, consecratedit to theirtutelarydeity.'ion" As this was a matter of some popular interest in connexwith the antiquities and early history of this country,Mr.WildequotedseveralextractsfromwhatSirWilliam593Betham has put together upon this subject, from GiollaKeavin, an Irish poet, who lived about A. D. 1072, in a poemcalled Reim re Riogh, or the Race of Kings-from the Annals of the Four Masters-and from the Book of Ballymote;from all which it would appear that the Irish poets andannalists were well acquainted, not only with the existenceof this Tower, but with many of the ancient bardic traditionsassigned to it: such as its being built as a watch- tower byBreogin, the son of Braha, who is also said to be the founderof the city of Brigantia, &c. &c."In the Spanish manuscript it is recorded that a stonebearing the following inscription was found built into thewall of an old house in the town of Corunna.LVPVS CONSTRVXIT EMVLANS MIRACVLAMEMPHISGRADIBVS STRAVIT YLAM.LVSTRANS CACVMINENAVESHOW! XD DVDV" The writer ofthe manuscript thinks that the dilapidationof the Hercules commenced in the middle ages, when it wasconverted into a castle or fortress belonging to the Archbishop of Santiago; that the stones and material of theouter staircase were at this time removed, and that sometrace of them may still be found in the fortifications oftheold town."Theresult ofthe commission to which allusion was madeat the commencement of this notice, was, that the SpanishGovernment determined to leave the ancient Pharos in ex-594istence, but to envelope it within the present modern granitebuilding, which was commenced in 1797, and is representedin the right-hand figure of the engraving at page 586. It is ahandsome square tower, built of close-grained white granite ,and not only contains between its massive walls the originalPharos, but is made to resemble it as much as possible; andon its exterior a projecting band of masonry exhibits theline of the original external staircase." No doubt can now any longer exist with regard to theposition and preservation of this most interesting remain,the Pharos of Hercules. At foot of the drawing which Mr.Wilde exhibited, the following inscription is decisive: ' Perspectiva que de muestra el estado de la terre antiqua llamadade Hercules quando de emprendio sure edificacion y revestimento de canteria por orden del Real consulado du la Coruna."" To establish this fact, and to record some additional notice regarding the traditions and early history of one of themost interesting structures at present remaining in Europe,must apologize for this lengthened notice. "Col. Jones made a communication concerning the discovery in the River Shannon, of a large collection of ancientbronze and iron weapons and utensils, &c. , which he presented to the Museum ofthe Academy, on the part of theShannon Commission.List of Antiquities found in the River Shannon at the undernamed places.150 Elfstones.KEELOGUE.I piece of soft Stone ( petrefaction) .10 Sword and Brass Spearheads.do.8 Small Brass Spear-heads.8 Do. Iron2 Iron Sword Blades.10 pieces of Teeth.1 piece of Deer's Horn.5951 piece of Wood, partly petrefied.3 Iron Battle-axes , or Tomahawks.10 Brass do. do.41 sundry broken Spearheads, Spurs, Ornamentsof Scabbards, Druid'sRings, &c. , &c.3 parts ofa Matchlock, Barrel, and Tube,BANAGHER.4 Lead Moulds, one withstamp ofCoins.1 Brass Dial.3 Brass Spear-heads.SHANNON BRIDGE.1 Brass Pin.BISHOP'S ISLAND.1 Brass Vessel.6 Elf- stones.2 Iron Spear-heads.3 Brass Tubes or Pipes(ornaments).1 piece of Deer's Horn.DERRYHOLMES.1 Iron Sword-blade.PORTUMNA.3 Pieces of Deer's Horn.3 Do. ofTeeth.ATHLONE.1 Two- edged Sword andHandle.2 Spear-heads.5 Brass Pins.1 Tin Box containing Coins.1 Grape Shot.1 Corroded Padlock.Sundry small articles , Pipes,&c. (in a small Box).RESOLVED, That the special thanks of the Academy bereturned to Col. Jones and the Officers of the ShannonCommission, for the collection of Antiquities now presented.

PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1844. No. 46.May 27.SIR WM. R. HAMILTON, LL. D., President, in the Chair.Captain O'Connor exhibited two twisted gold rings,brought from Africa and there used as current money.The President communicated a method of mentally approximating to the calculation of ancient eclipses, and appliedit to the eclipse of the moon recorded by Tacitus as havinghappened soon after the death of Augustus.Mr. J. Huband Smith drew the attention of the Academy to a report, that there was in contemplation the removal of a portion, if not the whole ofthe celebrated mound ofNew Grange, near Drogheda, to be broken up for the repair ofthe roads.RESOLVED, That it be referred to the Council to takesteps to ascertain the truth ofthe report, and in the eventof its proving true to take proper means to ensure thepreservation of this great and important national monument.598June 10.SIR WM. R. HAMILTON, LL. D., President, in the Chair.Charles Hanlon, Esq. , Maxwell M'Master, Esq. , ThomasOldham, Esq. , Philip Read, Esq. , Henry Roe, Esq., andRobert Wilson, Esq. , were elected Members of the Academy.Dr. Apjohn read an account of the constitution ofJade, and also oftwo ores of Manganese from the South ofCork.Dr. Apjohn observed that these minerals had been recently analysed in his laboratory, and as the results weresomewhat novel, he thought he might mention them to theAcademy; his principal object being that they might appearin the Proceedings, for the information of mineralogists andchemists.The Jade submitted to analysis was wrought into ornaments of various kinds, which were brought to Europe byCaptain Baddeley, who was engaged in several of the operations of the recent Chinese war. Its colour is white, with atinge of yellowish green . It has ahighly translucent. S.G. = 2, 965.tween rock crystal and topaz.splintery fracture, and isHardness over 7 , or beAlone before the blowpipeit glazes, but with great difficulty, on the surface.By exposure to a strong red heat, it gives off a littlewater, and becomes opake. Fluxed in the usual mannerwith carbonate of barytes, it was found to include no alkali. Another portion of it fused with a mixture of the carbonates ofpotash and soda, yielded the following quantitativeresults:599Silex .Alumina and trace of Oxideof Chrome ·Lime .MagnesiaWater•Loss( 1) (2)56.921 1.224(3)21.10• 2.980 0.058 1.00• 14.150 0.49622.275 1.076 }= 1.572 27.10 ·1.625 0.180 3.102.049100.000From the numbers in columns (2) and ( 3), which, calculated in the ordinary manner, represent the relative numbersof atoms of the various constituents, it is obvious that theempirical formula of this mineral is21 Si O₂3 + Ac₂O3 + 27 { MgO + 3 НО.Now, these atoms may be grouped so as to form a tersilicateof alumina, and a subsesquisilicate of lime and magnesia; sothat the following may be considered as the rational formulaof Chinese jade:JMgOAc₂ O3, 3 Si O, +9 ( 3 {Co0,, 2 Si O3 ) + 3 HO.In looking into works on mineralogy, I find that nephriteor jade has already been at least twice analysed, first, bySaussure, and secondly by Kastner; and, from the accountgiven by Beudant, of the specimen examined by the latter,it would appear to be the Chinese variety. The result,however, obtained by these chemists are quite irreconcileablewith each other, and with mine. Thus, Saussure found hisspecimen to contain 3 per cent. less silex than I have detected in mine, to include no magnesia, but instead thereof,the oxides of iron and manganese, and about 20 per cent. ofmixed soda and potash. Kastner obtained 6 per cent. lesssilex, about 7 per cent . more alumina, and 8 per cent. moreVOL. II. 3 D600magnesia, but no lime. The three specimens, therefore,differ as to the nature and relative proportion of their constituents. I may add, that it is not possible to representthe composition of any two of them by the same formula; sothat, admitting the correctness of the published analyses,we are entitled to conclude that minerals really different are,in works upon mineralogy, confounded together under thename ofJade or Neptrite.Ofthe ores of mangeneus, the first I shall notice is a specimen of psilomelanane, the black hæmatite of the older mineralogists, which I received some months since from R. W.Townsend, Esq. , and which occurs a little to the north ofthe village ofGlandore, in a mixed schistoze and arenaceousrock, which is coloured by Mr. Griffith, as old red sandstone. S. G. 4.071 . Hardness between fluor spar and apalite , occurs massive, but more generally in botryoidal andconcretionary forms. The following are its constituents,determined by an analysis very carefully conducted:Silex •BarytesOxide Copper ·(1) (2)8.5925.362 0.0691.254 0.031Deutox. 31.241 0.3937.212 Perox. 50.545 1.152Red Oxide Mang. ( Mn304) 74.574 =OxygenWater•• 3.006 0.334Confining our attention to the oxides of manganese andthe water, it is obvious, from the quotients in column (2) thatthe composition of the ore is very accurately represented bythe formula Mn2O3, HO+3 Mn O2, or that it is a compound ofone atom of manganite and three of pyrolusite. In the psilomelanite analysed by Turner, there were 4 atoms of sesquioxide to 15 of peroxide; in that analysed by Berthier, 3of sesquioxide to 17 of peroxide. It is obvious, therefore,601that the specimen I have examined is a new variety. But itis also peculiar in other respects. 1. It contains oxide ofcopper in appreciable quantity, a substance not occurring inthe other psilomelanes, though it was found by ProfessorDavy, of the Dublin Society, to the amount of 4.5 per cent.in a Swedish ore of manganese, which he considered to be abraunite (see Journal of Geol. Society of Dublin, vol. i .part 3.) 2. The amount of barytes included by it is butabout one-third of that found in the ores examined by Berthier and Turner.As respects the manner of the existence of the barytesalways found in psilomelane, and in small quantity in someof the other ores of manganese also; I may observe that itis the opinion of some high authorities in science , of M.Beudant, for instance, that it and the dentoxide are chemically united, the latter performing the function of an acid.If this idea be correct, it will follow that they are capable ofcombining in at least two widely different proportions, forthe psilomelanes of Berthier and Turner will , upon thisview, be represented by the formula 2 Bo O, 3 Mn2 03, andthat which I have analysed by the formula Bo O, 6 Mn2 O3, sothat the latter contains, combined with the same quantity ofbarytes, four times as much sesquioxide of manganese as theformer.This Cork psilomelane is obviously a rich ore of manganese, though of course inferior to the purer forms of pyrolusite. It exists in quantity in the district which I havementioned, and some cargoes of it have been brought intothe Dublin market, but have, I am told, been objected toby the manufacturers of the bleaching salt of lime, in consequence of its excessive hardness , and the consequent difficulty of reducing it to a fine powder.About three years ago, I received from Captain Kitto, aCornish miner, long resident in the south of Cork, an ore ofmanganese, which appeared so different from those with602which I was previously acquainted, that I was induced tosubmit it to analysis. It occurs in the locality already mentioned, at Rowry, a little to the east of Glandore, in lumpsof variable size, which, when broken, exhibit, though but illdeveloped, the faces of crystals belonging apparently to theright prismatic system, mixed, however, here and there withwhat would appear to be a brown hæmatite. Some ofthecrystalline portion of the ore, very carefully selected, gave,upon analysis, the following constituents:Silex •Perox. IronRed Ox. Mangan. 50.67( 1 ) (2)3.0834.88 0.436 20Sesquioxide 5.25 0.066 3OxygenWater .· 6.52) Peroxide 51.94 1.188 544.85 0.539 24100.00These results do not conduct to any very probable formula.But if we suppose that what is set down as sesquioxide isreally present as peroxide, a supposition which accordssufficiently well with the analysis, then the composition ofthis ore becomes very simple, being represented by theformula Fr₂ O3, HO+3 Mn O2, that is by one identical withthat which we have found for the psilomelane, when wesubstitute sesquioxide of iron for the sesquioxide of manganese. I have no doubt that this represents its realconstitution, so that it may be safely set down as a newand very distinct species. I may observe that this mineralanswers well for yielding oxygen, but is uneconomical as asource of chlorine, in consequence of the wasteful consumption of acid, in order to the saturation of the peroxide ofiron; one-half in fact of the acid is uselessly expended.Mr. William Andrews, Secretary to the Dublin NaturalHistory Society, read a paper upon the genera of Ferns0603Trichomanes and Hymenophyllum.His remarks werechiefly directed to the species of Trichomanes discovered byhim in September, 1842, in the western part of the Countyof Kerry, and which presented a variety of growth and stateoffructification so much more developed and characteristicof the genus of that beautiful fern than had hitherto beenmet with in Ireland, that determined him to examine itsaffinities with some of the exotic ferns, particularly withthose of the West India Islands.The Trichomanes was first discovered in Britain, by Dr.Richardson, at Belbank, near Bingley, Yorkshire, a wretchedspecimen of which is in the Banksian Herbarium, now in theBritish Museum: a figure of a barren frond is given in Dill.in Raii Syn . S. p. 127, t. 3. This specimen, however, nothaving been found in fructification, was supposed to beidentical with the Filix (Trichomanes) pyxidifera of Plumier, and was described as such by Hudson, in his FloraAnglica, p. 461: and this name it retained until its discovery, in the month of October, 1804, at Turk Waterfall, nearKillarney, by Mr. Mackay, Curator of the Botanic Gardenof Trinity College. Mr. Mackay obtaining this beautifulfern in fructification, forwarded specimens to Sir JamesEdward Smith, who at once decided its distinctness fromPlumier's plant, and considered it to be a new species, whichhe named and figured in English botany as Hymenophyllumalatum, from its winged stipe. The distinguished RobertBrown, the first physiological botanist of the day, correctedthis specific appellation to that of brevisetum (Br. in Hort.Kew. ed. 2, 5, p. 529), from the short and barely exsertedstate of the receptacles that the Killarney plants generallypresented. Mr. E. Newman, who has devoted so much attention to the specific characteristics of the British ferns,formed the first view, that the Killarney species perfectlyagreed with Willdenow's description (Sp. Plant. 5, p. 514)ofthe Speciosum of Teneriffe, and published it as such, in604his first edition of the History of British Ferns. The specific name brevisetum, however, was still retained throughthe several editions of the British Flora, until the discoveryby Mr. Andrews, in September, 1842, in a wild and woodedglen in the western part of the County of Kerry. Thestriking characters and fine state of fructification exhibitedby these splendid plants, the most rare and most beautifulof British ferns, and now altogether confined to the southwestern parts of Ireland, led Mr. Andrews to examine minutely, and to trace their affinities with the numerous exoticspecies of that beautiful genus; and from communicationswith Sir William J. Hooker, and to the great kindness ofthat most excellent botanist and encourager of science, andthe reference to his very extensive fern herbarium, it wastraced and detected to be the true Trichomanes radicans ofSwartz, setting aside the species brevisetum of the Englishflora, and the Speciosum of Willdenow. Thus the mildtemperature of the south-western parts of this country produced, in the utmost luxuriance oftropical growth, a plant peculiar to the West India Islands, and to the western coast ofSouth America. To Dr. Scouler's kindness Mr. Andrews wasalso much indebted for specimens of Trichomanes radicans ,and T. Scandens, collected by Dr. S. in Brazil, and whichenabled many doubts to be cleared .Mr. Andrews noticed a very remarkable character offructification in the new variety from Kerry, " that the capsules formed around the base of the receptacles within thecylindrical involucres, and as the receptacles elongated andbecame exserted considerably beyond the involucres, thecapsules continued forming in an even dense mass to the extremity of the receptacles." This is described as of rareoccurrence in Trichomanes. The Trichomanes reniformeof New Zealand, and the Hymenophyllum fuciforme ofChiloe, are noticed as having the capsules external to theinvolucres, but their being exposed to view was supposed605merely to result from the spreading and shrinking of thevalves. Loxsoma appears to be the only recorded genus aspossessing that peculiarity of fructification.The specific descriptions of Trichomanes radicans andits synonyma, are fully given in part 2, p. 125, of that invaluable work, Species Filicum, by Sir J. W. Hooker, recentlypublished.Professor Allman made some observations on Mr. Andrews's paper, in corroboration of its principles.DONATIONS.Proceedings of the Geological Society of London. Vol.IV. , Part 1. ( 1843 ) . Presented by the Society.Bulletin der Königl. Akademie der Wissenschaften zuMunchen. Nos. 1 to 55.Abhandlungen der Philosophisch. Philologischen Classeder Königlich Bayerischen Akademie der Wissenschaftenzu Munchen. Dritten Bandes dritte Abtheilung, in der Reiheder Denkschriften der XVIII. Band.Abhandlungen der Mathematisch. Physikalischen Classeder Königlich Bayerischen Akademie der Wissenschaftenzu Munchen. Dritter Band. Die Abhandlungen von denYahren, 1837, bis 43, enthaltend. Presented by the Academy ofMunich.Versuch einer objectiven Begründung der Lehre von derZusammensetzung der Kräfte. Von Dr. Bernard Bolzano.Presented by the Author.Prodromus zu einer neuen, verbesserten Darstellungsweiseder höhern analytischen Dynamik. Vom Grafen G. VonBuquoy, Ph. D., &c. Presented by the Author.

PROCEEDINGSOFTHE ROYAL IRISH ACADEMY.1844. No. 47.June 24.SIR WM. R. HAMILTON, LL. D., President, in the Chair.RESOLVED, on the recommendation of Council-That theAcademy do pay Mr. E. Curry £41 13s. , for completing theCatalogue of the Irish MSS. of the Academy, this sum including the money due to him at present.Sir William Betham gave notice that, at the next meetingof the Academy, he would move for—1st. A list of all papers or essays read before the Academy, in the departments of Belles Lettres and Antiquities,which were referred to Council for publication , from the 17thof March, 1828, to the 17th of March, 1844, containing thedates of such reading, the names of the authors , whetherordered by the Council for publication , and, if published inthe Transactions, with the dates of the Council's orderfor publication.2nd. An account of all sums of money expended for engraving copper- plates or wood- cuts, or making lithographs ,to illustrate such essays or papers, which, ordered by Council to be published, have or have not yet appeared in theTransactions of the Academy.3rd. An account of all sums of money expended on account of paper and printing of any such essay or essays, orVOL. II. 3 E608papers, which have been commenced, and are now in progress of printing; with the amount of liability of the Academy for what has not yet been paid.4th. A statement of the terms of any agreement or contract entered into by the Council, with the author or authorsof any such paper or essay, and the sum or sums of moneyadvanced on that account.5th . An account of all medals and rewards adjudged bythe Council, and paid to any author for papers and essays,during the said period, from the 17th of March, 1828, tothe 17th of March, 1844 , with the dates of such paymentsand delivery.6th. An account of the debts and liabilities of the Academy at this time, and also of their available assets.It was moved by Dr. Apjohn, That the Secretary ofCouncil be requested to provide the Academy, at the nextmeeting, with the information required in Sir WilliamBetham's notice.The motion, after discussion , was withdrawn.The Rev. H. Lloyd laid upon the table of the Academy amagnetical instrument, which had been recently constructedunder his direction by Mr. Jones of London, and which heproposed to denominate the " Theodolite Magnetometer."Much attention had of late been given to the construction of small magnetical instruments, for the use of travelling observers, and many improvements in their form hadbeen effected by Prof. Weber, Mr. Fox, and Lieut. Riddell.Prof. Lamont had also recently adopted magnets of a verysmall size in all the instruments employed by him in hismagnetical observatory, and had stated his conviction oftheir superiority over the larger magnets hitherto in use.Without entering at present into the grounds of this conviction, in the unlimited form in which it had been asserted609by Prof. Lamont, Mr. Lloyd said that, as respects certaininstruments intended for observations of a particular kind,there seemed now to be a pretty general agreement on thesubject. He had himself proposed an instrument for the determination of the changes of the Magnetic Inclination , inwhich the magnet was necessarily a small one; and the advantages of small magnets, in the delicate observation ofthe absolute Horizontal Intensity, seemed now to be fullyrecognized.

