{ "id": "8e8daa3fb1dc79ab7cd7f006898e22f30ff61b74", "text": "ADVERTISEMENT.\n\nThe Committee appointed by the Royal Society to direct the publication of the Philosophical Transactions, take this opportunity to acquaint the Public, that it fully appears, as well from the Council-books and Journals of the Society, as from repeated declarations which have been made in several former Transactions, that the printing of them was always, from time to time, the single act of the respective Secretaries till the Forty-seventh Volume; the Society, as a Body, never interesting themselves any further in their publication, than by occasionally recommending the revival of them to some of their Secretaries, when, from the particular circumstances of their affairs, the Transactions had happened for any length of time to be intermitted. And this seems principally to have been done with a view to satisfy the Public, that their usual meetings were then continued, for the improvement of knowledge, and benefit of mankind, the great ends of their first institution by the Royal Charters, and which they have ever since steadily pursued.\n\nBut the Society being of late years greatly enlarged, and their communications more numerous, it was thought advisable that a Committee of their members should be appointed, to reconsider the papers read before them, and select out of them such as they should judge most proper for publication in the future Transactions; which was accordingly done upon the 26th of March 1752. And the grounds of their choice are, and will continue to be, the importance and singularity of the subjects, or the advantageous manner of treating them; without pretending to answer for the certainty of the facts, or propriety of the reasonings, contained in the several papers so published, which must still rest on the credit or judgement of their respective authors.\n\nIt is likewise necessary on this occasion to remark, that it is an established rule of the Society, to which they will always adhere, never to give their opinion, as a Body, upon any subject, either of Nature or Art, that comes before them. And therefore the\nthanks, which are frequently proposed from the Chair, to be given to the authors of such papers as are read at their accustomed meetings, or to the persons through whose hands they received them, are to be considered in no other light than as a matter of civility, in return for the respect shown to the Society by those communications. The like also is to be said with regard to the several projects, inventions, and curiosities of various kinds, which are often exhibited to the Society; the authors whereof, or those who exhibit them, frequently take the liberty to report and even to certify in the public newspapers, that they have met with the highest applause and approbation. And therefore it is hoped that no regard will hereafter be paid to such reports and public notices; which in some instances have been too lightly credited, to the dishonour of the Society.\n\nThe Meteorological Journal hitherto kept by the Assistant Secretary at the Apartments of the Royal Society, by order of the President and Council, and published in the Philosophical Transactions, has been discontinued. The Government, on the recommendation of the President and Council, has established at the Royal Observatory at Greenwich, under the superintendence of the Astronomer Royal, a Magnetical and Meteorological Observatory, where observations are made on an extended scale, which are regularly published. These, which correspond with the grand scheme of observations now carrying out in different parts of the globe, supersede the necessity of a continuance of the observations made at the Apartments of the Royal Society, which could not be rendered so perfect as was desirable, on account of the imperfections of the locality and the multiplied duties of the observer.\nA List of Public Institutions and Individuals, entitled to receive a copy of the Philosophical Transactions of each year, on making application for the same directly or through their respective agents, within five years of the date of publication.\n\n**Observatories.**\n\nArmagh. \nCape of Good Hope. \nDublin. \nEdinburgh. \nGreenwich. \nKew. \nLiverpool. \nMadras. \nOxford (Radcliffe).\n\n**Institutions.