While engaged in considering the best form of an instrument intended for observations of the latter class, Mr. Lloydwas led to perceive, that the same apparatus might be madeto serve also in the determination of the Absolute Declination; and, by a few slight additions in the details of itsconstruction, in that of the variations ofthe three magneticelements. It may likewise be employed for all the usual purposes of a Theodolite; and thus, with the addition of an ordinary Inclinometer, a Chronometer, and a Sextant, constitute a complete magnetical equipment for the use ofthe travelling observer.The following is a brief description of the instrument.A divided circle, similar to that of a Theodolite, is supported on a tripod base, with levelling screws. This circle isnine inches+ in diameter; it is divided to 10' , and subdividedby two verniers to 10". The upper plate of the circle has twoprojecting arms, each carrying a pair of adjustable Y supports for the reading telescope , at a distance ofsix inches fromthe centre. The telescope rests in these supports on a tran-

• It may be proper to observe that this arrangement had occurred to the writer

before he had seen Prof. Lamont's account of his magnetical Theodolite, an instrument in which the same end is obtained , although by different means.† A circle six inches in diameter, and read to 20″, is sufficient for all the purposes of a travelling observer.One is sufficient, and the instrument will be so modified in all future constructions on the same plan.610sit axis, which is rendered horizontal by the help of a ridinglevel. The aperture of the object glass is eight- tenths of aninch; a glass scale , divided to the 4th of an inch , is fixedin its focus; and the eye tube is made to move across thescale in a dovetail slide.The magnets are hollow cylinders, each furnished as acollimator with an achromatic lens, and a fine line cut onglass in its focus. There are four such magnets: two ofthem being 3 inches long, and half an inch in exterior diameter, and two 3 inches long, and three- eighths of an inchin exterior diameter. The larger magnets are furnishedwith a Y stirrup, in which they may be inverted; the smallermagnets have the ordinary tubular stirrup, with a suspensionpin and screw socket. A hollow brass cylinder, ofthe samedimensions as the larger magnets, and carrying a small hollow cylindrical magnet within, serves to determine theamount of torsion of the suspension thread; it is likewisefitted up as a collimator.There are two boxes, within which the magnets are to besuspended. That belonging to the smaller magnets is arectangular box of copper, closed by mahogany sliding sides,and having a circular aperture at each end filled with parallel glass. It is 31 inches long, 1 inches wide, and 1 inchdeep, internally; and the thickness of the metal is a quarterof an inch, so that it may act powerfully as a damper. Asuspension tube of glass, eight inches long, is screwed intoan aperture in the top of the box; and is furnished with agraduated torsion cap at top, and a sliding suspension pin.This box is made to fit on the centre of the upper plateof the circle, and is capable of removal at pleasure. Thebox employed with the larger magnets is of wood , and ofthe same form as the copper box, but somewhat larger. Itis detached from the instrument, but may rest on the samestand . A small wooden piece with a mirror serves to illuminate the magnet collimator, either from above or from the611side, according as the light of day, or that of a lamp orcandle, is employed.The measuring rod employed in deflection experimentsis a compound bar of gun metal, formed of two bars, thelower of which has its surface horizontal, and the upper vertical. It is three feet in length,* and is graduated on its vertical surface. It is placed upon the upper plate of the circle,beneath the box, and at right angles to its longer sides; andit is so fixed that it may be removed with ease, and replacedexactly in the same position. The support of the deflectingmagnet slides upon the upper bar, and is furnished with avernier, by means of which the distance ofthe two magnetsmay be determined with accuracy and ease.The apparatus is furnished with two soft-iron hollowcylinders, nine inches long, and three-fourths of an inch indiameter, which fit in vertical sockets attached to the upperplate of the circle. By this addition the instrument is converted into an Induction Inclinometer, for the measurementofthe changes of the Inclination. By a slight addition to thesuspension apparatus, the instrument may likewise be usedas aBifilar Magnetometer, for the measurement ofthe changesof the Horizontal Force. These adaptations are, however, ofminor importance to the travelling observer, whose main concern is with the absolute determinations; and in a fixed observatory it is essential that there should be separate instruments for the separate purposes.The most convenient order ofthe observations to be madewith this apparatus, when employed by the travelling observer, is the following.1. Measurement of Absolute Declination.The copper box and measuring rod being removed, one

• For the purposes of the travelling observer, it will be more convenient that

this rod should be in two pieces. Two single bars, placed edgewise, will suffice.612of the larger magnets is to be suspended within the woodenbox, which should be placed on the same stand with the divided circle, at a distance not less than one foot from itscentre. The optical axis of the telescope, and that of themagnet-collimator, are then to be brought nearly into thesame right line , by an azimuth movement of the top of thestand, and by a small parallel movement ofthe box. Thetorsion of the suspension thread is then to be determined bythe help of the brass cylinder, and to be removed by meansof the torsion cap. The magnet being then replaced, thecoinciding division of the scale is noted, with the magnet direct and inverted, and the mean of the two readings is thedivision corresponding to the magnetic axis. The verniersof the circle being then read, the telescope is to be turneduntil the division so found coincides with a fixed mark, whoseazimuth is to be determined at leisure. The latter determination is made by the help of the same Theodolite, usedin combination with the Chronometer or Sextant.2. Observation of Vibration.The upper plate ofthe circle is to be moved to its originalposition, and clamped there.The coefficient of torsion of the suspension thread beingdetermined, by the help ofthe torsion cap and glass scale,the magnet is to be set in vibration, and the time of 200 vibrations determined in the ordinary manner. The arc ofvibration should be noted, by the help of the glass scale, atthe commencement and end of the observation, and the temperature recorded at the same times.3. Observation of Deflection.The wooden box being removed, the metal box and themeasuring rod are to be attached to the upper plate of theinstrument. One of the smaller magnets is then to be suspended; and the larger magnet being transferred to its support upon the measuring rod, at a fixed distance, the upperplate and telescope are to be turned until the collimator line613ofthe suspended magnet is seen to coincide with the centraldivision ofthe scale of the telescope. The verniers of thecircle being then read, the deflecting magnet is reversed, andthe telescope is moved until there is a new coincidence. Theverniers being again read, the difference of the two readingsis double the angle of deflection sought. It is necessary toeliminate the changes ofthe Magnetic Declination, which mayoccur between these two readings; and for this purpose thewooden box and one of the spare magnets may be employedby a second observer. But the same elimination may bemade as effectually by a single observer, by taking a series ofreadings with the deflecting magnet alternately in the twopositions. Finally, the observation is to be repeated withthe deflecting magnet at the same distance on the other sideof the suspended magnet, and the mean ofthe two resultstaken as the deflection corresponding to that distance.The quantity sought may be inferred from the angle ofdeflection at a single distance , with as much accuracy as isgenerally attainable in observations made in the open air, orin a tent; and, in such cases, it will generally be found moreadvantageous to multiply the observations at the same distance, in the manner already mentioned, than to repeat themat two or more distances . The distance should be aboutfive times the length of the magnets .The preceding arrangement is suggested chiefly in regardto the economy of time. But, when the observer has sufficient leisure, it is desirable that the time of observation ofthe two elements should be as near as possible to the epochsoftheir principal maxima or minima, the periodical variationbeing then least. For this purpose the observations shouldbe so arranged, that the middle of the observation of Intensity may fall between 10 and 10 A. M.; and that of the observation ofDeclination between 1 and 1½ P. M. In this case,then, the preceding arrangement should be nearly reversed.The observer should commence with the observation of de-614flection; proceed at once to the observation of vibration,determining the coefficient of torsion at the end; and, lastly,make the preliminary arrangements (of detorsion, &c. ) , forthe determination of the Declination , deferring the observation itself until 1 P. M. If there be a second observer, heshould undertake the observation of Inclination, and suchsextant observations as may be required for the determinationofthe Latitude, the Time, or the true Meridian. The observation ofInclination should be simultaneous with that of theHorizontal Intensity; the astronomical observations may bemade whenever most convenient.The Theodolite Magnetometer may likewise be employedwith advantage in a fixed observatory, especially in observations ofthe absolute Intensity; and it is worthy of remark,that if the differential instruments used in connexion withit be small ones, the circle of this instrument may be employed in their adjustments, and their construction thus reduced to the simplest possible form.Mr. Wm. R. Wilde read a notice of the opening of someTumuli, by Mr. Nugent, and the Rev. Dr. Todd (V. P.)on the part of Mr. Nugent, presented a stone of a peculiarform, found in one of the Tumuli described.The thanks of the Academy were given to Mr. Nugent,for his communication and donation.Mr. R. Mallet presented the results of his analysis of aporcelain clay, discovered some years ago by him, at Howth,and since extensively brought into use for the manufactureof cruciblés.The clay is found upon the southern side of the peninsula of Howth, which consists principally of quartz rock;it exists in large concretionary masses, or highly irregularbeds, and appears to have reached its present position by615the transport of water. It is found of every degree of fineness , from a coarse gritty mass of decomposing pebbles, withoccasional large nodules of friable felspar, to that of an impalpable colourless clay, like that of Dorsetshire , known aspipe-clay. This is soft, sectile, adheres to the tongue, andforms a strongly adhesive and plastic mass with water, capable of being moulded upon the potter's wheel into the finestforms.It bakes perfectly white , or occasionally of the slightestpossible rosy tint of white.Some of the masses of this mineral are strongly discoloured by iron and manganese, and imbedded in the finestparts are occasionally found a few fragments of marineshells, and bits of wood.By washing with abundance of water, a fine quartzosesand is separable from even the finest portions of this clay.This sand is white, but water separates from it a little sandof a darker colour, like common sea sand of the Dublincoast, and a few microscopic flakes of mica.A singular minute black worm is found in this clay,which may be worth the attention of naturalists.The clay, as dug out, does not efferversce with acid, andis insoluble in them; it yields no soluble matter to water,and appears to contain no alkali in any specimens yet examined.Mr. Mallet, however, has reason to think that the less.fully decomposed portions of the clay may contain alkali ina soluble condition, and hence render the material valuableas a manure.Some of the finest portion of the clay, washed from thesand, and dried at a temperature of 212° Fah. , was found byMr. Mallet to have the following composition . The analysishaving been conducted in the usual way, and with the usualprecautions, it does not seem necessary to detail its steps:VOL. II. 3 F616 .Silica,Alumina,Lime,Magnesia,Oxide of Iron,.Water, •67.96• 23.203.230.631.192.8099.01As no washing completely removes the presence of sand fromthis clay, which always feels gritty to a glass rod, and as itcontains comminuted mica, it could not be expected that itsanalysis should present a precisely mineralogical result.From the close analogy , however, which the above figurespresent to the composition of various felspathic rocks, asanalysed by Beudant, Berthier, &c. , there can be little doubtbut that the geothetic origin of this clay is the decompositionof felspar, or other allied granitic minerals. In fact the results approximate to the formula ( taking the iron and magnesia together).or,(AlSi15 + Ca + Mg + FeO) + HO,3 (Al + Si;) + ( Ca + Si¸) + (( Mg + FeO) +Si3) + HO.This clay is of very great economic value, and capable ofbeing used for the manufacture of the finer descriptions ofpottery or even of porcelain; it has, however, hitherto onlybeen brought into use for the manufacture of crucibles, byMr. Mallet.The President read a paper on an improvement in thedouble achromatic object glass.DONATIONS.Life of W. V. Morrison, Esq., M.R.I.A.Morrison, Esq. Presented by the Author.By John617Bericht über die zur Bekanntmachung geeigneten Verhandlungen der Königl. Preuss. Akadémie der Wissenschaften zu Berlin, 1842-1843.Abhandlungen der Königlichen Akademie der Wissenschaften zu Berlin ( 1841 ) . Presented by the Academy.Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen. Erster Band. Von den Jahren 1838-1841. Presented by the Society.Almanach der Königlichen Bayerischen Akademie derWissenschaften zu München ( 1843). Presented by the Academy.Leitfaden zur Nordischen Alterthumskunde herausgegeben von der Königlichen Gesellschaft für Nordische Alterthumskunde ( 1837).Die Königliche Gesellschaft für Nordische Alterthumskunde zu Kopenhagen (Jan. 27, 1842).Memoires de la Société Royale des Antiquaires du Nord1840-1843. Presented by the Society.Fasciculus Inscriptionum Græcarum. Edidit JacobusKennedy Bailie, S. T. P. Presented by the Author.Proceedings of the Chemical Society of London. Part 6.Presented by the Society.Journal of the Statistical Society of London. Presentedby the Society.Literarische Sympathien oder industrielle Buchmacherei.By Dr. J. G. Flügel. Presented by the Author.Bjorgynjar Hatfskinn. Presented by Dr. Robt. Graves,M.R.I.A.The Numismatic Chronicle for April, 1844. Presentedby the Numismatic Society.Journal ofthe Franklin Institute. 5th Volume, 3rd Series .Presented by the Institute.An Olla Podrida, or Scraps Numismatic, Antiquarian,618and Literary. By Richard Sainthill.Author.Presented by theJournal ofthe Geological Society ofDublin. Vol. III . Part1 , No. 2. Presented by the Society.Sixteen Specimens of Chinese Cash. Presented by RobertMallet, Esq.Archives du Museum d'Histoire Naturelle.Livraison 4. Presented by the Directors.Tome III.Memorie dell I. R. Istituto Lombardo di Scienze lettereed Arti. Vol. I. Presented by the Institute.Edinburgh Astronomical Observations.Presented by the Royal Astronomical Society.Vol. V., 1839.Greenwich Magnetical and Meteorological Observations,1840-1841 . Presented by the Royal Astronomical Society.L'Art de connaitre les Pendules et les Montres. Par J.B. A. Henri Robert. Presented by T. Hutton, Esq.Puits Artesien de l'Abattoir Grenelle. Presented by T.Hutton, Esq.On the Industrial Resources of Ireland. By RobertKane, M.D. Presented by the Author.APPENDIX.No. I.LIST OF SUBSCRIBERSTOTHE FUNDFOR THE PURCHASE OF THECOLLECTION OF IRISH ANTIQUITIES, COINS, ANDMEDALSOF THE LATEVERY REV. HENRY R. DAWSON,DEAN OF ST . PATRICK'S, DUBLIN.The Names marked thus [ * ] are Members ofthe Royal Irish Academy.£ s. d.

• Adare, Edwin Visct. , M. P. ,

Waterloo Crescent, Dover, 10 0 0Armagh, Archbp. of, Rt. Hon..·555 IS SOOOOO5 01 1 00 01 0 01 0 00and Most Rev. Lord J. G.De la Poer Beresford,Alley, George, Esq. ,Adair, Thos. Benjamin, Esq. , 1

• Anster, John , Esq. , LL. D. ,
• Apjohn, James, Esq. , M.D.,
• Brady, Rt. Hon. Maziere,

(Chief Baron of the Exchequer),

• Brisbane, Sir Thomas M.,
• Beaufort, Captain R. N., •
• Barrington, Matthew, Esq. , 5
• Bolton, Chichester, Esq.,
• Borrowes, Robert, Esq.,
• Botfield, Beriah, Esq. , M.P. , 5
• Bailie, Rev. Jas. Kennedy,

D. D. , ·

• Blood, Bindon, Esq . , Edin- burgh,

Brooke, William, Esq.,Bernard, Lord,Barton, John, Esq.,

• Bergin, Thomas F. , Esq. ,

··•332200000£ s .20d.Brought forward 68 14 Bennett, Robert, Esq. , Cork,(Recorder),Butt, Isaac, Esq . , LL. D.,

• Ball, Robert, Esq.,
• Banks, John T., M. D. ,

Barrington, Edward, Esq. ,Barrington, Richard, Esq. ,Barlow, Wm. Thos. , Esq., 1

• Bateson, Robert, Esq. , .
• Beatty, Thomas E., Esq. ,

M. D.,• •

• Beauchamp, H. C., Esq . ,

M. D. ,•OOOOOOOOOO1 0·• • • 1111 00 001 0 00 001 0• 1 0 01 0 0111ooooooo 0 00 00 00 00 00 0• 0 01 0 090 16 0Bellingham, O'Brien , Esq . ,

• Benson, Chas. , Esq. , M.D.,

Bewley, Henry, Esq.,Blacker, William , Esq. ,Blair, James K. , Esq. , Tem55 00 0ple, London,3 3 0. Bland, F. , Esq.,Boileau, G. W., Esq. ,0 Boileau, S. , Esq.,0 * Bolton, W. E. , Esq. ,0 Bottomley, William , Esq. ,0 * Bowles, John A., Esq. ,1 10 0 Boyle , James, Esq. ,68 14 0aii£ s.d.Broughtforward, 90 16 0Brocas, Henry, Esq. ,Brocas, William , Esq. ,

• Burrowes, John, Esq. ,

1 01£ S. d.Brought forward, 219 16 Cramer, Maurice, Esq. ,0• 1 0 0Corrigan, D. J. , Esq. , M. D., 1 0 0Crosthwaite, Leland, Esq. ,0 10 0• 0 1 0 0

• Burton, F. W., Esq. , 0 0 Curry, William, Esq. , • 1 0 0
• Butcher, Rev. S. , F.T.C.D. , 0 0
• Butler, Rev. Richard, Trim,

Butler, Colonel,0 0Clinche, H. O. B. , Esq. ,Curry, Eugene, Esq. ,0 10 00 01 0 0· 1 0 0. 1 0 020 0 0• 10 0 02200• 20 0 00 0. 10 0 0• 5 0 0• 5 0 055 00 03320000000 0Butler, Rev. Wm. Archer,Bruce, Haliday, Esq. ,Blacker, Stewart, Esq. ,

• Cooper, E. J. , Esq. , M. P. ,
• Callwell, Robert, Esq.,
• Courtenay, H. , Esq. ,
• Caulfield, Hon. Henry,

Cane, Richard, Esq. ,

• Cane, Edward, Esq. ,
• Carr, George, Esq.,

Clibborn, Edward, Esq. ,Close, Colonel,

• Conway, F. W., Esq. ,

Cooper, J. Sisson, Esq. ,

• Cusack, James, Esq. , M.D.,

Clogher, Bishop of, The Hon. and Rt. Rev. LordRobert Ponsonby Tot- tenham, D. D. ,Curran, W. H. , Esq. ,Caledon, Countess of,• ·• •• •Chapman, Benjamin James,Esq. , M. P. , •

• Chetwode, Edward Wilmot,

Esq., .

• Clendinning, Alex. , Esq. ,
• Croker, Charles P., Esq. ,

M. D. , •Calvert, Adam, Esq. ,

• Cane, Arthur, Esq. ,

· •

• Carmichael, Richard, Esq. ,

M. D. ,

• Carmichael, Andrew, Esq.,

•522200002110000001 0 01

• Carter, S. , Esq.,

1

• Cash, George, Esq. , . • 1 0 0

Cather, Thomas, Esq. , 1 0 0

• Churchill, Dr., 1 0 0
• Clarke, Thomas, Esq. ,

Close, J. S. , Esq. ,

• Cole, Owen Blayney, Esq. ,
• Colomb, Lieut. - Colonel,
• Combe, George, Esq.,

Conyngham, Wm. Lenox,Esq. , ·Cooke, J. R., Esq.,

• Corballis, John R. , Esq. ,

Corballis, James, Esq. , .

• Coulter, Thos. , Esq. , M. D. ,

0 00 00 0· 1 0 00 0•· 011 0219 16De Grey, Thomas Philip Earl ( Lord Lieutenant) ,and Donation of a large Gold Collar,Dunraven,Wyndham Henry Wyndham, Earl of, .Downshire, Arthur BlundellSandy Trumbull, Marquis of,Dick, Quinton, Esq . , M. P. ,London, . .

• Darley, Frederick, Esq. , •
• Doyne, Charles, Esq. ,

Digby, Thomas G. , Esq. ,Daly, James, Esq.,

• Davidson, John, Jun. , Esq. ,

Armagh,

• Davy, Edmund, Esq. ,

Deane, Sir Thomas,

• Dixon, Rev. R. V.,

Dobbs, Joseph, Esq.,Doherty, John, Esq. ,Donegan, John, Esq.,

• Downes, George, Esq. ,
• Drummond, Rev. Dr.,

Duke, Jemmet, Esq. ,

• Dunlop, Durham, Esq. ,
• Elrington, Rev. Dr.,

Enniskillen, William loughby, Earl of,Eliot, Lord,0521100000OOOOO• 10 0 00001 10 001 0 000 00 00 00 00 00 01 0 0• 0 0• 1 0 010 0 0Wil- 00

• Edington, William, Esq. , 0

Eustace, John, Esq. , M. D. ,Edgeworth, M. P., Esq. ,Fitzwilliam, Chas. William Earl,. •Fortescue, Hugh, Earl of,

• Foster, Hon. Justice,

Ferrier, James, Esq. ,Fitzgibbon, Gerald, Esq. ,Fortescue,••555100000000 10 0 20522000 00 00 0Esq. , • 2 0 01 100• 1 0 0• 1 0 0

• Ferrier, Alex. Jun. , Esq. ,
• Ferguson, Hugh, Esq. , M.D. ,
• Ferguson, Samuel, Esq.,

Ferrier, Alexander, Esq. ,

• Finlay, John, Esq. , LL. D. ,

Finn, Rev. Charles, P. P. .1 0 01 0 0389 6iii.Brought forward, 389 Fitzgerald, John, Esq. ,Fitzpatrick, P. V., Esq. ,

• Foot, Simon, Esq. ,

Foot, Lundy E., Esq.,Forster, Robert, Esq. ,Fox, Rev. J. W.

• Goff, Rev. Thomas,

Goold, Thomas, Esq. ,

• Graves, Rev. C., F. T. C. D.,

Guinness, Arthur, Esq. ,Gordon, Robert, Esq. ,Gordon, R., Esq. , Cheltenham ,Gosford, Archibald Earl of,

• Graves, Robert J. , Esq. ,

M. D. ,

• Grierson, G. A. , Esq. ,
• Grubb, Thomas, Esq. ,

•••L S. d.6 00 00 Haffield, Arthur, Esq. ,0 Hall, S. C. , Esq., .0 Hall, Mrs. S. C., .0 * Hamilton , John, Esq. ,1 0Brought forward, 517 Hackett, Michael, Esq. , •£ s. d. 20000oo. 14000 ....055532OOOO2220020OOOOO000· 0 00 00 022222OOOOOGuinness, Ben. Lee, Esq., 2 0 0Guinness, A. Lee, Esq.,

• Graham, Professor, ( Edin- burgh,
• Grimshaw, Wrigley, Esq.,

M. D. ,Gill, M. H., Esq., .Goold, Francis, Esq. ,Gordon, R. H., Esq. ,0 01 01 11 0 00 01 0 00 0• 1 0 01 00 10 00209500000OOOOO•1010 .55 0 03 000හය

• Griffith, Richard, Esq. ,

Guinness • , W. N., Esq. ,Gilmore, J. B. Esq. , Q. C.,Garrett, Henry, Esq.,Herbert, Hon. Sydney,

• Hume, A. Esq.,
• Hutton, Thomas, Esq • .
• Hill, Lord George, A.,
• Hudson, Henry, Esq. , M. D. * Hudson, William Elliott,

Esq. ,

• Hamilton, Sir W. R., LL. D. P. R. I. A. ,

Hutchins, Samuel, Esq. , 3Hall,Lieut.Colonel H. , London,Homan, Sir W. J., Bart.

• Hart, A. Searl, LL. D. ,

F. T. C. D. ,Haughton, James, Esq. ,Haughton, William , Esq. ,Hone, Joseph, Esq. ,.

• Hope, Thomas C. Esq. ,

M. D., Edinburgh,

• Horner, Rev. James,

Herrick, J. E., Esq. ,Hutton, Mrs. Thomas,•2271• • •·••·002200222200000000

• Hamilton, Chas. W., Esq. ,

Hamilton, Dacre, Esq. ,

• Hanna, Samuel, Esq. , M.D.,

Hanna, William , Esq. ,

• Hardiman, James, Esq. ,
• Harrison, R. , Esq. , M. D. , .

Hewson, John, Esq. ,

• Hill, William, Esq. ,

•

• Hincks, Rev. Thomas, LL.D.
• Houston, John, Esq. , M. D. ,

Hunt, Percival, Esq. , M. D.,

• Hutton, E., Esq. , M. D. ,

Hutton, Henry, Esq. ,Hutton, Rev. Joseph,Hyndman, George C. , Esq. ,

• Hemans, G. W., Esq. ,

Healy, F. W., Esq. , .Irwin, Rev. Alexander,

• Jones, Robert, Esq. ,

11 0 01 0 01 0 01 0 01 0 01 0 01 0 01 0 01 0 0· 1 0 0· • 1 0 01 0 010 0• 0 10 00 5 0· 3 0 0+ • 332300• 0• 1 0 01 0 01 0 0• 1 0 0. 1 0• 10 5050•· 10OOOOOO~·D55530000022 200000

• Jones, Colonel Harry D.,

Johnson, Hon. Justice,James, Sir J. K. , Bart. ,

• Jellett, John H. , F. T. C. D. ,

Johns, Alexander, Esq. ,Johnson, Edmund, Esq.,Johnston, Rev. Richard,Jacob, John, Esq. , M. D. ,Kildare, Marquis of,

• King, Hon. James,

Kemmis, Henry, Esq.,

• Knox, G. James, Esq. ,
• Kent, William T., Esq. ,

Kinsella, Rt. Rev. Dr.,Kennedy, George A. , Esq. ,M. D.,

• Kerry, Knight of, ( Right Honourable Maurice Fitzgerald) , • •
• Kane, R. J. , Esq. , M. D. ,
• Kyle, William C., Esq. ,

LL. D. ,Kane, William, Esq. ,

• Kelly, T. F., Esq. ,

••1 0

• Kelly, D. H. Esq. ,

10 0 Kerr, Doctor, 1CO0 00 00 0OOOOO 00 OOOOO22 210 000 00 00 01 0 Leinster, Augustus Frede- 1 0 rick, Duke of, 20 0 0517 4 0 614 11 0ivBroughtforward, 614 11 * Leitrim, Rt . Hon. Natha- niel Earl of,Lorton, Robert Edward Viscount,Larcom, Captain R. E.,

• Lloyd, Rev. Humphrey, D.D. ,

F.T.C.D. ,Lucas, Edward, Esq. ,Lismore, Very Rev. Henry Cotton, LL. D. , Dean of

• Lyle, Acheson, Esq. , •

Latham, Oliver, Esq. ,Lindsay, John, Esq. ,

• Lambert, Rev. Charles J. ,
• La Touche, G. D. , Esq. ,

Lee, Rev. Wm. , F.T.C.D.,Lees, Doctor,

• Lenegan, J., Esq. ,
• Litton , Samuel, Esq. , M.D.,

Lloyd, William T., Esq. ,

• Longfield, William, Esq. ,
• Mac Cullagh, James, Esq. ,

LL. D., F. T. C. D. ,Midleton, George A. , Vis- count,·

• Marsh, Sir H., Bart. , M.D.,
• Macartney, J. Esq. , M. D.,
• Monsell, William , Esq. ,

Moore, Edward, Esq. ,

• Murchison, Rodk. Impey,

Esq. , F. R. S., V. P. G. S.

• Mollan, John, Esq . , M. D. Macdonnell, Alex. , Esq.

•·••.£ S. d.020 0 05 05 0 0 350 00 0322210 000 00 0 O2OOoooooooo£ s: d.Broughtforward, 764 0Meiklam, John, Esq. ,

• Montgomery, Wm. F., Esq.,

M. D., •Mullen, George, Esq. ,

• Mulvany, W. T. , Esq. ,
• Murray, William , Esq. ,
• Mackay J. T., Esq. ,

Newport, Sir John, Bart. ,Nelson, Joseph, Esq. ,Newman, Miss,Norreys, Sir Chas. DenhamOrlando Jephson, Bart. ,

• Newenham, Thomas, Esq . ,
• Napier, Jeseph, Esq .,

Nicholson, Mrs. ,Nicholson, G. A., Esq. ,·••.4901 01 01 01100005OOOOO000532 2211000000000 01 0 01 0 01 0 01 0 0 * Nicholson, J. A., Esq. , 01 0 0 Nolan, James Joseph, Esq., 0 01 0 0 Nugent, Daniel, Esq. , • . 1 0 0• 1 0 0 Nugent, William, Esq.,21 0 0• 20 0505505000OOOOO.

• O'Halloran, Major Gen. Sir Joseph, K. C. B. ,

O'Connell, Daniel, Esq. ,M. P.,O'Hara, C. K., Esq. ,••0 * O'Grady, M. M., Esq. , M.D., 2• 0 * O'Brien, Sir Lucius, Bart. ,5 0053222211IIIOOOOOOHHO00 0 000 001 0• 1 000

• Magrath, Sir George, M.D., 200 * Maguire, William, Esq. ,

Molyneux, Sir G. Bart. ,M'Carthy, Alexander, Esq. ,Maturin, Edmund, Esq. ,Macan, John, Esq. ,Mac Clean, Samuel, Esq .,M'Carthy, Justin, Esq. ,Mac Donnell, James, Esq. ,M. D., Belfast,·

• Mac Donnell, J. , Esq. , M.D. * Mac Donnell, Rev. Dr. ,

••1 01 0 01 0• 01 011F. T. C. D. ,M'Glashan, James, Esq. , 1

• M'Neece, Rev. T., F.T.C.D. ,
• Mallet, Robert, Esq. ,

Martin, John, Esq. , .

• Mason, H. J. M., Esq.

LL. D. (and donation of agold Fibula),Massy, Hugh, Esq. ,

• Mayne, Rev. Charles,

1 0 00 0764 0 00001 pdO33111· 5 0 000001 00 00 00 01 0 01 0 001 0 01 0 0· • 1 0 0• 0 10 0• 10•

• O'Ferrall, J. M. , Esq . , M.D. O'Brien, A. S., Esq. , M. P. O'Brien, W. S. , Esq. , M.P. 1

O'Callaghan, Isaac, Esq. , 1

• O'Conor, Matthew, Esq. ,

O'Dwyer, Andrew C., Esq. ,

• Orpen, T. H. , Esq. , M. D.,
• Orpen, C. H., Esq. , M. D. ,
• Owen, John U., Esq. , M.D. * Owen, Jacob, Esq.,

O'Donovan, John, Esq.,

• Pim, James, Jun. , Esq. ,

Perry • • · , John, Esq. ,Pim, George, Esq. ,

• Portlock, Captain R. E.,

Pakenham, Hon. and Rev.Archdeacon ,

• Petrie, Geo. , Esq. , R.H.A.,
• Phibbs, William , Esq. ,

Purser, John, Esq. ,

• Parker, A. , Esq.,

•053300000000•3 00 00 00 0· 0 01 0 0 2222- ,Patterson, Chas. , Esq. , M. D, 1 0 0Patterson, R., Esq. ,Pepper, Colonel,Perry, James, Esq. ,Pim, W. H., Esq. ,•1 0 01 0 00 01 0 0849 17 0No. IV.ACCOUNTOF THEROYAL IRISH ACADEMY,FROM 1ST APRIL, 1843, TO 31ST MARCH, 1844.THE CHARGE.Balance in favour of the Public, as per last £ S. d.Audit,1844),·Parliamentary Grant for 1843 (paid Jan. 4,Quarterly Warrants from Treasury,THREE PER CENT. CONSOLS SOLD:£ S. d.210 13 9300 0 0146 17 8Total from Treasury,446 17 81843, August 12, 14, £300, at 941 per,Interest 40 days,282 11 30 19 8283 10 11Brokerage,Total Proceeds Consols sold,OLD 3 PER CENT. STOCK SOLD:1843, August 12, 14, £50, at 101 per,Interest 40 days,Brokerage,Total Proceeds old 3 percent. Stock sold, .07 6283 3 5• 50 16 30 3 1051 0 101 350 18 10INTEREST ON STOCK:£ S. d.Halfyear's on 1665 Ditto,1643 194 2, 3 per Cents. ,6, 329 1 429 99 28 13 11Ditto,Ditto,99 1394 17 8, 3 "" 20 17 322 1117 1 10, 3Total Interest on Stock (exclusive of brokerage, 5s. 6d. , ) Šf"" 16 13 1095 6 41087 0 0xxviii£ S. d. £ S. d.Broughtforward, . 1087 0 0PUBLICATIONS AND BOOKS SOLD:Boone, Messrs. , balance of their account to31st December, 1843,ONE YEAR'S RENT OF STABLE to Nov. 1,1843,LIFE COMPOSITIONS:J. Pickford, M. D.,ENTRANCE FEES:Hon. and Very Rev. the Dean of St. Pa- trick's,Goddard Richards, Esq., •14 6 321 0 015 15 01843,22 5Rev. F. Crawford,J. Wynne, Esq. ,·•J. George Abeltshauser, Esq.,G. J. Allman, M. D.,H. L. Lindsay, Esq.,Rev. John Homan,John M'Mullen, Esq. ,Matthew Dease, Esq.,J. Pickford, M. D.,99""""999999cccrcr orc5 05 05 5 05 05 5 05 5 05 5 05 0"" 5 5 099 5 0"" 5 5 0Sir M. Chapman, Bart. , 99 5 0E. Bewley, M.D., • 5 5J. Neville, Esq., 99 5 5 0Henry Clare, Esq., . ""5 5 0William Henry, Esq., ""5 5 0William McDougall, Esq. , 99 5 5 0Total Entrance Fees, • 89 5 0-ANNUAL SUBSCRIPTIONS AND ARREARS:W. Andrews, Esq. , due March 16, 1843,C. T. Webber, Esq.,The Archbishop of Dublin,William Hill, Esq., •Sir Thomas Staples, Bart. ,F. M. Jennings, Esq.,James Pim, Jun. , Esq. ,Rev. William Lee,William Gregory, M. D.,W. Longfield, Esq. ,Rev. R. V. Dixon,Ditto,Rev. Richard Butler,J. Nelson, Esq. ,G. D. La Touche, Esq.,99 99"" 999999 99 • 99 ""· ""• 99 99 • 99 9999 9922 1842,1843,99 99 •222222222222 2 202 02 02 02 02 02 02202 2 02 0202202 2 02 2 099 39 2 2 031 10 0 1227 6 3xxixBroughtforward, ·J. T. Banks, M. D. , due March 16, 1843,A. Smith, M.D., .Thomas Newenham, Esq., .F. W. Conway, Esq.,W. Blacker, Esq.,Sir J. K. James, Bart., .Jacob Owen, Esq.,Sir W. Betham, Knt. ,William Hogan, Esq. ,W. Drennan, Esq.,G. Fitzgibbon, Esq.,Rev. James Wills,··و,£ 8. d. £ S. d.31 10 0 1227 632 2 02202 2 0"" 2 2 02 2 0• · 99 "" 2 2 0· 99 2 2 0• "" "" 2 20"9 99 2 2 099 "" 2 2 0"" 2 2 099 99 2 2 0Hon. Justice Crampton, LL. D., 99 2 2 099 99 2 2 099 2 2 0""2 2 039 29 2 2 099 99 2 2 099 ""220• "" 99 2 2 099 99"" "" 2 2 099 99 2 2• 99 29 2 2 0"" 1844,99 1843,22 ""99 99"" 99 2 2 099 2 2 029 99 2 2 0· 9999 """" 2 2 022 ""2 2 0"" ""22 0"9 ""2 2 0• 99 ""2 2· 99 99 2 2· 99 99 2 2 099 99 2 2 099 ""2 2 099 99 22 0• 29 99 2 2 099 "" 2 2 0· • "" "" 2 2 0"" "" 2 2 0W. B. Wallace, Esq.,W. T. Mulvany, Esq.,F. Churchill, M.D.,A. Ferrier, Esq., .J. S. Cooper, Esq.,John Mollon, M.D.,F. W. Burton, Esq.,W. T. Lloyd, Esq. ,G. Wilkinson, Esq.,J. Wynne, Esq.,Thomas F. Kelly, LL.D.,Sir L. O'Brien, Bart. ,Charles Vignoles, Esq. ,Edward Cane, Esq.,G. W. Hemans, Esq. ,John Finlay, LL.D.,Charles Doyne, Esq. ,Rev. Thomas Stack,.R. A. Wallace, Esq. ,Thomas Grubb, Esq. ,Rev. R. Chatto,Rev. James Reid,·•John Toleken, M.D.,James Patten, M. D.,Right Hon. Chief Baron,Edmund Davy, Esq. ,C. W. Hamilton, Esq.,J. H. Jellett, Esq., .James Apjohn, M.D.,E. J. Cooper, Esq. ,R. Adams, Esq. ,C. E. H. Orpen, M.D.,•••22 02 2 02202 2 0220126 0 0 1227 6 31XXXBroughtforward,Hon. James King, due March 16, 1843,M. Longfield, LL. D.,Rev. H. F. C. Logan, D. D.,J. Osborne, M. D.,•J. Huband Smith, Esq.,G. A. Frazer, Esq.,Abraham Abell, Esq. ,Ditto, •William Barker, M.D.,Robert Tighe, Esq., .R. Law, M.D.,Rev. John West, D.D.,R. Graves, M. D.,John Ball, Esq.,·• •T. E. Beatty, M. D., .H. C. Beauchamp, M. D.,R. C. Walker, Esq. ,W. Monsell, Esq. ,William Stokes, M. D.,J. T. Young, Esq.,R. Reid, M. D.,99S. d. £126 0 0 1227220002 2 02 002 2 0

• 15:15, 2 August 2024 (CEST)15:15, 2 August 2024 (CEST)15:15, 2 August 2024 (CEST)15:15, 2 August 2024 (CEST)15:15, 2 August 2024 (CEST)15:15, 2 August 2024 (CEST)15:15, 2 August 2024 (CEST)15:15, 2 August 2024 (CEST)15:15, 2 August 2024 (CEST)~