**\n\nBarbadoes . . . Library and Museum. \nCalcutta . . . Asiatic Society. \nCambridge . . . Geological Museum. \nCambridge . . . Philosophical Society. \nCape Town . . . South African Library. \nDublin . . . Royal Dublin Society. \nEdinburgh . . . Royal Irish Academy. \nLondon . . . Admiralty Library. \nChemical Society. \nEntomological Society. \nGeological Society. \nGeological Survey of Great Britain. \nHorticultural Society. \nInstitute of British Architects. \nInstitution of Civil Engineers. \nLinnean Society. \nLondon Institution. \nQueen's Library. \nRoyal Asiatic Society. \nRoyal Astronomical Society. \nRoyal College of Physicians. \nRoyal Geographical Society. \nRoyal Institution of Great Britain. \nRoyal Medical and Chirurgical Society. \nRoyal Society of Literature. \nSociety of Antiquaries. \nSociety of Arts. \nThe Treasury Library. \nUnited Service Museum. \nZoological Society. \nMalta . . . Public Library. \nManchester . . . Literary and Philosophical Society. \nOxford . . . Ashmolean Society. \nRadcliffe Library. \nSwansea . . . Royal Institution. \nSydney . . . University Library. \nWoolwich . . . Royal Artillery Library.\n\n**Belgium.**\n\nBrussels . . . Royal Academy of Sciences.\n\n**Denmark.**\n\nAltona . . . Royal Observatory. \nCopenhagen . . . Royal Society of Sciences.\n\n**France.**\n\nMontpellier . . . Academy of Sciences. \nParis . . . Academy of Sciences. \nDépot de la Marine. \nEcole des Mines. \nGeographical Society. \nGeological Society. \nJardin des Plantes. \nSociété d'Encouragement pour l'Industrie Nationale. \nToulouse . . . Academy of Sciences.\n\n**Germany.**\n\nBerlin . . . Royal Academy of Sciences. \nJena . . . Cesarean Acad. of Naturalists. \nFrankfort . . . Natural History Society. \nGiessen . . . University. \nGöttingen . . . University. \nHamburg . . . Naturwissenschaftlicher-Verein. \nKönigsberg . . . Königlichen Physikalisch Ökonomenischen Gesellschaft. \nLeipzig . . . Royal Saxon Society of Sciences. \nMannheim . . . Observatory. \nMunich . . . Royal Academy of Sciences. \nPrague . . . Bohemian Society of Sciences. \nVienna . . . Imperial Academy of Sciences. \nWürzburg . . . Physico-Medical Society.\n\n**Hungary.**\n\nPesth . . . Hungarian Academy of Sciences.\n\n**Italy.**\n\nMilan . . . Institute of Sciences, Letters and Arts. \nModena . . . Italian Society of Sciences. \nNaples . . . Institute of Sciences. \nPalermo . . . Academy of Sciences and Letters. \nRome . . . Academy de' Nuovi Lincei. \nTurin . . . Royal Academy of Sciences. \nVenice . . . Institute of Sciences, Letters, and Arts.\n\n**Java.**\n\nBatavia . . . Batavian Society of Sciences.\n\n**Netherlands.**\n\nAmsterdam . . . Royal Institute. \nHaarlem . . . Dutch Society of Sciences. \nRotterdam . . . Batavian Society of Experimental Philosophy.\n\n**Portugal.**\n\nLisbon . . . Royal Academy of Sciences.\n\n**Russia.**\n\nMoscow . . . Imperial Society of Naturalists. \nPulkowa . . . Observatory. \nSt. Petersburg . . . Imperial Academy of Sciences.\n\n**Spain.**\n\nCadiz . . . Observatory. \nMadrid . . . Royal Academy of Sciences.\n\n**Sweden and Norway.**\n\nChristiania . . . Royal University. \nDrontheim . . . Royal Society of Sciences. \nGottenburg . . . Kgl. Vetenskaps och Vitterhets Samhälle. \nStockholm . . . Royal Academy of Sciences.\n\n**Switzerland.**\n\nBern . . . Allg. Schweizerischen Gesellschaft. \nGeneva . . . Société de Phys. et d'Hist. Naturelle.\n\n**United States.**\n\nAlbany . . . New York State Library. \nBoston . . . American Academy of Sciences. \nCambridge . . . Harvard University. \nPhiladelphia . . . Academy of Natural Sciences. \nWashington . . . Smithsonian Institution. \nObservatory.\n\nThe fifty Foreign Members of the Royal Society.\nA List of Public Institutions and Individuals, entitled to receive a copy of the Astronomical Observations (including Magnetism and Meteorology) made at the Royal Observatory at Greenwich, on making application for the same directly or through their respective agents, within two years of the date of publication.\n\n| Observatories | Institutions |\n|------------------------|---------------------------------------------------|\n| Altona | Aberdeen University |\n| Armagh | Berlin Academy |\n| Berlin | Bologna Academy |\n| Breslau | Boston American Academy of Sciences |\n| Brussels | Brunswick U.S. Bowdoin College |\n| Cadiz | Cambridge Trinity College Library |\n| Cambridge | Cambridge U.S. Harvard University |\n| Cape of Good Hope | Dublin University |\n| Coimbra | Edinburgh University |\n| Copenhagen | Royal Society |\n| Dorpat | Glasgow University |\n| Dublin | Göttingen University |\n| Edinburgh | Leyden University |\n| Helsingfors | London Board of Ordnance |\n| Königsberg | Queen's Library |\n| Madras | Royal Institution |\n| Mannheim | Royal Society |\n| Marseille | Oxford Savilian Library |\n| Milan | Paris Academy of Sciences |\n| Munich | Board of Longitude |\n| Oxford | Dépôt de la Marine |\n| Palermo | Pesth Hungarian Academy |\n| Paris | Philadelphia American Philosophical Society |\n| Seeberg | St. Andrews University |\n| Trevandrum | St. Petersburg Imperial Academy |\n| Tübingen | Stockholm Royal Academy of Sciences |\n| Turin | Upsal Royal Society |\n| Vienna | Waterville, Maine (U.S.) College |\n| Wilna | |\n\n| Individuals | |\n|------------------------|---------------------------------------------------|\n| Christie, S. H., Esq. | Twickenham |\n| Lubbock, Sir John William, Bart. | London. |\n| Lowndes' Professor of Astronomy | Cambridge. |\n| Plumian Professor of Astronomy | Cambridge. |\n| President of the Royal Society | London. |\n| Ross, Rear-Admiral Sir J. C. | Aylesbury. |\n| Smyth, Vice-Admiral W. H. | Aylesbury. |\n| South, Sir James | Kensington. |\n| The Earl of Rosse | Parsonstown. |\nA List of Observatories, Institutions and Individuals, entitled to receive a Copy of the Magnetical and Meteorological Observations made at the Royal Observatory, Greenwich.\n\n### Observatories\n\n- **Bombay**\n- Cambridge, United States\n- Christiania\n- Gotha\n- Heidelberg\n- Kew\n- Kremsmünster\n- Leipzig\n- Marburg\n- Prague\n- Stockholm\n- Toronto\n- Upsal\n- Washington\n\n### Institutions\n\n- **Bombay** Geographical Society.\n- Bonn University.\n- Boston, U.S. The Public Library (late Bowditch).\n- Cambridge Philosophical Society.\n- Cherkow University.\n- Falmouth Royal Cornwall Polytechnic Society.\n- London House of Lords, Library.\n- House of Commons, Library.\n- King's College.\n- Royal Society.\n- University College, Library.\n- Oxford Radcliffe Observatory.\n- Paris Meteorological Society.\n- St. Bernard Convent.\n- Washington Smithsonian Institution.\n- Woolwich Office of Mag. and Met. Publication.\n\n### Individuals\n\n- Bache, Dr. A. D. Washington.\n- Barlow, P., Esq. Charlton.\n- Ballot, Dr. Buys Utrecht.\n- Dove, Prof. H. W. Berlin.\n- Erman, Dr. Adolph Berlin.\n- Fox, R. W., Esq. Falmouth.\n- Gilliss, Lt. J. M., U.S. Navy Washington.\n- Harris, Sir W. Snow Plymouth.\n- Howard, Luke, Esq. Tottenham.\n- Kaemtz, Prof. L. F. Dorpat.\n- Kreil, Prof. K. Vienna.\n- Kupffer, A. T. St. Petersburg.\n\n(Twelve copies for distribution to the Russian Mag. and Met. Obs.)\n\n- Lloyd, Rev. Dr. Dublin.\n- Loomis, Prof. E. New York University.\n- Lovering, Prof. J. Cambridge, U.S.\n- Pegado, Dr. Lisbon.\n- Phillips, Prof. John Oxford.\n- Quetelet, A. Brussels.\n- Sabine, Major-General, R.A. London.\n- Senftenberg, Baron von Prague.\n- Vernon, G. V., Esq. Manchester.\n- Wartmann, Prof. Elie Geneva.\n- Younghusband, Lieut.-Col., R.A. Woolwich.\nCONTENTS.\n\nI. The Bakerian Lecture.—On the Absorption and Radiation of Heat by Gases and Vapours, and on the Physical Connexion of Radiation, Absorption, and Conduction. By John Tyndall, Esq., F.R.S., Member of the Academies and Societies of Holland, Geneva, Göttingen, Zürich, Halle, Marburg, Breslau, la Société Philomathique of Paris, &c.; Professor of Natural Philosophy in the Royal Institution, and in the Government School of Mines ........................................... page 1\n\nII. On an Extension of Arbogast's Method of Derivations. By Arthur Cayley, Esq., F.R.S. .................................................................................................................. 37\n\nIII. On the Equation for the Product of the Differences of all but one of the Roots of a given Equation. By Arthur Cayley, Esq., F.R.S. .................................................................................................................. 45\n\nIV. On the Synthesis of Succinic and Pyrotartaric Acids. By Maxwell Simpson, M.B. Communicated by Dr. Frankland, F.R.S. .................................................................................................................. 61\n\nV. On the Calculus of Symbols, with Applications to the Theory of Differential Equations. By W. H. L. Russell, Esq., A.B. Communicated by Arthur Cayley, Esq., F.R.S. .................................................................................................................. 69\n\nVI. On the Properties of Liquid Carbonic Acid. By G. Gore, Esq. Communicated by Professor Tyndall, F.R.S. .................................................................................................................. 83\n\nVII. On Magnetic Storms and Earth-Currents. By Charles V. Walker, Esq., F.R.S., F.R.A.S. .................................................................................................................. 