""""2• "" 9999 2 2 0• 99 1842, 2 2 0• 99 1843, 2 2 0· 99 ""2 2 0• 99 ""2 2 0• 2 2 099 99• 99 99 2 2 0"" 99 2 2 099 99 2 2 0• 99 99 2 2 0. 99 99 2 2 0· 99 99 2 2 0• · • 22 99 2 2 0• • 99 2 2 0· 99 ""2 2 0"" 99 2 2 0• • 99 1841, 2 2 099 1843, 2 2 02 2 0 "" 2999991842,1843,2 2 02 2 099 99 2 2 0John Hart, M. D., 99 2 2 0M. Barrington, Esq. ,•2 2 0 29 99H. H. Joy, Esq., . "" 99 2J. Anster, LL. D., 22099 99 2 0W. R. Wilde, Esq., 99 99 2 2 0W. T. Kent, Esq., 99 99 22 2 02 0 99• 99 202 2 0 99• 99 2 2 099 99 2 2 0• • · "" 99• 99 1844, 22 2 02 0"" 1843,· 9915222020"" 99 2 2 099 1844,22 2 0· 22 99 20་Rev. Matthew Horgan,Oliver Sproul, Esq.,Arthur Jacob, M. D.,J. F. Lynch, Esq.,R. W. Smith, Esq.,Wrigley Grimshaw, M. D.,•R. Dickinson, Esq.,R. Mallet, Esq.,S. Carter, Esq.,M. O'Conor, Esq.,W. F. Montgomery, M. D.,G. M'Dowell, Esq.,Ditto,Rev. Edward Marks, D. D.,G. A. Kennedy, M.D., .A. Lyle, Esq., .F. Churchill, M.D., .B. J. Chapman, Esq. ,S. d.63220 10 0 1227 63xxxiBrought forward,William Farran, Esq. , due March 16, 1843 ,E. S. Clarke, Esq. ,John Dalton, Esq., .29999999Total Annual Subscriptions and Arrears,THE TOTAL CHARGE, .£ 8. d. £ S. d.220 10 0 1227 6 32202 22 200000226 16 0• •£ 1454 2 3XxxiiTHE DISCHARGE.ANTIQUITIES PURCHASED AND repaired.Armstrong, Robert, drawing ofthe Magrathtomb, 18th October, 1844,Davis, E., great seal of George I., Nov. 13th,1843,Donegan, John, for antique gold ornament,Feb. 19th, 1844,Gerin, Michael, a bronze antiquity, to June 3rd, 1843,Glennon, Richard, spear, Oct. 12th, 1843,Reilly, Peter, shoes, &c. to May 20th, 1843,Ditto, a brass vessel, June 13th, 1843,Ditto, sundries, Oct. 11th, 1843,Sharkey, William, gold cinerary boxes andfibulæ,Underwood, J., for bell, to August 11th,1843,Ditto,Ditto,·celt, Oct. 10th, 1843,dirk, Nov. 3rd, 1843,Total Antiquities purchased and repaired,BOOKS, PRINTING, STATIONERY, &c.Allen, J. W., Lithography, &c. , to July 4th,1843,Curry, Eugene, Catalogue of Manuscripts,to April 7th, 1843,£ s. d. £ s. d.11005 013 16 000001 150 70 102100 8 0OOOOO15 10 00 5 0 OOO0 4 00 10 037 1 015 17 911 4 0Ditto, ditto, June, 5th, 1843, 12 12 0Ditto, ditto, July 17th, 1843, 12 12 0Ditto,Ditto,Ditto,ditto, Nov. 6th, 1843,ditto, Nov. 13th, 1843,ditto, from 11th Dec.,33 12 02 2 01843, to Feb, 19th, 1844, 21 0 0Dalton, John, for book on Drogheda, to Dec.21st, 1843,Gill, M. H., printing Proceedings and Cir- culars, Dec. 31st, 1842,1 4 053 0 10 Ditto, ditto, Transactions, March16th, 1843, 264 10 4427 14 11 37 1 0xxxiii£ s. d. £ 8. d.Broughtforward,Hanlon, George, for woodcut of ogham stone to Nov. 18th, 1843,Hodges and Smith, books, & c . , to June,1843, ·Johnson and Co., advertising Transactions,to June 30th, 1843,Kirkwood, John, printing and engraving,March, 24th, 1843, .427 14 11 37 1 080•30049 9 725 16 610 8 9Mullen, G., book binding, to March 20th,1843,32 3 11Ditto,Ditto,ditto,ditto,June 30th, 1843, 58 1 6Jan. 31st, 1844, 16 6921 02 0Oriental Translation Fund, subscription for961842 and 1843,Perry and Co., paper, to June 28th, 1843,Plunket, James, 24 sheets of drawings forCatalogue of Antiquities, to Dec. 24th,1843,Reilly, John, four volumes of the Transactions, Feb. 5th, 1844, .Taylor, R. and J. E., twenty Scientific Memoirs, Part II. , to Jan. 31st, 1843,Total Books, Printing, Stationery, &c. ,COALS, CANDLES, OIL, & c.Kenny, M., for stove coals, toJuly 20th, 1843,Rathborne, J. & H., for candles, to May 27th,1843,19 10 01 0 0600672 12 51 5 06 17 11Todhunter, J., coals, to March 30th, 1843,Total Coals, Candles, Oil, &c.,0 19 69 2 5CONTINGENCIES, &c.Carriage of parcels, to Nov. 28th, 1843,Clibborn, E., incidentals, to April 3rd,1843,Ditto, per treasurer,Clifford, for gum, to Oct. 23rd, 1843,Declaration in Court of Exchequer, and carhire, to Dec. 6th, 1843, CElliot, carriage ofparcels, to May 29th, 1843,1 15 10 0000 18 46 43 10Fannin, ditto, May 22nd, 1843,Ditto,ditto,Ditto, ditto,Jan. 22nd, 1844,ditto,Maguire, twine, June 16th, 1843,OOOOOO 0 2 60 5 00 3 00 1 00 0 100 1 03 17 8 718 15 10xxxivBroughtforward, .Pamplin, William, carriage of parcels, June£ S. d. £ S. d. 4833 178∞718 15 1026th, 1843,Patten, J. , ditto, Dec. 27th, 1843,Postages, to June 23rd, 1843,Ditto, Dec. 31st, 1843,Ditto, ditto,100000 10 101196006080606 100 5Postage stamps, to March 25th, 1843,Power ofattorney to Boyle and Co., to sellStock, •Stamp on Government Grant, paid Jan. 4th,1844,Subscription to Mr. Ryland, to reimburse his expenses in carrying the Act of6 & 7Victoria, •Total Contingencies, &c.REPAIRS OF HOUSE, &c.•Brown, J., cleaning windows, to June 2nd,1843, ·Ditto, glazing ditto, Feb. 3rd, 1843,Clibborn, Edward, sundries used in cleaninghouse, to July 16th, 1843,• 1 0 00 5 010 10 028 13 11 10 00 7 05 0 0Mullen, Wm. , sweeping chimneys, to May 17th, 1843, 0 11 6Total Repairs of House, &c. 7 8 6REPAIRS OF FURNITURE, &c.Allen, E., towels, to April 28th, 1843,Casey, Paul, repairing locks, to March 20th,1843,1 19 110 5 4Duffy, John, altering table, to March 10th,1843, 1 4 0Edmundson and Co., for lamps, &c. , to March11th, 1843, · 3 12 9Kane, B., removing and cleaning carpet, July1st, 1843, . 0 7 6Ditto,Perry and Co., locks, to July 6th, 1842,Sharp and Co., repairs of clocks, & c. , March 7th, 1843,ditto, June 28th, 1843,100 18 102 40 15 6Surnam, George, repairs, to April 1st, 1843,Total Repairs of Furniture, &c. ,7 17 618 3 8773 1 1XXXV£ S. d. £ S. d.Brought forward, 773 1 1RENT, TAXES, INSURANCE, &c.Borough rate, made 30th Sept. 1842,Boyle and Co., allowance for poor rate paidby them on stable, to Nov. 1st, 1843,Grand Jury cess, half year, Easter, 1843,£ s.Insurance at Globe, Dec. 25th, 1844, 5 13Ditto, National, Dec. 26th, 1844, 5Ditto, ditto, Dec. 25th, 1844, 4• •d.613 62 61 10 0 136 33 15 0Ministers' money, to Sept. 29th, 1843,Parish cess, to Sept. 29th, 1843,Pipe water, to June 24th, 1843,Police tax, to March, 25th, 1843,Ditto, to Sept. 29th, 1843,•159 6215 51 17 61 7 82 3 91 17 64 1 3• 52 4 6Truell, R. H., half year's rent, toAug. 1st, 1843,Ditto, ditto, Feb. 1st, 1844, 52 4 6Wide street tax, Easter, 1843, •Total Rent, Taxes, Insurance,SALARIES, SERVANTS' WAGES, &c.Clibborn, Edward, for one year's salary asAssistant Librarian and Clerk, to March16th, 1844,Conroy, P., delivering notices, to June 8th,1843,Drummond, Rev. W. H., Librarian, year'ssalary, to 16th March, 1844,Hamilton, Wm. , wages and allowance as porter, to April29th, 1843,Ditto, to July 15th, 1843,Ditto, to Nov. 18th, 1843,Ditto, Christmas allowances, toDec. 25th, 1843,Ditto, wages and allowance, Jan.15th, 1844,4 12 26 11 811 17 0Ditto,104 9 01 17 6138 9 1120 0 001621 0 0• 2 2 05 5 4ditto, Feb. 19th, 1844, 3 5 10 33 14 0174 15 6911 10 2gxxxviBroughtforward,Kane, Bernard, extra evening porter, April 3rd, 1843,£ S. d. 16£ s. d. 12174 15 6 911 10 2£ S. d.• 1 8 01 0Feb. 29th,1 1 03 10 0Ditto, ditto, June 26th, 1843, 1Ditto, ditto,1844,Kane, Robert, M. D., Secretary of Council,year's salary, to March 16th, 1844,Lockett, J., for porter's clothes,to March 29th, 1843,Ditto,21 0 0• 3 19 8jacket, Aug. 10th, 0 18 0Mac Cullagh, J., Secretary of Academy,year's salary, to March 16th, 1844,Pim, J. jun. , Esq. , Treasurer, year's salary,to March, 16th, 1844,Singleton, J., for porter's hat, to April 26th,1843,Sinton, Thomas, Assistant Clerk,2 weeks, to March 25th, 1843, 2 10 0Ditto, 4 weeks, June 13th, 1843, 4 0 0Ditto, 3 weeks, Dec., 14th, 1843, 3 0 04 17 821 0 021 0 00 16 0Smith, John, assistant porterfrom March 17th to April20th, 1843,Ditto,Ditto,9th, 1844,•to June, 3rd, 1843,from July 29th to Jan.Ditto, from Jan. 29th to Feb.13th, 1844,9 10 0· 1 3 6• 1 4 61 0 00 10 03 18 0Wiseheart, J. , clerk at Meetings,to April 25th, 1843,Ditto, June 13th, 1843, .Ditto, from 14th Nov., 1843,to Jan. 8th, 1844,Ditto, from 22nd Jan. to Feb.12th, 1844,0 15 00 15 00 10 00502 50Total Salaries, Servants' Wages, &c.,262 12 21174 2 4Xxxvii£ S. d. £ S. d.Broughtforward, . 1174 2 414·THREE AND A HALF PER CENT. GOVERNMENTSTOCK PURCHASED.£ S. d.28 15 4 costTHREE PER CENT. CONSOLS PURCHASED.£ S. d.22 4 2 costCUNNINGHAM FUND.29 1 420 17 3West and Son, gold medal, to June 24th,1843,19 15 10THE TOTAL DISCHARGE,Balance in favour of the Public,1243 16 9210 5 6/The Charge as above, 0 1454 23STATE OF THE BALANCE.1843.31st March. In Bank of Ireland,£ S. d.209 6 3In Treasurer's hands, as per this Account, 0 19 3Balance as above, . £210 5 6The Treasurer reports, that there is to the credit of the Academy inthe Bank of Ireland, £1117 18. 10d. in Three per Cent. Consols, and£ 1643 19s. 6d. in Three and a half per Cent. Government Stock, thelatter known as the Cunningham Fund.31st March, 1844.(Signed),ROBERT BALL,Treasurer.

No. V.METEOROLOGICAL JOURNALCOMMENCING1ST JANUARY, 1843, and eNDING 31ST DECEMBER, 1843,BYGEORGE YEATES.THE accompanying paper is a Meteorological Journal,shewing the maximum and minimum points the Thermometer indicated, the Height of the Barometer, and the Amountof Rain.The first column gives the thermometric results; thesecond gives the barometric pressure, in inches and thousands of an inch; the third gives the amount of rain thathas fallen, in thousands of an inch. These observationshave been made as nearly as possible to 10 o'clock , A. M. , eachday throughout the past year. They are tabulated eachmonth, so as to shew the quantity of rain that has fallenduring that period. Twelve months are then made up,which shews the year's rain to be 23.440 inches.It may not be out of place to mention the description ofinstruments which were made use of on the occasion.The temperature was observed with a pair ofDr. Rutherford's self-registering thermometers. The barometer is similar to one first made by me for Dr. Apjohn, and under hisdirections; it is a very simple instrument, and extremely convenient for daily or rapid observations; there is no floatinggauge used , nor is it necessary to make any observation at thecistern; the fluctuations in the height here are nearly allavoided, by very much increasing the area of the cistern overhxlthat ofthe tube; in this instance it is as 1 to 500, the diameterof the tube being; it is graduated to the five-hundredth ofan inch, and reads as 1000. From this arrangement it is evident that any deviation produced in the surface of the cistern, from the rise or falling of the mercury in the tube,will be inappreciable , and does not amount to the errors ofobservation. The rain-gauge is also similar to one which Imade for Dr. Apjohn at the same period . In superficial areait measures 1000 inches; the rain is collected in a vesselwhich is graduated into cubic inches, consequently, whenone inch by measure is indicated by the graduations, it denotes that ofan inch of rain has fallen on the surfaceabove, and as the receiver is graduated into cubic inches allthe way, it gives at once the decimal, until you come to 1000cubic inches, which is equivalent to 1 inch of rain: this gaugeadmits ofthe most simple verification .xliJANUARY.Thermometer. Barometer. Rain. Wind.Max. Min.1 52° 33° 30.3502 40 34 30.1503 43 32 30.4 46 29 29.950 .151S. W.S. W. by S.N. W. by W.N. W.5 40 35 30.104 .080 N. W. by W.6 47 35 30.150 .030 W.7 48 3929.820 .009 W.8 44 32 29.260 .150 W.9 41 30 29.470 .050 S. W.10 44 32 29.100 .200 W. S. W.11 36 29 29.010 .075 W.12 36 29 29.016 1.050 W.13 38 31 28.100 .385 S. W.14 37 30 28.726 .080 N. W.15 35 26 28.950 N.E.16 37 26 29.850 .100 N. E.17 44 30 30.100 .030 N.W.18 48 42 30.314 W.19 49 42 30.40020 48 41 30.12021 46 38 29.500W.N. W.N.W.22 48 42 29.755 S. W.23 49 40 29.580 .004 S. W.24 49 44 29.610 .100 S.25 49 41 29.960 S. W.26 49 46 30.050 .035 S. W.27 52 46 29.864 W. by S.28 53 49 29.770 .025 W.29 52 44 29.850 ⚫035 W. by S.30 53 46 29.75031 48 48 29.550S. W.W.h 2xliiFEBRUARY.Thermometer. Barometer. Rain. Wind.Max. Min.1 49° 39 29.650 .0602 47 36 29.600 .095W. by S.W.3 41 35 29.300 .130 N. W.4 40 25 30,000 .003 N. by W.5 39 32 29.970 .008 N.W.6 40 33 30.150 • N. by W.7 43 33 30.200 .040 N. E.8 43 40 30.154 N. E.9 43 38 30.162 • N. E.10 42 35 30.146 .008 E. N. E.11 40 35 30.140 .006 E.12 40 34 30.170 .020 E.13 42 36 30.120 E.14 40 33 29.860 E. N. E.15 35 24 29.530 N. E.16 3217 3672521 29.28429.596N. E.N. N. E.18 39 30 29.636 E. by N.19 40 32 29.446 .020 E.20 40 34 29.224 .675 S. E.21 45 37 29.252 .145 S. E.22 47 39 29.348 .090 E.23 42 38 29.440 .210 E.24 45 40 29.610 .115 E. S. E.25 47 41 29.716 E. S. E.26 41 3529.700 E.27 39 35 28.371 E.28 41 35 29.420 .010 E.xliiiMARCH.Thermometer. Barometer. Rain. Wind.Max. Min.12343° 34° 29.350 .100 E.45 28 30.070 E.3 44 32 30.216 N. W.4 42 27 30.468 E. by N.5 39 33 29.970 .008 E.6 41 32 30.1507 42 33 30.2008 43 30 30.1509 43 39 30.16010 42 35 30.140 .06011 42 35 30.140 .04012 55 44 29.793 .025 S. E.13 54 38 29.650 N. W.14 47 39 29.518 .430 N. E.15 46 38 29.900 .070 E.16 48 39 29.826 E.17 57 40 29.620 N.E.18 56 41 29.892 E.19 54 42 29.846 .055 N. E.20 53 41 29.480 E.21 55 46 29.250 .085 E.22 59 46 29.200 .160 N. E.23 59 45 29.410 .380 E. by N.24 55 46 29.562 .100 S. E.25 52 45 29.850 .130 S. E.26 53 39 29.900 E.27 53 3829.750 E.28 53 37 29.32829 53 37 29.97630 52 39 29.47831 57 45 29.320xlivThermometer.APRIL.Barometer. Rain. Wind.Max. Min.1 59° 47° 29.250 , 015 S. E.232 58 46 29.350 .145 W.3 62 44 29.700 .0304 58 40 29.200 .130 W.5 58 47 29.300 .002 W. by S.6 64 47 29.600 .006 W.7 56 46 29.320 .465 S. W.8 61 42 29.500 .100 W.9 59 42 29.774 .090 W.10 46 32 30.040 .002 N. W.11 49 33 30.150 .090 N. W.12 50 33 30.050 N. W.13 54 32 30.076 N.14 53 40 29.950 .010 N. W.15 61 42 29.500 .100 N. E.16 54 44 29.950 N. W.17 67 40 30.050 N. E.18 62 44 30.050 E.19 64 48 29.900 E. by N.20 67 48 29.650 .020 E.21 65 46 29.750 .055 N. W.22 54 44 29.760 .025 W.23 55 40 30.010 .020 W.24 62 42 29.970 .350 N. E.25 53 46 29.620 .270 W. by N.26 53 35 29.600 .155 N. by W.27 58 36 29.850 .195 W. by S.28 58 41 29.650 .340 W. by S.29303355 42 29.720 .030 E. by N.63 43 30.020 E. by N.xlvMAY.Thermometer. Barometer. Rain. Wind.Max. Min.1 66° 43° 30.250 E. by N.2 67 47 30.250 N. E. 3 69 44 29.960 .020 E. 4 63 42 29.700 .060 W. 5 64 37 20.578 W. 6 60 38 29.600 N. W. 7 58 41 29.600 .016 E. 8 59 42 29.716 .002 N. E. 9 62 42 29.950 N. E.10 67 46 30.150 N. E.11 62 45 30.150 N. E.12 64 50 39.250 .140 S. by E. 13 62 50 29.826 .205 S.14 67 43 29.750 E. by N.15 64 49 29.500 E. by S.16 67 49 29.600 E. by S.17 54 47 29.800 .200 E. by N.18 60 44 30.050 .180 E.19 66 46 19.968 .080 N.20 64 45 29.620 .900 N. E.21 51 46 09.560 1.320 E. by N.22 55 47 29.700 .130 E.23 59 47 29.722 .026 E. by N.24 62 43 29.570 .120 E. by N.25 60 44 29.964 .645 E. N. E.26 635029.550 .205 S.27 60 48 29.530 W.28 60 48 29.750 .140 E. by N.29 62 45 30.050 .115 E. by N.30 63 46 30.016 W.31 62 50 29.800 .140W.xlviThermometer.JUNE.Barometer. Rain. Wind.Max. Min.1 2 365° 54° 29.468 .300 E.2 63 52 29.270 .268 S. W.62 50 29.370 .024 N. W.4 53 45 29.700 .240W.5 54 44 29.814 .590W.6 54 42 30.038 .035 N. W. 7 59 46 29.600 .015 W. 8 59 49 28.900 .125 W. 9 61 49 29.400 .080 N. W.10 62 48 29.94411 63 49 30.210 N. W.12 63 45 30.200 N. E.13 71 50 30.12814 70 49 30.050 .360 E. by N.15 65 53 30.050 .240 E.16 65 53 30.114 E.17 72 51 30.150 E.18 70 53 30.128 E.19 80 57 30.050 N. E.20 72 51 30.250 N. E.21 74 55 30.150W.22 65 55 30.150 N.23 69 49 30.150 E.24 74 52 30.130W.25 80 56 30.074 S. E.26 74 52 30.300 S. E.27 75 50 29.900 N. E.28 78 55 29.850 W.29 77 50 29.950 W.306965 52 29.950 S. W.xlviiThermometer.JULY.Barometer. Rain. Wind.Max. Min.1 68° 55° 30.000 S. W. 232 72 56 29.864 .080 W. by S. 3 73 57 29.850 E. 4 74 54 30.000 E. 5 74 53 29.700 .120 W. 6 63 52 29.720 .110 S. E. 7 70 53 29.760 .020 S. E. 8 70 54 29.050 .020 W. 9 63 51 30.150 N.10 71 54 30.250 N. E.11 69 49 30.564 N. W.1271 53 30.250 .120 W.13 67 56 30.200 .380 W.14 68 53 30.200 .105 W.15 65 58 30.140 W.16 70 53 30.250 W.17 71 58 30.250 .012 W.18 76 58. 29.950 .106 S. W.19 74 54 29.850 N.W.20 79 50 29.800 W.21 65 53 29.800 W.22 65 55 29.760 S. W.23 66 50 29.750 .020 N.W.24 69 48 30.160 N. W.25 69 54 30.250 S. W.26 72 61 30.250 .060 W. by S.27 72 54 30.150 .030 N. W.28 67 53 30.006 .115 W. by S.29 66 55 29.634 .315 W. by S.30 68 52 29.700 .050 N. W.31 68 52 30.000 .110 N. W.xlviiiThermometer.AUGUST.Barometer. Rain. Wind.Max. Min.721 66° 57° 29.900 S. W.2 70 56 29.500 .220 W.3 70 54 29.420 .170 S. W.4 68 53 29.560 .280 W.5 64 51 30.000 .080 W.6 75 54 30.100 .018 W.7 74 62 30.150 S. W.8 70 54 30.200 .110 S. by W.9 7350 30.25010 74 55 30.32411 77 55 30.350W.S. W.S. by E.12 73 55 30.270 E.13 73 55 30.250 S. E.14 73 54 30.050 E.15 67 57 30.000 .040 E.16 65 57 30.108 N. E.17 74 54 30.200 E.18 78 57 30.200 S. E.19 78 56 29.950 E. by S.20 78 57 29.908 .060 N. E.21 71 54 29.600 N. E.22 74 44 29.370 .195 S. W.23 73 45 29.750 S.24 71 56 29.700 .175 S. W.25 70 56 29.850 .090 S. W.26 71 58 29.750 S.27 71 54 30.660 S.28 72 56 29.700 .030 S. E.29 71 54 30.078 .073 N. W.30 7031 735950930.200 N. E.52 30.200 S. W.xlixThermometer.SEPTEMBER.Barometer. Rain. Wind.Max. Min.1 72° 48° 30.250 E. 232 7268 30.410 E.74 61 30.300 S. E.4 74 51 30.500 N. E.5 73 48 30.500 S.6 74 49 30.370 W.7 76 50 30.300 W.8 80 56 30.272 E.9 76 58 30.200 E.10 75 59 30.000 .010 E.11 67 53 29.950 .270 S. E.12 70 46 30.400 S. W.13 72 51 30.220 E.14 66 50 29.958 N. E.15 66 57 29.850 .065 W.16 65 57 30.000 W.17 64 57 30.150 E.18 68 55 30.100 N. E.19 70 55 30.300 .035 E.20 69 53 30.150 S.21 69 58 30.300 N. E.22 67 56 30.52223******64 45 30.624W. by S.N.24 61 53 30.600 W.25 62 48 30.450 N. W.26 60 46 30.300 N. W.27282930ི མ་ སྐྱ57 41 29.900 • N. W.54 35 30.000 .007 W.54 45 30.100 W.62 48 29.950 .250 W.1Thermometer.OCTOBER.Barometer. Rain. Wind.Max. Min.12363° 56° 30.050 W.2 64 51 30.150 .240 W.3 61 49 30.100 .004 W.4 62 53 30.200 .010 W.5 69 52 29.950 W. by S.6 68 57 29.500 .060 W. by S.7 70 57 29.500 .0258 64 61 29.850 .510N. W.N.9 66 44 29.520 .145 W.10 58 40 29.870 .025 S.W.11 56 46 29.760 .330 W.12 54 38 29.410 .250 N. W.13 50 3729.690 .040 S. W.14 50 32 29.810 .008 N. W.15 49 33 29.870 W. by N.16 49 33 29.750 · N. W.17 46 30 29.664 .005 N. W.18 46 35 29.618 .140 W.19 45 30 30.122 W. by N. 20 66 30 30.412 W.21 52 40 30.050 .130 W.22 55 44 29.810 .025 S. W.23 58 46 30.050 W.24 55 48 29.600 .060 S. W.25 54 37 29.430 .600 W.26 47 34 29.610 W. by N.27 47 31 29.400 E.28 46 31 29.460 .420 W.29 463129.500 W. by S.30 44 32 29.400 .075 W.31 44 30 29.550 .200 W.liThermometer.NOVEMBER.Barometer. Rain. Wind.Max . Min.1 45° 33° 29.650 .025 W. 2348 31 29.800 S. E.52 42 29.400 .005 E.4 55 43 29.500 .035 S. W.5 54 35 30.030 .150 W.6 57 43 29.820 .090 W. by S.7 55 45 29.700 .095 W.8 50 37 29.716 N. W.9 43 32 29.916 .004 N. W.10 49 41 29.400 .030 W.11 52 44 30.050 .007 N. W.12 49 44 30.120 S. W.13 48 37 30.250 .008 S. W.14 45 35 30.320 S. S. W.15 44 31 30.150 .005 S. W.16 44 35 30.150 .170 S. W.17 50 40 29.600 .009 W. S. W.18 48 37 29.330 .005 W. S. W.19 44 34 29.460 .118 S. W.20 48 34 29.580 .204 S.W.21 50 42 29.350 .446 S. byW.22 54 40 29.350 .634 W. by N.23 40 38 29.49024 46 34 29.470W.W. by N.25 44 32 29.450 .130 E. by N.26 53 42 29.300 .185 S. W. 222227 54 48 29.450 .070 S. W.28 51 44 30.100 S. W.29 54 39 30.450 W. by S.30 52 39 30.100 W.liiDECEMBER.Thermometer. Barometer. Rain. Wind.Max. Min.1251 ° 39° 30.120 W.2 50 39 30.170 .004 W.3 51 44 30.350 .004 S. W.4 52 43 30.270 .003 S. W.5 52 45 29.900 W. by S.6 51 41 30.350 .040 W. by S.7 53 43 30.100 .012 W. by S.8 53 44 30.300 .012 W.9 49 45 30.296 W.10 52 46 30.150 W.11 4936 30.100 .002 S. E.12 50 45 30.350 .050 E. by S.13 50 43 30.320 .003 W. by S.14 51 45 30.430 S. W.15 57 47 30.350 S. by W.16 50 48 30.450 W. by S.17 54 45 30.460 .004 S. W.18 50 43 30.450 W. by S.19 49 44 30.300 S. W.20 52 46 30.150 S. W.21 53 41 30.300 E. by N.22 55 42 30.300 E. by N.23 54 45 30.250 S. by W.24 57 53 30.400 .004 S. W.25 56 48 30.310 E.26 51 41 30.350 N. W.27 50 42 30.424 W. S. W.28 51 47 30.460 S. E.29 50 46 30.350 W. S. W.30 46 44 30.150 W. S. W.31 50 43 30.100 W. S. W.liiiJanuary,February,March, .April,May,June,July,••· ·•August,September,October,November,December,GENERAL RESULTS.AMOUNT OF RAIN. MEAN TEMP.Inches.• 2.589 • 420· 1.635 34• · 1.643 382.643 411· 4.644 611• 2.778 6711.773 68• 1.541 70.637 67• 1.912 56· · 1.998 49.138 5123.440BAROMETER.Greatest pressure, August 27,Lowest point, January 13, ·THERMOMETER.Maximum, September 8, . •Minimum, February 16, .2, Grafton-street.80°• 2130.66028.100

THEROYAL IRISH ACADEMY,MARCH 16, 1843.Patroness:HER MOST SACRED MAJESTYTHE QUEEN.Visitor:HIS EXCELLENCY THE LORD LIEUTENANT OFIRELAND.President:SIR WILLIAM ROWAN HAMILTON, LL. D.Vice-Presidents.REV. HUMPHREY LLOYD, D. D.REV. JAMES HENTHORN TODD, D. D.REV. JOSEPH HENDERSON SINGER, D. D.JAMES APJOHN, M. D.COUNCIL.Committee of Science.REV. FRANC SADLEIR, D. D.,PROVOST.REV. HUMPHREY LLOYD, D. D.JAMES APJOHN, M. D.aJAMES MAC CULLAGH, LL. D.REV. WM. D. SADLEIR, A. M.ROBERT BALL, ESQ.ROBERT KANE, M. D.iiCommittee of Polite Literature.HIS GRACE THE ARCHBISHOP OFDUBLIN.REV JOSEPH H. SINGER, D. D.SAMUEL LITTON, M. D.REV. WM. H. DRUMMOND, D. D.REV. CHAS. R.ELRINGTON, D.D.REV. CHARLES W. WALL, D. D.JOHN ANSTER, LL. D.Committee of Antiquities.GEORGE PETRIE, ESQ., R. H. A.REV. JAMES H. TODD, D. D.HENRY J. MONCK MASON, LL.D.SAMUEL FERGUSON, ESQ.JOSEPH H. SMITH, ESQ.JAMES PIM, JUN. , ESQ.CAPTAIN LARCOM, R. E.Officers.Treasurer. -JAMES PIM, JUN. , ESQ.Secretary ofthe Academy. -JAMES MAC CULLAGH, LL. D.Secretary ofCouncil. -ROBERT KANE, M. D.Secretary ofForeign Correspondence. -REV. HUMPHREY LLOYD, D.D.Librarian.- REV. WILLIAM H. DRUMMOND, D. D.Clerk and Assistant Librarian. -EDWARD CLIBBORN.NOTE. The Members ofthe Academy are particularly requestedto communicate to the Assistant Librarian, any corrections in thislist which they may consider necessary.MEMBERS.The Names of Life Members are marked with an Asterisk.

• Adare, Edwin Viscount, M. P. F. R. S. F. R. A. S. Dunraven Castle, Glamorganshire, and 76, Eaton- square,

London.

• Andrews, Thomas, M. D. 65, Chester-square, Belfast.
• Armstrong, Andrew, Esq. , A. M. 17 , College.
• Arthur, Thomas, Esq.

Ashburner, John, M. D. 55, Wimpole-street, London.Abell, Abraham Esq. Cork.Adams, Robert, Esq. V. P. Royal College of Surgeons.11, Great Denmark- street.Allman, George James, Esq. Grattan-street.Andrews, William, Esq., Sec. Natural History Society.18, Leinster-street.Anster, John, LL. D. 5, Lower Gloucester-street.Apjohn, James, M. D. Professor of Chemistry, Royal College of Surgeons. V. P. Geological Society of Dublin.-VICE-PRESIDENT. 28, Lower Baggot-street.Armstrong, William, Esq. 5, Lower Dominick- street.

• Bailie, Rev. James Kennedy, D.D. Ardtrea, Stewarts-

town.Bald, William, Esq. , F. R. S. E.

• Ball, Robert, Esq. Sec. Royal Zoological Society of

Ireland. Local Sec. Botanical Society of Edinburgh.3, Granby-row.

• Bateson, Sir Robert, Bart. , M. P. Belvoir Park, Belfast.
• Bateson, Robert, Esq., D. L. Belvoir Park, Belfast.

biv

• Beaufort, Francis, Esq. , F. R. S. F. G. S. F. R. A. S., &c .

Captain R. N. Admiralty, London.

• Benson, Charles, Esq. , M. D. Professor of Physic, Royal

College of Surgeons. 34, York-street.

Bergin, Thomas F., Esq. , 5, Westland Row.

• Blacker, Stewart, Esq. 20, Gardiner's-place.
• Blood, Bindon, Esq. Edinburgh.

Bolton, William Edward, Esq.

• Botfield, Beriah, Esq. , M. P.
• Boyton, Rev. Charles, D. D.

5, Nelson-street.London.Tullyagnish, Letterkenny.

• Boyle, Alexander, Esq. Killiney, and 35 College-green.
• Bruce, Haliday, Esq. 37, Dame-street.

Ball , John, Esq. 85, Stephen's-green, South.Banks, John T., M. D. 8, Lower Merrion-street.Barker, Francis, M. D. Professor of Chemistry, University of Dublin. 22, Lower Baggot- street.Barker, William, M. B. 8, Hatch-street.Barrington, Matthew, Esq. 50, Stephen's-green, East.Beatty, Thomas E., M. D. 17 , Merrion-square, North.Beauchamp, Henry C. , M. D. 114, Lower Baggot-st.Betham, Sir William, Knt. Ulster King of Arms. F.S. A.,F. R. A. S. , V. P. Royal Dublin Society. StradbrookHouse, Black Rock.Blacker, William, Esq. Armagh.Bolton, Chichester, Esq. 1 , Upper Merrion-street.Booth, Rev. James, A.M. Bristol.Borough, Sir Edward, Bart. 18, Leinster-street.Brady, Right Hon. Maziere, A. M. Lord Chief Baron.61, Harcourt-street.Burrowes, John, Esq. 1 , Herbert-street.Burton, Frederick W., Esq. , R.H.A. 65, Harcourt-street.Butcher, Rev. Samuel, Fellow of Trinity College. College.Butler, Rev. Richard. Trim.

• Callwell, Robert, Esq. 22, Herbert-place.

V

• Campbell, William W., M. D. Port Stewart, Coleraine.

Carmichael, Andrew, Esq. 24, Rutland-square, North.

• Carmichael, Richard, Esq. 24, Rutland-square, North.

Carne, Joseph, Esq. , F. R. S. F. G. S. Penzance.

• Carson, Rev. Joseph, A. M., Fellow of Trinity College.

College.

• Caulfield, Hon. Henry.

Hockley, Armagh.Chamley, George, Esq. 6, Belvidere Place.

• Charlemont, Francis William Earl of. Charlemont House.
• Chetwode, Edward Wilmot, Esq. Woodbrook, Portarlington .
• Clare, John Earl of. Mount Shannon, Killaloe.
• Clarke, Thomas, Esq. 123, Lower Baggot-street.

Clendinning, Alexander, Esq. Westport.

• Colby, Lieut. - Colonel Thomas, Royal Engineers, LL. D.

F. R. S. L. and E. F. G. S. F. R. A. S. &c. OrdnanceSurvey Office, Phoenix Park, and Tower, London.

• Cole, Owen Blayney, Esq. Merrion-square, North.
• Colvill, William C., Esq. 6, Bachelor's Walk.
• Conroy, Edward, Esq. Kensington, London.
• Corballis, John R., Esq. 15, Baggot-street.
• Cork, Cloyne, and Ross, Right Rev. Samuel Kyle, D. D.,

Lord Bishop of Cork.

• Coulter, Thomas, M. D. College.
• Courtney, Henry, Esq. 24, Fitzwilliam-place.
• Croker, Thomas Crofton, Esq. , F. S. A. London.
• Croker, Charles P., M. D. 7, Merrion-square, West.
• Cubitt, William, Esq. , F. R. S. F. R. A. S.

George-street, Westminster, London.8, Great

• Cusack, James W., Esq. , M. D., Sec. Royal College of

Surgeons. 3, Kildare-street.Cane, Arthur B. Esq. 60, Dawson- street.Cane, Edward, Esq. 60, Dawson-street.Carr, George, Esq. 18, Mountjoy-square, South.Carter, Samson, Esq. Kilkenny.Cash, George, Esq. Broomfield, Malahide.b 2viCather, Thomas, Esq. 20, Blessington-street.Chatto, Rev. Robert, A. M. Whickham Cottage, Gateshead.Chapman, B. I., Esq. Killua Castle, Athboy.Churchill, Fleetwood, M. D. 136 , Stephen's-green, West.Clarke, Edward S., Esq. 18, York-street.Conway, Frederick W., Esq. Rathmines, and 11 , Trinitystreet.Cooper, Edward J., Esq. M. P. Markree Castle, Colooney.Cooper, Jonathan Sisson, Esq. 15, Upper Merrion-street.Courtenay, Rev. Reginald.Crampton, Hon. Justice, LL. D. 50, Baggot-street.Crampton, Sir Philip, Bart. President, Royal ZoologicalSociety of Ireland. 3, Merrion-square, North.Crawford, Francis, Esq. 51 , Harcourt- street.Culley, Robert, Esq. Kingstown.

• Davis, Charles, M. D.
• D'Olier, Isaac M., Esq.

33, York-street.Booterstown.

• Drummond, Rev. William Hamilton, D. D.-LIBRARIAN.

28, Lower Gardiner-street.D'Alton, John, Esq. 48, Summer-hill.Darley, Frederick, Esq. 25, Lower Fitzwilliam-street.Davidson, John, Jun. , Esq. Armagh.Davy, Edmund, Esq. , F. R. S. Professor of Chemistry,Royal Dublin Society.Dickinson, Robert, Esq. 79 , Lower Gardiner-street.Disney, Ven. Brabazon William, Archdeacon of Raphoe.16, Fitzwilliam-square, South.Dixon, Rev. Robert Vickers, A. M. Fellow of TrinityCollege. 10, College.Downes, George, Esq. , A. M. Black Rock.Doyne, Charles, Esq. Newtown Park, Black Rock.Drennan, William, Esq. 4, Eccles-street.Drury, William V. M. D. Edinburgh.viiDublin, Most Rev. Richard Whately, D. D. Archbishopof. V. P. Royal Zoological Society of Ireland. Palace, Stephen's-green, North.Dunlop, Durham, Esq. 6, Lower Abbey-street.

• Elrington, Rev. Charles Richard, D. D., Regius Professor

of Divinity, University of Dublin. Trinity College.Edington, William, Esq. Treasurer of the Geological Society of Dublin. 18 , Leinster-street.

Fitzgerald and Vesci, Right Hon. William Vesey Lord,D. C. L. F. R. S. Merrion-square, North.Fitzgerald, Rev. Michael.

• Fitzgerald, Right Hon. Maurice, Knight of Kerry.
• Fitz Wygram, Sir Robert, Bart. Connaught-place, London.
• Fortescue, Thomas, Esq. , M. P. Ravensdale-park, Flurry

Bridge.

• Foot, Simon, Esq. Hollypark, county ofDublin.
• Frazer, R. Murray, Esq.

Fitzgibbon, Gerald, Esq. 29, Gloucester-street, Upper.Farran, William, Esq. 76, Abbey-street.Ferguson, Hugh, M. D. 62, Sackville-street.Ferguson, Samuel, Esq. 56, Lower Dominick-street.Ferrier, Alexander, Jun. , Esq. , A.M. Rathmines.Finlay, John, LL. D. 31 , North Cumberland-street.Frazer, George Alexander, Esq. Lieutenant R. N.

• Goff, Rev. Thomas. Black Rock.

Gough, George Stephens, Esq. , A. B.

• Graves, Rev. Charles, A. M. Fellow of Trinity College.

2, College.

• Grierson, George A., Esq. Queen's Printing Office, 19 ,

Essex-street, West.

• Griffith, Richard, Esq. , F. R. S. E. F. G.S. V.P. Geological Society of Dublin. 2, Fitzwilliam-place.

viiiGayer, Arthur E., LL. D. 47, Upper Mount- street.Gore, William R., M. D. Limerick.Graves, Robert J., M. D. King's Professor of the Institutes of Medicine. 4, Merrion-square, South.Gregory, William, M. D. F. R. S. E. Aberdeen.Gregory, Very Rev. James, A. M. Dean of Kildare. 17 ,Fitzwilliam-street, Upper.Grimshaw, Wrigley, M. D. 11 , Molesworth-street.Grubb, Thomas, Esq. 1 , Upper Charlemont-street.

• Hamilton, Sir William Rowan, Knt., LL. D. F. R. A. S.

Astronomer Royal of Ireland, and Andrews' Professorof Astronomy inthe University of Dublin. - PRESIDEnt.Observatory, Dunsink.

• Hanna, Samuel, M. D., A. M. 18, Granby-row.
• Hardiman, James, Esq. Galway.
• Harrison, Robert, M. D. Professor of Anatomy and

Surgery, University of Dublin. 1 , Hume-street.

Hart, Andrew Searle, Esq. , LL. D. Fellow of Trinity College, College.Haygarth, William, Esq.

• Hill, Edward, Colonel.
• Hill, Lord George A. Updown House, Sandwich.

Belfast.31 , York-street.

• Hincks, Rev. Thomas, LL. D.
• Houston, John, Esq., M. B.
• Hudson, Henry, Esq. , M. B. 24, Stephen's-green, North.
• Hume, Arthur, Esq. 63, Dawson-street.
• Hutton, Robert, Esq. , F. G. S. Putney Park, Surrey, and

15, Manchester Buildings, London.

• Hutton, Thomas, Esq. , F. G. S. V. P. Geological Society

of Dublin, Treasurer of the Royal Zoological Societyof Ireland. Elm-Park, and 116, Summer-hill.

• Hutton, Henry, Esq. 18, Gardiner's-place.

Hamilton, Charles William, Esq. , F. G. S. Sec. GeologicalSociety of Dublin. 13 , Mountjoy-square, East.ixHamilton, John, Esq. 13, Nassau-street.Hardy, Simeon, Esq. 15, Fitzwilliam-square, North.Hardy, Philip Dixon, Esq. Greenfield Lodge, Stillorgan,and 3, Cecilia-street.Hart, John, Esq. , M. D. V. P. Royal Zoological Societyof Ireland. 3, Ely-place.Hemans, G. W., Esq. , C. E. 22, Marlborough-st.Hill, William, Esq. Donnybrook, Doneraile, Cork.Hodder, Thomas, Esq. , R. M. Kildare-street.Hogan, William, Esq. A.M. Fitzwilliam-place.Homan, Rev. John, A. M. Seapoint House, BlackRock.Horgan, Rev. Matthew. Blarney, Cork.Hudson, William E. Esq. 39, Upper Fitzwilliam-street.Hughes, William John, Esq. 49, Westland-row.Hutton, Edward, Esq., M. D. 29, Gardiner's-place.

• Jessop, Frederick Thomas, Esq . Doory Hall, Longford.
• Johnson, Hon. Justice, LL. D. 45, Harcourt-street.

Jones, Lieut. -Col. Harry D., M. I. C. E.Donnybrook, and Custom-house.Flora Villa,Jacob, Arthur, M. D. V. P. Geological Society of Dublin.Professor of Anatomy, Royal College of Surgeons .23, Ely-place.James, Sir John Kingston, Bart. 9, Cavendish-row .Jellett, J. H., Esq. , Fellow of Trinity College. College.Jennings, Francis M., Esq. Cork.Jones, Robert, Esq. Fortland, Dromore, West.Joy, Henry Holmes, Esq. , A. M. Treasurer of the Geological Society of Dublin. 17, Mountjoy-square,East.Kelly, Dennis Henry, Esq. Castle Kelly, Mount Talbot,Roscommon.

• Kiernan, George, Esq. London.

X

• Knox, Rev. Thomas.
• Knox, George J., Esq.
• Knox, Rev. H. Barry.

River Glebe, Toomavara, Nenagh.1 , Maddox-street, London.Deanery House, Hadleigh, Suffolk.

• Kyle, William Cotter, LL. D. 8, Clare-street.

Kane, Robert, M. D. Professor of Natural Philosophy,Royal Dublin Society. - SECRETARY OF COUNCIL.Black Rock.Kelly, Thomas F. , LL. D.Kennedy, George A., M. D.88, Lower Mount-street.President of the King andQueen's College of Physicians. 25, Talbot-street.Kent, William T., Esq. 37, College-green.King, Hon. James. Mitchelstown Castle, Mitchelstown.Kingsley, Jeffries, Esq. 11 , Westmoreland-street.Knox, Rev. Robert. See House, Limerick.

• Larcom, Thomas A., Captain , R. E.

Office, Phoenix Park.Ordnance Survey

• Lardner, Rev. Dionysius, LL. D. F. R. S. L. and E.,

F. R. A. S.

• La Touche, David Charles, Esq. , Bank, Castle-street.
• La Touche, William Digges, Esq. 3, Fitzwilliam-square,

East.

• Leader, Nicholas P., Esq. Dromagh Castle, Castle Mills,

Cork.Leitrim, Rt. Hon. Nathaniel Earl of. Killadoon, Celbridge.Lenigan, James, Esq. Castle Fogarty, Thurles.

• Litton, Samuel, M. D.

Professor of Botany, Royal DublinSociety. 10 , Lower Gloucester-street.Lloyd, Rev. Humphrey, D. D., F. R.S., Fellow of TrinityCollege, Prof. Nat. Phil.-Vice-President and SeCRETARY OF FOREIGN CORRESPONDENCE . 35, College.Luby, Rev. Thomas, D. D., Fellow of Trinity College.15, College.La Touche, George Digges, Esq. 91, Baggot-street.Law, Robert, M.D. 34, Granby-row,xiLee, Rev. William, A. M., Fellow of Trinity College.College.Levinge, Godfrey, Esq. Cullion, Mullingar.Lindsay, Henry, Esq. Armagh.Lloyd, William T., Esq. 10 ,Logan, Rev. H. F. C., D. D.Longfield, Mountifort, LL. D.English Law, University ofsquare, West.Crescent, Upper Mount-st.Oscott, Birmingham.Professor of Feudal andDublin. 6, FitzwilliamLongfield, William, Esq. 19, Harcourt-street.Lyle, Acheson, Esq. , A. M. Treasurer of the GeologicalSociety of Dublin. 17 , Gardiner's-place.Lynch, J. F. , Esq. 19 , Belvidere-place.

• Mac Carthy, Viscount de. Toulouse.
• Mac Cullagh, James, LL. D., F. R. S. , Fellow of Trinity

College, Prof. Math. -SECRETARY OF THE ACADEMY.College.

• Mac Donnell, John, M. D. 4, Gardiner's-row.
• Mac Donnell, Rev. Richard, D. D.

Trinity College. College.Mackay, James Townsend, Esq.race.M'Kay, Rev. Maurice, LL. D.Senior Fellow of5, Haddington TerDrogheda.M'Neece, Rev. Thomas, A. M., Fellow of Trinity College.College.

• Macniell, John, Esq. , F. R. S. F. R. A. S. , Professor ofthe

Practice of Engineering, University of Dublin . 9 ,Whitehall-place, London.

• Magrath, Sir George, K.H. M.D. F.R.S. F.L.S. F.G.S.

Plymouth.Mahony, Pierce, Esq. 23, William-street.

• Marsh, Sir Henry, Bart. M. D. V. P. Royal Zoological

Society of Ireland . 24, Molesworth-street.

• Martin, Rev. John C. , D. D. Killesandra.

xii

• Mason, Henry Joseph Monck, LL. D.

Henrietta-street.

• Mayne, Rev. Charles, Killaloe.
• Miller, Rev. George, D. D. Armagh.

Queen's Inns,Mac Cullagh, W. Torrens, Esq. 8, Upper Gloucester-st.Mac Dowell, George, Esq. Fellow of Trinity College.26, College.Magee, James, Esq. 39, Leeson-street.Mallet, Robert, Esq. 8, Ryder's Row, Capel-street.M'Mullen, John, Esq. William-street.Marks, Rev. Edward, D. D. Molyneux Asylum, Peterstreet.Mollan, John, M. D. 32, Gloucester-street.Monsell, William, Esq. Tervoe, Limerick.Montgomery, William F., M. D. 18, Molesworth- street.Morrison, Sir Richard. 49, Upper Mount-street.Mulvany, W. T., Esq. Dovehouse, Black Rock.Murphy, Patrick M., Esq. 33, Lower Baggot-street.Murray, William, Esq. , 72, Lower Gardiner-street.

• Napier, Joseph, Esq. 17, Mountjoy-square, South.
• Nicholson, John A., Esq. , M. B. Clontarf.

Nelson, Joseph, Esq. 7, Gardiner's-place.Newenham, Thomas, Esq.wood.Sandford Cottage, Cullens-

• Odell, Edward, Esq. Carriglea, Dungarvan.
• O'Ferrall, Joseph M., Esq. 38, Rutland-square, West.
• O'Reilly, Miles John, Esq.

Orpen, Thomas Herbert, M. D. 13, South Frederick-street.

• Orpen, John Herbert, LL. D. 13, South Frederick-street.

Owen, John Underhill, M. D.O'Brien, Sir Lucius, Bart. Dromoland, Newmarket-onFergus, Clare.O'Conor, Matthew, Esq. 5, Mountjoy-square, South.xiiiO'Grady, Michael Martin, M. D. La Mancha, Swords.O'Grady, James, Esq. , LL. D. 25, Denzille-street.Ogilby, Robert L., Esq. Dungiven.O'Halloran, Major- General Sir Joseph, K. C. B. 51 , Upper Seymour-street, Portman-square, London.Orpen, Charles Edward Herbert, M. D. Woodside, Liverpool.Osborne, Jonathan, M. D. 26, Harcourt-street.Otway, Cæsar G., Esq., A. B.Owen, Jacob, Esq. 2, Mountjoy- square, West.

• Parker, Alexander, Esq. Rathmines.

Petrie, George, Esq., R.

• Phibbs, William, Esq.
• Pim, George, Esq.

Island.H. A. 21 , Great Charles-street .Seafield, Sligo.Brennanstown, and 15, Usher's

• Porter, Rev. Thomas H., D. D. Ballymully Glebe, Dungannon.
• Portlock, Joseph Ellison, Esq. , R. E. F. R. S. F. G. S.

V. P. Geological Society of Dublin. V.P. Royal Zoological Society of Ireland . 50, Upper Sackville-street.Prior, Rev. Thomas, D. D. Senior Fellow of TrinityCollege. College.

• Prior, James, Esq. 14, Oxford Terrace, Hyde Park,

London.Pakenham, Hon. and Very Rev. Henry, Dean of St. Patrick's. 19 , Merrion-square, N., and Deanery-house.Palmer, Abraham, Esq. , M.B. 38, York-street.Patten, James, A. M., M. D. Belfast.Pim, James, Jun. , Esq.-TREASURER. Monkstown Castle,and 35, College-green.Ponsonby, The Hon. Frederick. 36 , Kildare-street.

• Radcliffe, Right Hon. John, LL. D. Judge of the Court

of Prerogative. 14, Hume-street.xiv

• Renny, H. L., Esq. Assistant Professor of the Practice

of Engineering, University of Dublin. Sec. Geological Society of Dublin. Royal Hospital.

• Rhodes, Thomas, Esq. Shannon Commission.

Roberts, Rev. John Cramer.

• Robinson, Rev. Thomas Romney, D. D. Observatory,

Armagh.

• Rosse, Right Hon. The Earl of. Birr Castle, Parsonstown.
• Rowan, Rev. Arthur B., A. M. Bellmount, Tralee.

Richards, Goddard, Esq. Ardamine, Co. Wexford.Reid, Rev. James. Clontarf.Reid, Robert, M. D. 16 , Belvidere-place.Roberts, William, Esq. , Fellow of Trinity College. College.

• Sadleir, Rev. Franc, D. D. Provost of Trinity College.-

Provost's House, College.

• Sadleir, Rev. William Digby, A. M. Fellow of Trinity

College. 4, College.

• Singer, Rev. Joseph Henderson, D. D., Senior Fellow of

Trinity College. -VICE- PRESIDENT. 4, College.

• Smith, Rev. George Sidney, D. D. Professor of Biblical

Greek, University of Dublin. 9, College.

• Stewart, Hon. Alexander. 5, Foley-place, London.
• Stokes, Whitley, M. D., Lecturer in Natural History, University of Dublin. 16, Harcourt-street.

Strong, Rev. Charles, A. M. Cavendish-row.Salmon, George, Esq. , Fellow of Trinity College. 24 ,College.Sirr, Rev. Joseph D'Arcy. Claremorris, Mayo.Smith, J. Huband, Esq. A.M. 1 , Holles-street.Smith, Robert William, Esq. 62, Eccles-street.Smith, Aquilla, M. D. 120, Lower Baggot- street.Sproule, Oliver, Esq. 39, Blessington-street.Stack, Rev. Thomas, Fellow of Trinity College. College.XVStaples, Sir Thomas, Bart.Merrion-square, E.Sissane, Co. Tyrone, and 11 ,Sterling, A. C. ( Captain, 73rd Regt) . Royal Barracks.Stokes, William, M. D. Regius Professor of Medicine.5, Merrion-square, North.

• Thompson, David P. Esq. Burnham House, Dingle.

Thompson, James, Esq. 46, Charlemont-place, Glasgow.

• Todd, Rev. James Henthorn, D. D. , Fellow of Trinity College.—VICE- PRESIDENT. 35, College.
• Traill, Rev. Robert, D. D. Westskull Rectory, Skibbereen.
• Trimlestown, John Thomas Lord. Trimlestown Castle.
• Turner, William, Esq.

Tighe, Robert, Esq. 14, Fitzwilliam-square, North.Toleken, John, Esq., M. D., Fellow of Trinity College.College.

• Vandeleur, Crofton Moore, Esq. Kilrush, county ofClare.

Vignoles, Rev. Charles, D. D. Dublin Castle.Vignoles, Charles, Esq., F. R. A. S.London.

• Wall, Rev. Charles William, D. D.

Trinity College. 20, College.Trafalgar-square,Senior Fellow of

• Wall, Rev. Richard, D. D. 6, Hume-street.
• Walshe, Francis Weldon, Esq. Upper Glentworth-street,

Limerick.

• Weaver, Thomas, Esq., F. R. S. F. G. S. London.
• Webb, William, Esq. Mount-street, Lower.
• Weld, Isaac, Esq., F. G. S. Sec. Royal Dublin Society,

Ravenswell, Bray.

• Westenra, Hon. H. R.
• Williams, Thomas, Esq. Drumcondra Castle, and 38,

Dame-street.xvi

• Williams, Richard Palmer, Esq. Drumcondra Castle, and

38, Dame-street.

• Wilson, Rev. James, D. D. 10, Harrington- street.
• Wilson, Thomas, Esq. Westbury, and 15, Upper Templestreet.

Walker, Roger Chambers, Esq. 2, Granby-row.Wallace, Robert Alexander, Esq . , A. M. 12, GreatGeorges-street, North.Wallace, William Baily, Esq. 63, Blessington-street.Warburton, Elliott, Esq. Kildare-street.Watson, Henry, Esq. Limerick.Webber, Charles T. , Esq. 22, Upper Gloucester- street.West, Rev. John, D. D. 25, Herbert-place.Whiteside, James, Esq., A. M. 2, Mountjoy-square, N.Wilde, William R., Esq. 15, Westland-row.Wilkinson, George, Esq. 4, North Frederick-street.Wills, Rev. James. Suirville, Waterford.Wynne, John, Esq. Hazlewood, Co. Sligo.Young, John T., Esq. Philpotstown, Navan.xviiHONORARY MEMBERS.Abrahamson, General T. Copenhagen.Airy, George Biddell, Esq. M. A. F. R. S. V. P. R.A. S.Astronomer Royal. Observatory, Greenwich.Amyot, Thomas, Esq. F. R. S. Treas. S. A.street, Westminster, London.13, JamesBabbage, Charles, Esq. M. A. F. R. S. L. & E. F. R. A. S.&c. 1 , Dorset- street, Manchester-square, London.Baily, Francis, Esq. D.C.L. V.P.R.S. Pres. R.A.S. F.L.S.F.G.S. &c. 37, Tavistock-place, Russell-square, London.Berzelius, Jens Jacob.Brewer, James N. , Esq.Stockholm.Brewster, Sir David, K. H. LL. D. F. R. S. L. & E. F. G. S.F. R. A. S. &c. St. Leonard's College, St. Andrew's.Brisbane, Lieut. - General Sir Thomas Mac Dougal, K. C. B.D.C.L. F.R.S. Pres. R.S.E. F.R.A.S. &c .town, Kelso.Brongniart, Alexandre. Paris.MakersBrown, Robert, Esq. D. C. L. F. R. S. L. & E. V. P. L. S.&c. 17 , Dean-street, Soho-square, London.Carlisle, Nicholas, Esq. K.H. D.C.L. F.R.S. Sec. S.A. &c.Somerset House, Strand, London.Clanny, W. R. M.D. F. S. A. London.Colby, Colonel Thomas, Royal Engineers, LL. D. F.R.S.L.& E. F. G. S. F. R. A. S. &c .Tower, London.Combe, George, Esq. Edinburgh.Ordnance Map Office,Cooper, Charles Purton, Esq. LL. D. F. R. S. F. S. A.Lincoln's Inn, London.xviiiDalton, John, Esq. D. C. L. F. R. S. &c. Manchester.Daubeny, Charles Giles Bridle, M.D. F.R.S. F.L.S. F.G.S.Professor of Chemistry and of Botany, Oxford. Oxford.Donop, Baron. Saxe Meiningin.Dumas, Jean Baptiste. Paris.Dupin, Charles, Baron. Paris.Edgeworth, Miss Maria, Edgeworthstown.Ellis, Sir Henry, K.H. F.R. S. Sec. S. A. Librarian of theBritish Museum.Forshall, Rev. Josiah, M. A. F. R. S. F. S. A. British Museum .Gauss, Karl Friedrich. Gottingen.Gräberg, Count. Florence.Graham, Robert, M.D. F.R. S. E. Professor of Botany,Edinburgh. Edinburgh.Greville, R. K. LL.D.Halliwell, James Orchard, Esq. , F. R. S. F. S. A. Selip, Oxfordshire.Hamilton, Francis, M. D. F. R.A. S.Harcourt, Rev. William V. Vernon, M.A. F. R. S. F. G. S.York.Haughton, Sir Graves Chamney. K.H. M. A. F. R. S. &c .14, Grafton-street, Bond- street, London.Herschel, Sir John Frederick William, Bart. D.C.L. F.R.S.L.& E. F. G. S. F. R. A. S., &c. Collingwood, near Hawkhurst, Kent.Herschel, Miss Caroline.Hobhouse, Right Hon. Henry.Hooker, Sir William Jackson, K. H. LL. D. F. R. S. F. S. A.F.L.S. F.G. S. &c. Kew.Hope, Thomas Charles, M.D. F.R.S. V.P.R.S.E. &c.Edinburgh.Jameson, Robert, Esq. F. R. S.L. & E. F. L. S. F.G.S. &c .Regius Professor of Natural History, Edinburgh. Edinburgh.xixKönig, Charles, Esq. K. H. F. R.S. F. L. S. &c . BritishMuseum.Lagasca, Doctor. Madrid.Liebig, Justus. Giessen.McLaughlin, David, M. D. Paris.Macedo, Sinor, Jacquine Jose da Costa. Sec. Royal Academy of Sciences of Lisbon. Lisbon.Madden, Sir Frederick, K. H. F. R. S. F.S. A. BritishMuseum.Murchison, Roderick Impey, Esq. F. R. S. Pres. G. S. 16 ,Belgrave-square, London.Northampton, Spencer Joshua Alvyne, Marquess of, Pres.R.S. F.G.S. &c. 145, Piccadilly, and Castle Ashby,Northampton.Norwich, Right Rev. Edward Stanley, Lord Bishop of, D.D.F. L. S. F. G. S. F.Z. S. 38, Brook-street, London, andNorwich.Parry, Sir William Edward, Knt. D. C. L. Captain R. N.F. R. S. F. R. A. S. &c. 2, New-street, Spring Gardens,London.Phillipart, Sir John.Prichard, James Cowles, M. D. F. R. S. &c. Bristol.Quetelet, Adolphe Jacques, Director of the Observatory ofBrussels. Brussels.Rafn, C. C. Sec. Royal Society of Northern Antiquaries ofCopenhagen. Copenhagen.Rennie, George, Esq. , V. P. R. S. 21 , Whitehall Place,London.Rosellini, Professor. Florence.Schumacher, Heinrich Christian. Altona.Sedgwick, Rev. Adam, M. A. F. R. S. F. G.S. F.R.A.S.Woodwardian Lecturer, Cambridge. Cambridge.Smyth, William Henry, Esq. , Captain R.N. D. C. L. For.Sec. R. A. S. F. R. S. F.S. A., &c. Chelsea, London.XXSomerville, Mrs. Mary.Chelsea.South, Sir James, Knt. F.R.S.L. & E. F.L.S. F.R.A.S. &c.Observatory, Camden Hill, Kensington.Sussex, His Royal Highness Augustus Frederick Duke of,K.G. F.R.S. F.S.A. &c. Kensington Palace, London.Sykes, Lieut- Colonel William Henry, F. R. S. F. L. S.F. G. S., &c. 47, Albion-street, Hyde-park, London.Taylor, Thomas, M. D. Cork.Thomson, Thomas, M.D. F. R. S. L. & E. F. L. S. F. G. S.Regius Professor of Chemistry, Glasgow. Glasgow.Turner, Dawson, Esq. F. R.S. F. S. A. F.L.S. &c. Yarmouth.Walsh, Rev. Robert, LL. D. 53, Summer Hill.Wallace, Professor. Edinburgh.Wheatstone, Charles, Esq. , F. R. S., Professor of Experimental Philosophy, King's College. London.Whewell, Rev. William, D. D. F. R. S. F. S. A. F. G. S.F. R. A. S. , Master of Trinity College, Cambridge.Cambridge.THEROYAL IRISH ACADEMY,MARCH 16, 1846.Patroness:HER MOST SACRED MAJESTY,THE QUEEN.Visitor:HIS EXCELLENCY THE LORD LIEUTENANT OFIRELAND.President.REV. HUMPHREY LLOYD, D. D.Elected 16th March, 1846.Vice-Presidents,(Nominated by President. )GEORGE PETRIE, ESQ.CAPTAIN LARCOM, R. E.SIR WILLIAM R. HAMILTON, LL. D.REV. FRANC SADLEIR, D. D., PROVOST OF T. C. D.Appointed.COUNCIL.Committee ofScience.1808. REV. FRANC SADLEIR, D. D.,1827. SIR W. R. HAMILTON, LL. D.PROVOST.1833. JAMES APJOHN, M. D.1837. JAMES MAC CULLAGH, LL. D.1838.-ROBERT BALL, ESQ.1840. SIR RObert Kane, M. D.1844.-G. J. ALLMAN, M. B.aiiAppointed.Committee of Polite Literature.1816.-SAMUEL LITTON, M. D.1821 .1838.1844.REV. WILLIAM H. DRUMMOND, D. D.REV. CHARLES W. WALL, D. D.1842.-JOHN ANSTER, LL.D.REV. CHARLES GRAVES, A. M.1844. REV. SAMUEL BUTCHER, A. M., F. T. C. D.1845. REV. JAMES WILSON, D. D.Committee of Antiquities.1830.- GEORGE PETRIE, Esq. , R. H. A.1837. - REV. JAMES H. TODD, D. D.1839.-HENRY J. MONCK MASON, LL.D.1842.-J. HUBAND SMITH, A. M.1842.-CAPTAIN LARCOM, R. E.1845. WILLIAM R. WILDE, ESQ.1846.-FREDERICK W. BURTON, ESQ. , R. H. A.Officers.Treasurer.-ROBERT BALL, ESQ.Secretary ofthe Academy. -REV. J. H. TODD, D. D.Secretary of Council. -REV. CHAS. GRAVES, A. M.Secretary ofForeign Correspondence.-REV. SAMUEL BUTCHER.Librarian.- REV. WILLIAM H. DRUMMOND.Clerk and Assistant Librarian.- EDWARD CLIBBORN.NOTE. The Members ofthe Academy are particularly requestedto communicate to the Assistant Librarian any corrections in thisList which they may consider necessary.MEMBERS.The Names of Life Members are marked with an Asterisk.

• Adare, Edwin Viscount, M. P. F. R. S. F. A. S. Dunraven Castle, Glamorganshire, and 76, Eaton-square,

London.

Andrews, Thomas, M. D.

Armstrong, Andrew, Esq. ,65, Chester-square, Belfast.A. M. 17 , College.

• Ashburner, John, M. D. 55, Wimpole-street, London.

Abell, Abraham, Esq. Cork.Abeltshauser, J. George, Esq. A. M., Queen's Professorof French and German. 9, College, and 72, Talbotstreet.Adams, Robert, Esq. , V. P. Royal College of Surgeons.11 , Great Denmark-street.Alcorn, John, Esq. 20, Rathmines Road.Allman, George James, M. B. , Professor of Botany,T. C. D. 30, College.Andrews, William, Esq. , Sec. Natural History Society .18, Leinster-street.Anster, John, LL.D. 5, Lower Gloucester-street.Apjohn, James, M. D., Professor of Chemistry, RoyalCollege of Surgeons. V. P. Geological Society ofDublin.- VICE PRESIDENT. 32, Lower Baggot- street .Armstrong, William, Esq. 5, Lower Dominick-street.

• Bailie, Rev. James Kennedy, D.D. Ardtrea, Stewartstown.
• Bald, William , Esq. , F. R. S. E.

a 2iv

• Ball, Robert, Esq.-TREASURER.

Director UniversityMuseum. Secretary Royal Zoological Society of Ireland.Sec. Geological Society, Dublin. Local Sec. BotanicalSociety of Edinburgh. Local Sec. Ray Society, &c.3, Granby Row.

• Ball, John, Esq. 85, Stephen's-green.
• Banks, John T. , M. D. 29, Lower Merrion-street.
  • Bateson, Sir R., Bart. Belvoir Park, Belfast.
• Beaufort, Francis, Esq. , F. R.S. F. G. S. F. R. A. S. , &c .

Captain R. N. Admiralty, London.Benson, Charles, M. D. Professor of Physic, RoyalCollege of Surgeons. 34, York- street.

• Bergin, Thomas F., Esq. 49, Westland Row.
• Blacker, Stewart, Esq. 20, Gardiner's-pláce.

Blood, Bindon, Esq. Ennis.

• Bolton, William Edward, Esq. 5, Nelson-street.
• Botfield, Beriah, Esq., M. P. London.
• Boyle, Alexander, Esq. Killiney, and 35, College-green.
• Bruce, Haliday, Esq. 37, Dame- street.
• Butcher, Rev. Samuel, Fellow of Trinity College. College.

Baker, Matthew, Esq. 10, Gloucester- street.Baker, Abr. W., Esq.46, Blessington-street.Barker, Francis, M. D.sity of Dublin. 26,Ballytobin House, Callan, andProfessor of Chemistry, UniverLower Baggot-street.Barker, William, M. B. 39, Hatch-street.Barrington, Sir Matthew, Bart. 50, Stephen's-green, East.Beatty, Thomas E., M.D. 18, Merrion-square, North.Beauchamp, Henry C., M. D. 145, Lower Baggot-street.Betham, Sir William, Knt. , Ulster King of Arms. F. S. A.F. R. A. S. V. P. Royal Dublin Society. StradbrookHouse, Black Rock.Bevan, Philip, M. D. 1 , Hatch-street.Bewley, Edward, M.D. Moate, G.Blacker, William, Esq. Armagh.yBlake, Patrick Joseph, Esq. 11 , Great George's- street,North.Bolton, Chichester, Esq. 1 , Upper Merrion-street.Borough, Sir Edward, Bart. 18, Leinster-street.Bournes, Charles, Esq. , C. E. Monastereven.Brady, Rt. Hon. Maziere, A. M. Lord Chief Baron .26, Pembroke-street.Burrowes, John, Esq. 1 , Herbert-street.Burton, Frederick W., Esq. , R. H. A. 2, Salem-place,Wellington-square.Butler, Rev. Richard.Butler, Thomas, Esq.Trim.St. James's Park, Kilkenny.

• Callwell, Robert, Esq. 25, Herbert Place.

Campbell, William W., M.D. Port Stewart, Coleraine.

• Carmichael, Andrew, Esq. 24, Rutland-square, North.

S.

• Carmichael, Richard, Esq. 24, Rutland- square, North.
• Carne, Joseph, Esq. , F. R. F. G. S. Penzance.
• Carson, Rev. Joseph, A. M. F. T. C. College.
• Caulfield, Hon. Henry.

Chamley, George, Esq.1Hockley, Armagh.6, Belvidere Place.

• Charlemont, Francis W. Earl of. Charlemont House.
• Chetwode, Edward Wilmot, Esq. Woodbrook, Portarlington.
• Clarke, Thomas, Esq. 124, Lower Baggot-street.

Clendinning, Alexander, Esq. Westport.Colby, Lieut.- Colonel Thomas, Royal Engineers, LL.D.F. R. S. L. and E. F. G. S. F. R. A. S. , &c. Southampton."

• Cole, Owen Blayney, Esq. 9, Gresham Terrace, Kings-

town.Colvill, William C., Esq. 7, Bachelor's Walk.

• Connolly, Daniel, LL.D. 7, Fitzwilliam-place.

Conroy, Edward, Esq. Kensington, London.Corballis, John R., LL.D. Q. C. 19, Baggot-st. , Lower.vi

• Cork, Cloyne, and Ross, Rt. Rev. Samuel Kyle, D.D.,

Lord Bishop of. Cork.Courtney, Henry, Esq. 24, Fitzwilliam-place.

• Croker, Thomas Crofton, Esq. , F. S. A. London.

Croker, Charles Philips, M.D. 7, Merrion-square, West.

• Cubitt, William, Esq. , F. R. S. F. R. A. S. 8, Great

George-street, Westminster, London.

• Cusack, James W., M.D., Sec. Royal College of Surgeons. 3, Kildare-street.

Cane, Arthur B. , Esq. 61 , Dawson- street.Cane, Edward, Esq. 60, Dawson- street.Cane, Richard, Esq. 61 , Dawson- street.Carr, George, Esq. 18 , Mountjoy-square, South.Carter, Samson, Esq. Kilkenny.Cash, George, Esq. Broomfield, Malahide.Cather, Thomas, Esq. 20, Blessington- street.Chapman, Sir Montague Louth, Bart. Killua Castle,Clonmellan.Chapman, B. I., Esq. Killua Castle, Clonmellan.Chatto, Rev. Robert, A. M. Rockfield House, near Monmouth.Churchill, Fleetwood, M.D. 137 , Stephen's-green, West.Clare, Henry, Esq. 14, Warrington-place, and PostOffice.Claridge, James, Esq. 9, Dawson- street.Clarke, Edward S., Esq. 18, York-street.Close, James S., Esq. 2, Gardiner's- row.Connell, Rev. John, Chaplain of the Royal Hospital,KilmainhamConway, Frederick W., Esq. Rathmines, and Suffolk-st.Cooke, Adolphus, Esq. Cooksborough, Mullingar.Cooper, Edward J. , Esq. Markree Castle, Colooney.Cooper, Jonathan Sisson, Esq. 9, Upper Merrion- street.Cotton, Very Rev. Henry, LL.D., Archdeacon of Casheland Dean of Lismore. Thurles, Co. of Tipperary.viiCrampton, Hon. Justice, LL.D. 3, Kildare-street.Crampton, Sir Philip, Bart. President Royal ZoologicalSociety of Ireland . 14, Merrion-square, North.Crawford, Rev. Francis. Newtown Hamilton, Loughall.Culley, Robert, Esq. Kingstown.Curran, John Oliver, M. B. 1 , Waterloo Road.

• Davis, Charles, M.D. 33, York-street.
• D'Olier, Isaac M., Esq. Booterstown.
• Drummond, Rev. William Hamilton, D. D.-LIBRARIAN.

27, Lower Gardiner- street .

Drury, William V., M. D. 9, Lower Merrion- street .D'Alton, John, Esq. 48, Summer-hill.D'Arcy, John, Esq. Clifton Castle, Galway, and 32,Molesworth-street.Darcy, Matthew, Esq. Raheny Lodge.Darley, Frederick, Esq. 26, Lower Fitzwilliam-street.Davidson, John, Jun., Esq. Armagh.Davy, Edmund, Esq. , F. R. S. Professor of Chemistry,Royal Dublin Society.Deane, John Connellan, Esq. 1 , Platanus Buildings.Dease, Matthew O'Reilly, Esq. 50, Dominick-street, andNicholastown, Co. Louth.Deasy, Rickard, Esq. 184, Great Brunwsick- street.Disney, Ven. Brabazon William, Archdeacon of Emly.Dixon, Rev. Robert Vickers, A. M. F.T. C. 10, College.Dobbs, William Carey, Esq. 21 , Fitzwilliam-place.Doyne, Charles, Esq. Newtown Park, Black Rock.Drennan, William, Esq. Glassnevin Lodge.Dublin, Most Rev. Richard Whately, D. D., Archbishopof. V. P. Royal Zoological Society of Ireland. Palace,Stephen's-green, North.Dunlop, Durham, Esq. 7, Lower Abbey-street.Dunraven, Right Hon. Earl of. Adare Abbey, Adare.viii

• Elrington, Rev. Charles Richard, D.D., Regius Professor

of Divinity, University of Dublin. Trinity College.Edington, William, Esq. Treasurer of the Geologica.Society of Dublin. 18, Leinster-street.

Eiffe, James S., Esq. 1 , South Crescent, Bedford-square,London.Ellis, Conyngham, Esq. 4, Fitzwilliam-place.Enniskillen, Earl of. Florence Court.Evans, John T., M. D. 34, Westland-row .Fitzgerald, Right Hon. Maurice, Knight of Kerry.Forster, Robert, Esq. Springfield, Dungannon.

• Fortescue, Thomas, Esq. , M. P. Ravensdale Park, Flurry

Bridge.

• Foot, Simon, Esq. Holly Park, County ofDublin.

Farnham, Baron ( Henry). Farnham, County Cavan.Farran, William, Esq. 17, Lower Dominick-street.Ferguson, Samuel, Esq. 56. Lower Dominick-street.Ferrier, Alexander, Jun . , Esq.. A. M. Rathmines.Finlay, John, LL.D. 31 , North Cumberland-street.Fitzgibbon, Gerald, Esq. 29, Gloucester-street, Upper.Franks, Robert, Esq. 136, Stephen's-green .Frazer, George Alexander, Esq., Captain R. N., afloat.Gough, George Stephens, Esq., A. B.

• Graves, Rev. Charles, A. M., Fellow of Trinity College.

Professor of Mathematics.-SEC. OF COUNCIL. 12,Fitzwilliam-square, West.

Grierson, George A., Esq. Queen's Printing Office, 19,Essex-street, West.

• Griffith, Richard, Esq. , F. R. S. E. , F. G. S. V. P. Geological Society of Dublin. 2, Fitzwilliam-place.

Galbraith, Jos. A., Fellow of Trinity College. College.Gayer, Arthur E., LL.D. 47 , Upper Mount-street.Getty, Edmund, Esq. Belfast.ixGoold, Wyndham, Esq. 21 , Merrion-square, North.Gore, William, M.D. Limerick.Graves, Robert J., M. D. King's Professor of the Institutes of Medicine. 4, Merrion- square, South.Gregory, William, M.D. F. R. S. E. Edinburgh.Gregory, Very Rev. James, A. M., Dean of Kildare.17 , Fitzwilliam- street, Upper.Grimshaw, Wrigley, M.D. 11 , Molesworth- street.Grubb, Thomas, Esq. Bank ofIreland, and 8, LeinsterTerrace, Rathmines.

• Hamilton, Sir William Rowan, Knt., LL.D. F. R. A. S.

Astronomer Royal of Ireland , and Andrews' Professorof Astronomy in the University of Dublin.tory, Dunsink.

• Hanna, Samuel, M.D. A. M. 16, Granby-row.
• Hardiman, James, Esq.
• Harrison, Robert, M.D.

Galway.ObservaProfessor of Anatomy and Surgery, University of Dublin. 1 , Hume-street .

• Hart, Andrew Searle, LL.D., Fellow of Trinity College.

College.Harvey, W. H., M.D. College.

• Hemans, G. W., Esq. , C. E. 52, Lower Sackville-street.
• Hill, Lord George A. Updown House, Sandwich.
• Hincks, Rev. Thomas D., LL.D. Belfast.
• Hudson, Henry, Esq. , M. B. 24, Stephen's-green, North.

Hutton, Robert, Esq. , F. G. S. Putney Park, Surrey,

and 15, Manchester Buildings, London.

• Hutton, Thomas, Esq. , F. G.S. V.P. Geological Society

of Dublin. Treasurer of the Royal Zoological Societyof Ireland. Elm Park, and 116 , Summer-hill.

• Hutton, Henry, Esq. 18, Gardiner's-place.

Halpin, Rev. Nicholas John. 14, Seville-place.Hamilton, Charles William, Esq. , F. G. S. Sec. Geological Society of Dublin. 1 , Great Denmark-street,XHamilton, G. A., Esq. , M. P. Hampton Hall.Hamilton, John, Esq. 37, Westland- row .Hanlon, Charles, Esq.Hardy, Philip Dixon,Peremount, Rathgar.Esq. Greenfield Lodge, Donnybrook, and 23, Upper Sackville-street.Hart, John, M. D. Professor of Descriptive Anatomy tothe Royal College of Surgeons. 67, Charlemont-street.Haughton, Samuel, Esq. , Fellow of Trinity College. College.Henn, William, Esq. 17, Merrion-square, South.Hill, William, Esq. Donnybrook, Doneraile, Cork.Hogan, William, Esq. , A. M. Haddington Terrace, Kingstown.Hogan, William, Esq. , C. E. 49, Lower Sackville- street.Homan, Rev. John, A.M.Hudson, William E., Esq. 39 , Upper Fitzwilliam-street.Hughes, Henry G., Esq. , Q. C. 22, Lower Fitzwilliamstreet.Hutton, Edward, Esq. , M.D. 29, Gardiner's-place.

• Jessop, Frederick Thomas, Esq. Doory Hall, Longford.
• Jones, Lieut. - Colonel Harry D., M. I. C. E. Sea-view

Terrace, Donnybrook, and Custom- House.Jacob, Arthur, M. D. Professor of Anatomy, Royal College of Surgeons. 23, Ely-place.James, Sir John Kingston, Bart. 9, Cavendish-row.James, Henry, Esq. , Captain R. E. Custom-House.Jameson, James, Esq. Marrowbone-lane, and Montrose,Stillorgan-road.Jellett, J. H., Esq. , Fellow of Trinity College. College.Jennings, Francis M., Esq. Brown- street, Cork.Joy, Henry Holmes, Esq. , A. M. Treasurer of the Geological Society of Dublin. 17 , Mountjoy-square, East.Kelly, Dennis Henry, Esq. Castle Kelly, Mount Talbot,Roscommon.xi

• Kildare, Marquis of. Carton, Maynooth, and 13, Lower

Dominick-street.

• Knox, Rev. Thomas. River Glebe, Toomavara, Nenagh.
• Knox, George J. , Esq. 1 , Maddox-street, London.
• Knox, Rev. H. Barry. Deanery House, Hadleigh, Suffolk.

Kyle, William Cotter, LL.D. 8, Clare- street.Kane, SirRobert, M. D. Professor of Natural Philosophy,Royal Dublin Society. Black Rock.Kelly, Thomas F., LL.D. Clonturk House, Drumcondra.Kennedy, George A. , M. D. President of the King andQueen's College of Physicians. 15, Talbot- street.Kennedy, James Birch, Esq. 30, Gardiner's-place.Kent, William T., Esq. 37 , College-green.King, Hon. James. Mitchelstown Castle, Mitchelstown.King, Charles Croker, M.D. 43, Hardwicke-street.

• Larcom, Thomas A., Captain , R. E.

Office, Phoenix Park.Ordnance Survey

• Lardner, Rev. Dionysius, LL.D. F.R.S.L. & E. F.R.A.S.
• La Touche, David Charles, Esq. Bank, Castle-street.
• La Touche, William Digges, Esq. 34, Stephen's-green,

North.

• Leader, Nicholas P., Esq. Dromagh Castle, Castle Mills,

Cork.

• Leinster, his Grace the Duke of. Carton, Maynooth, and

13, Lower Dominick- street .

• Leitrim, Rt. Hon. Nathaniel Earl of. Killadoon, Celbridge.

Lenigan, James, Esq.

• Litton, Samuel, M.D.

Castle Fogarty, Thurles.Professor of Botany, Royal DublinSociety. School ofMedicine, Cecilia- street.Lloyd, Rev. Humphrey, D. D. F. R. S., Senior Fellow ofTrinity College. Prof. Nat. Phil. - PRESIDENT. 35,College, and 17, Fitzwilliam-square, South.

• Luby, Rev. Thomas, D.D. Fellow of Trinity College.

3, College.xii

• Lucas, Right Hon. Edward. 52, Stephen's-green.

La Touche, George Digges, Esq. 94, Lower Baggot-st.Law, Robert, M. D. 34, Granby-row .L'Estrange, Francis, Esq. Dawson- street.Lee, Rev. William, A. M. , Fellow of Trinity College .College.Le Fanu, William, Esq. Granby- row .Levinge, Charles Wm., Esq. Levington Park, Mullingar.Lindsay, Henry, Esq. Armagh.Lloyd, William T. , Esq. 10, Crescent, Upper Mount-st.Lloyd, William, M.D. Belgrave-place, Cork.Logan, Rev. H. F. C., D.D. St. Mary's College, Oscott,Birmingham.Longfield, Mountifort, LL.D., Professor of Feudal andEnglish Law, University of Dublin. 6, Fitzwilliamsquare, West.Longfield, William, Esq. 19, Harcourt-street.Longfield, Rev. George, F. T. C. D. College.Lyle, Acheson, Esq. , A. M. Treasurer of the GeologicalSociety of Dublin. 17 , Gardiner's-place.Lynch, J. F., Esq. 19, Belvidere-place.Mac Carthy, Viscount De. Toulouse.

• Mac Cullagh, James, LL.D. F. R. S. F. T. C.

Math. College.

• Mac Donnell, John, M.D. 4, Gardiner's-row.

Prof.

• Mac Donnell, Rev. Richard, D.D. S. F. T. C. College.
• Mackay, James Townsend, Esq. College Botanic Garden,

and Dawson Grove, Beggar's-bush.

M'Kay, Rev. Maurice, LL.D. Drogheda.

• M'Neece, Rev. Thomas, A. M. F. T. C. College.
• Mac Neill, Sir John, LL.D. F.R.S. F. R. A. S. Professor of the Practice of Engineering , University of

Dublin. 9, Whitehall-place, London, and 28, Rutlandsquare, Dublin.xiii

Magrath, Sir George, K. H. M.D. F. R. S. F. L. S.F.G.S. Plymouth.Mahony, Pierce, Esq. 23, William- street.Marsh, Sir Henry, Bart. , M.D. V. P. Royal GeologicalSociety of Ireland. Merrion-square, North.Martin, Rev. John C., D.D. Killesandra.

• Mason, Henry Joseph Monck, LL.D. Queen's Inns,

Henrietta-street.

• Mayne, Rev. Charles. Killaloe.
• Miller, Rev. George, D.D. Armagh.

Mac Cullagh, W. Torrens, Esq. 8, Upper Gloucester- st.Macdonnell, James S, Esq. , C. E. 27, Rutland-square.Mac Dowell, George, Esq. , F. T. C. 26, College.Mac Dougall, William, Esq. Holly Park, and 65, Hảrcourt- street.Mac Master, Maxwell, Jun. 97, Grafton- street.M'Mullen, John, Esq. William-street.Madden, Richard Robert, M. D. Lisbon.Magee, James, Esq. 39, Leeson- street.Mallet, Robert, Esq. Capel- street.Marks, Rev. Edward, D.D. Molyneux Asylum, Peter-st.Massy, Henry W., Esq. Rosanna, Tipperary.Mollan, John , M.D. 33, Gloucester-street.Monsell, William, Esq. Tervoe, Limerick.Montgomery, William F. , M.D. 20, Molesworth-street.Moore, David, Esq. Glassnevin .Morrison, Sir Richard, Knt. 21 , Ely-place.Morton, Pierce, Esq., A. M. Kilnacroft House, Cavan,and Belfield House, Rathmines.Mulvany, W. T., Esq. Dundrum Lodge, Dundrum, andOffice ofPublic Works, Custom-House.Murray, William, Esq. 68, Lower Gardiner-street.Napier, Joseph, Esq. 17 , Mountjoy-square, South.Neville, John, Esq. , C. E. Dundalk.xiv

• Nicholson, John A. M. B. Clontarf.

Neligan, J. Moore, M. D. 16, Leeson-street.Nelson, Joseph, Esq. 7, Gardiner's-place.Newenham, Thomas, Esq. Sandford Cottage, Cullen'swood.Nugent, Arthur R., Esq. Portaferry House, Portaferry.

• Odell, Edward, Esq. Carriglea, Dungarvan.
• O'Ferrall, Joseph M., Esq. 35, Rutland-square, West.
• O'Reilly, Miles John, Esq.

Orpen, John Herbert, LL.D. 13, South Frederickstreet.

• Owen, John Underhill, M. D.

O'Brien, Sir Lucius, Bart. Dromoland, Newmarket-onFergus, Clare; 3, Fitzwilliam-place.O'Brien, W. S., Esq. , M. P. 11 , Westland-rowO'Driscoll, W. Justin, Esq. 28, Lower Fitzwilliam-street.O'Gorman, N. Purcell, Esq. 45, Blessington- street.O'Grady, Michael Martin, M. D. La Mancha, Swords.O'Grady, James, Esq. , LL.D. 27 , Denzille-street.O'Meagher, Stephen, D. L. Kilmoylen, Cahir.Oldham, Thomas, A. M. F. G. S. Professor of Geologyin the University of Dublin. 28, Trinity College.Osborne, Jonathan, M. D. 26, Harcourt- street.Otway, Cæsar G., Esq. , A. M. Custom-House.Owen, Jacob, Esq. 2, Mountjoy-square, West.

• Parker, Alexander, Esq. Rathmines.
• Petrie, George, Esq. , R. H. A. 21 , Great Charles-street.
• Phibbs, William, Esq. Seafield, Sligo.
• Pickford, James H., M. D. Brighton.
• Pim, George, Esq. Brennan's- town, and 15, Usher's

Island.

• Porter, Rev. Thomas H., D. D. Tullahogue, Dungannon.

XV

Portlock, Joseph Ellison , Esq. , R. E. F. R. S. F. G. S.V. P. Geological Society of Dublin. V. P. RoyalZoological Society of Ireland. 50, Upper Sackville-st.

• Prior Terrace, Hyde Park, , James, Esq. 14, Oxford

London.Pakenham, Hon. and Very Rev. Henry, Dean of St. Patrick's. 40, Harcourt-street, and Deanery House.Palmer, Abraham, Esq. , M. B. 38, York-street.Patten, James, A. M., M. D.Phillips, John, Esq. York.Belfast.Pigot, Right Hon. D. R. 8, Merrion-square, South.Pim, James, Jun. , Esq. Monkstown Castle, and 35, College-green.Ponsonby, The Hon. Frederick. 36, Kildare-street.Porter, Rev. Classon. Larne.Preston, Algernon, Esq. Sandymount Park.

• Renny, H. L., Esq. , C. E.
• Rhodes, Thomas, Esq. , C. E. Shannon Commission.
• Roberts, Rev. John Cramer. Sallymount, Kilcullen.
• Robinson, Rev. Thomas Romney, D. D. Observatory,

Armagh.

• Roe, Henry, Esq. 2, Fitzwilliam- square, East.
• Rossmore, Baron. Rossmore Park, and TheDell, Windsor.

Rosse, Rt. Hon. The Earl of. Birr Castle, Parsonstown.

• Rowan, Rev. Arthur B., A. M. Bellmount, Tralee.

Reade, Philip, Esq. Wood Park, Scariff.Redington, Thomas N., Esq. , M. P. Kilcornan .Richards, Goddard, Esq. Ardamine, Co. Wexford.Reid, Rev. James. Clontarf.Reid, Robert, M.D. 41 , Belvidere-place.Roberts, William, Esq. , Fellow ofTrinity College . College.

• Sadleir, Rev. Franc, D. D. Provost of Trinity College.

Provost's House, College.xvi

Sadleir, Rev. William Digby, D.D., Fellow of TrinityCollege. 4, College.

• Salmon, Rev. George, Fellow of Trinity College. 24,

College.

• Sherrard, James Corry, Esq. 2, Great George's- street,

Westminster.

Singer, Rev. Joseph Henderson, D.D., Senior Fellow ofTrinity College. 4, College.

• Sirr, Rev. Joseph D'Arcy, D.D. Foxford, Suffolk.
• Smith, Rev. George Sidney, D.D. Professor of Biblical

Greek, University of Dublin. 9, College.

• Stewart, Hon. Alexander. 5, Foley-place, London.
• Strong, Rev. Charles, A. M. 6, Cavendish-row.
• Sweetman, Walter, Esq. 4, Mountjoy-square, North.

Savage, Marmion W., Esq. 2, Hume-street.Sausse, M. R., Esq. 5, Hume-street.Sharp, Richard, Esq. 36, Westmoreland- street.Smith, J. Huband, Esq. , A. M. 1 , Holles-street.Smith, Robert William, Esq. , M. D. 63, Eccles- street.Smith, Aquilla, M. D. 12, Lower Baggot- street.Sproule, Oliver, Esq. 42, Blessington- street.Stack, Rev. Thomas, Fellow of Trinity College. College.Staples, Sir Thomas, Bart. Sissane, Co. Tyrone, and11 , Merrion-square, East.Stapleton, Michael H., M. B. 1 , Mountjoy-place.Starkey, Digby Pilot, Esq. Sandy- Cove Terrace, Kingstown, and Accountant- General's Office, Four- Courts.Sterling, A. C., Captain. 2, South-place, Knightsbridge,London.Stokes, William , M.D. Regius Professor of Medicine.5, Merrion-square, North.

• Tenison, Edward King, Esq. Kilronan, Keadue, Carrickon- Shannon.
• Thompson, James, Esq. 46, Charlemont-place, Glasgow.

xvii

• Todd, Rev. James Henthorn, D. D., Fellow of Trinity

College. VICE- PRESIDENT. 35, College.

• Traill, Rev. Robert, D.D. Westskull Rectory, Skibbereen .
• Turner, William, Esq.

Talbot, James, Esq. Evercreech- House, Shepton- Mallet,Somersetshire.Tennant, James Emerson, Esq.Tighe, Robert, Esq. 14, Fitzwilliam-square, North.Toleken, John, Esq. , M.D., Fellow of Trinity College.College.Townsend, William R., C. E. Derry, Roscarberry.Tuffnell, T. Jolliffe, M. D. 58, Lower Mount-street .Tyrrell, John, Esq. Devonshire.

• Vandeleur, Crofton Moore, Col. Kilrush, County ofClare.

Vignoles, Very Rev. Charles, D.D., Dean of Ossory.Kilkenny.Vignoles, Charles, Esq. , F. R. A. S. Trafalgar-square,London.

• Wall, Rev. Charles William, D. D., Senior Fellow of

Trinity College. 20, College.

• Wall, Rev. Richard H., D.D. 6, Hume-street.
• Walshe, Francis Weldon, Esq. Upper Glentworth- street,

Limerick.

• Weaver, Thomas, Esq. , F.R. S., F. G. S. London.
• Weld, Isaac, Esq. , F. G.S. Sec. Royal Dublin Society.

Ravenswell, Bray.

• Williams, Thomas, Esq. Drumcondra Castle, and 38,

Dame-street.

• Wilkinson, James Tandy, Esq. M. D. Limerick.

Williams, Richard Palmer, Esq. Drumcondra Castle, and38, Dame-street.

• Wilson, Rev. James, D.D. 10, Harrington-street.

bxviii

Wilson, Thomas, Esq. Westbury, and 15, Upper Templestreet.

• Wilson, Robert, Esq. 31 , Leeson-street.

Walker, Roger Chambers, Esq. 2 Granby-row.Wallace, Robert Alexander, Esq. , A. M. 3, Palace- street.Wallace, William Baillie, Esq. A. M. 3, Palace-street.Waller, John Francis, Esq. 4, Herbert-street.Wallscourt, Baron (Josh. Henry) . Ardfry, Co. Galway.Watson, Henry, Esq. Limerick.Webber, Charles T., Esq. 22, Upper Gloucester- street.West, Rev. John, D.D.Wilde, William R., Esq.Wilkinson, George, Esq.Williams, Charles Wye, Esq.Williams, Robert C., M. D.28 , Herbert-place.15, Westland-row.4, North Frederick-street.Liverpool.58, Upper Mount- street.Wills, Rev. James. Suirville, Waterford.Wilme, Benjamin P., Esq. , C. E. Featherstone Buildings,Bedford-row, London.Wingfield, Hon. and Rev. William . Abbeyleix.Wynne, John, Esq. Hazlewood, Co. Sligo.Yeates, George, Esq. 2, Grafton-street.Young, John T., Esq. Philpotstown, Navan.OMITTED IN THEIR PROPER PLACES.Aldridge, John, M. D. Park-street.Lefroy, George, Esq. 18, Leeson-street.HONORARY MEMBERS.Elected.1832. Abrahamson, General T. Copenhagen.1832. Airy, George Biddell, M. A. F.R.S. V. P. R. A. S.Astronomer Royal. Observatory, Greenwich.1835. Amyot, Thomas, F. R. S. Treas. S. A. 13, Jamesstreet, Westminster, London.1844. Arago, M. Paris.1826. Babbage, Charles, M. A. F. R. S. L. & E. F. R. A. S.,&c. 1, Dorset- street, Manchester-square, London.1829. Berzelius, Jens Jacob.1826. Brewer, James N., Esq.Stockholm.1822. Brewster, Sir David, K.H. LL.D. F.R. S. L. & E.F. G.S. F.R. A. S., &c. St. Leonard's College,St. Andrew's.1836. Brisbane, Lieut. - General Sir Thomas Mac Dougal,K.C.B. D.C.L. F.R.S. Pres. R.S.E. F.R.A.S. ,&c. Makers-town, Kelso.1825. Brongniart, Alexandre. Paris.1826. Brown, Robert, D. C. L. F. R.S. L. &E. V. P. L. S.,&c. 17, Dean-street, Soho-square, London.1815. Carlisle, Nicholas, Esq. , K.H. D. C. L. F.R.S.Sec. S. A. , &c. Somerset House, Strand, London.1808. Clanny, W. R., M. D. F. S. A. London.1825. Colby, Colonel Thomas, R. E.F. G.S. F. R. A. S., &c.Tower, London.LL.D. F.R. S. L. & E.Ordnance Map Office,1835. Combe, George, Esq. Edinburgh.1833. Cooper, Charles Purton, LL.D. F. R. S. F. S. A.Lincoln's Inn, London.XXElected.1836. Daubeny, Charles Giles Bridle, M. D. F. R. S.F. L. S. F. G. S. Professor of Chemistry and ofBotany. Oxford.1835. Donop, Baron. Saxe Meiningin.1841. Dumas, Jean Baptiste. Paris.1820. Dupin, Charles, Baron.1842. Edgeworth, Miss Maria.Paris.Edgeworthstown.1832. Ellis , Sir Henry, K. H. F. R. S. Sec. S. A. Librarian of the British Museum.1832. Forshall, Rev. Josiah, M.A. F. R. S. F.S. A. British Museum.1843. Gauss, Karl Friedrich. Gottingen.1843. Gräberg, Count. Florence.1836. Graham, Robert, M. D. F. R. S. É. Professor ofBotany, Edinburgh. Edinburgh.1825. Greville, R. K., LL.D.1841. Halliwell, James Orchard, Esq., F. R. S. F. S. A.Selip, Oxfordshire.1820. Hamilton, Francis, M. D. F. R. A. S.1836. Harcourt, Rev. William V. Vernon. M. A. F. R.S.F.G.S. York..1832. Haughton, Sir Graves Chamney, K. H. M. A.F. R. S., &c. 14, Grafton-street, Bond-street,London.1826. Herschel, Sir John Frederick William , Bart. , D. C. L.F. R. S. L. & E. F. G. S. F. R. A. S. , &c. Collingwood, near Hawkhurt, Kent.1838. Herschel, Miss Caroline.1835. Hobhouse, Right Hon. Henry.1825. Hooker, Sir William Jackson, K. H. LL.D. F.R.S.F.S. A. F.L. S. F. G. S., &c. Kew.1820. Hope, Thomas Charles, M.D. F.R.S. V.P.R.S. E. ,&c. Edinburgh.1832. Jameson, Robert, Esq., F. R. S. L. & E. F. L. S.F. G. S., &c. Regius Professor of Natural History,Edinburgh. Edinburgh.xxiElected.1835. König, Charles, Esq. , K. H. F.R. S. F. L. S. , &c .British Museum.1833. Lagasca, Doctor. Madrid.Liebig, Justus. Giessen.1830. M'Laughlin, David, M. D. Paris.1836. Macedo, Sinor, Jacquine Jose da Costa, Sec. RoyalAcademy of Sciences of Lisbon. Lisbon.1832. Madden, Sir Frederick, K. H. F. R. S. F. S. A.British Museum.1836. Murchison, Sir Roderick Impey, Knt. , F. R. S.Pres. G. S. 16, Belgrave-square, London.1838. Northampton, Spencer Joshua Alvyne, Marquess of,Pres. R. S. F. G. S. 145, Piccadilly, and CastleAshby, Northampton.1836. Norwich, Right Rev. Edw. Stanley, Lord Bishop of,D. D. F. L. S. F. G. S. F. Z. S. 38, Brookstreet, London, and Norwich.1828. Parry, Sir William Edward, Knt., D. C. L. CaptainR. N. F. R. S. F. R. A. S., &c. 2, New-street,Spring Gardens, London.1825. Phillipart, Sir John.1836. Prichard, James Cowles, M.D. F. R.S., &c . Bristol.1841. Quetelet, Adolphe Jacques, Director of the Observatory of Brussels. Brussels.1827. Rafn, C. C. Sec. Royal Society of Northern Antiquaries of Copenhagen. Copenhagen.1836. Rennie, George, Esq. , V. P. R. S. 21 , Whitehallplace, London.1823. Schumacher, Heinrich Christian. Altona.1835. Sedgwick, Rev. Adam, M. A. F. R. S. F. G. S.F. R. A. S. Woodwardian Lecturer, Cambridge.Cambridge.1837. Smyth, William Henry, Esq. ,For. Sec. R.A. S. F. R. S.London.Capt. R. N. D. C. L.F. S. A., &c. Chelsea,xxiiElected.1834. Somerville, Mrs. Mary. Chelsea.1826. South, Sir James, Knt. , F. R. S. L. & E. F. L. S.F. R. A. S., &c. Observatory, Camden-hill, Kensington.1836. Sykes, Lieut. - Colonel William Henry, F. R. S.F. L. S. F. G. S., &c. 47 , Albion-street, HydePark, London.1816. Taylor, Thomas, M. D. Cork.1836. Thomson, Thomas, M.D. F. R.S. L. & E. F.L.S.F. G.S. Regius Professor of Chemistry, Glasgow.Glasgow.1805. Turner, Dawson, Esq. F. R. S. F. S. A. F. L. S.,&c. Yarmouth.1833. Walsh, Rev. Robert, LL. D.1842. Wheatstone, Charles, Esq. ,Finglass.F. R. S., Professor ofExperimental Philosophy, King's College. London.1836. Whewell, Rev. William, D. D. F. R. S. F. S. A.F. G. S. F. R. A. S. , Master of Trinity College,Cambridge. Cambridge.1846. Wordsworth, William, Esq. Rydallmount.

{{GFDL}}