89\n\nVIII. On the Surface-condensation of Steam. By J. P. Joule, LL.D., F.R.S., President of the Literary and Philosophical Society of Manchester, &c. .................................................................................................................. 133\n\nIX. On the Effect produced on the Deviations of the Compass by the Length and Arrangement of the Compass-Needles; and on a New Mode of correcting the Quadrantal Deviation. By Archibald Smith, Esq., M.A., F.R.S., late Fellow of Trinity College, Cambridge; and Frederick John Evans, Esq., R.N., Superintendent of the Compass Department of Her Majesty's Navy .................................................................................................................. 161\n\nX. Liquid Diffusion applied to Analysis. By Thomas Graham, F.R.S., Master of the Mint .................................................................................................................. 183\nXI. On the Porism of the in-and-circumscribed Polygon. By Arthur Cayley, Esq., F.R.S. . . .\npage 225\n\nXII. Tables of the Weights of the Human Body and Internal Organs in the Sane and Insane of both Sexes at various Ages, arranged from 2614 post-mortem examinations. By Robert Boyd, M.D., F.R.C.P.L., Physician to the Somerset County Lunatic Asylum. Communicated by Dr. Sharpey, Sec. R.S.\n\nXIII. On a New Auxiliary Equation in the Theory of Equations of the Fifth Order. By Arthur Cayley, Esq., F.R.S. . . .\n263\n\nXIV. A Seventh Memoir on Quantics. By Arthur Cayley, Esq., F.R.S. . . .\n277\n\nXV. On Systems of Linear Indeterminate Equations and Congruences. By Henry J. Stephen Smith, M.A., Fellow and Mathematical Lecturer of Balliol College, Oxford. Communicated by J. J. Sylvester, Esq., F.R.S. . . .\n293\nLIST OF ILLUSTRATIONS.\n\nPlate I.—Professor Tyndall on the Absorption and Radiation of Heat by Gases and Vapours.\n\nPlates II. III. IV.—Mr. C. V. Walker on Magnetic Storms and Earth-Currents.\n\nPlate V.—Messrs. Smith and Evans on the Effect of the Length of the Compass-Needle on the Deviations of the Compass.\nCONTENTS.\n\nXVI. On the Method of Symmetric Products, and on Certain Circular Functions connected with that Method. By the Rev. Robert Harley, F.R.A.S., Corresponding Member of the Literary and Philosophical Society of Manchester. Communicated by A. Cayley, Esq., F.R.S. .................................................. page 327\n\nXVII. On the Double Tangents of a Curve of the Fourth Order. By Arthur Cayley, Esq., F.R.S. ........................................................................................................... 357\n\nXVIII. Electro-Physiological Researches.—Eleventh Series. On the Secondary Electromotor Power of Nerves, and its Application to the Explanation of certain Electro-Physiological Phenomena. By Signor Carlo Matteucci. Communicated by General Sabine, Treas. and V.P.R.S. ........................................................................................................... 363\n\nXIX. On Liquid Transpiration in relation to Chemical Composition. By Thomas Graham, F.R.S., Master of the Mint ........................................................................................................... 373\n\nXX. On the Structure and Growth of the Tooth of Echinus. By S. James A. Salter, M.B. Lond., F.L.S., F.G.S. Communicated by Thomas Bell, Esq., F.R.S. ........................................................................................................... 387\n\nXXI. On Fermat's Theorem of the Polygonal Numbers.—Part I. By Sir Frederick Pollock, F.R.S., Lord Chief Baron, &c. &c. ........................................................................................................... 409\n\nXXII. On the Great Magnetic Disturbance which extended from August 28 to September 7, 1859, as recorded by Photography at the Kew Observatory. By Balfour Stewart, A.M. ........................................................................................................... 423\n\nXXIII. On the Sources of the Nitrogen of Vegetation; with special reference to the Question whether Plants assimilate Free or uncombined Nitrogen. By John Bennet Lawes, F.R.S., F.C.S., Joseph Henry Gilbert, Ph.D., F.R.S., F.C.S., and Evan Pugh, Ph.D., F.C.S. ........................................................................................................... 431\nXXIV. On the Indian Arc of Meridian. By the Venerable J. H. Pratt, M.A., Archdeacon of Calcutta. Communicated by Professor Stokes, Sec. R.S. . . . page 579\n\nXXV. Notes on the Generative Organs, and on the Formation of the Egg in the Annulosa. By John Lubbock, Esq., F.R.S. . . . . . . . . . . . . . . . . . . . 595\n\nXXVI. On the Influence of Atmospheric Pressure upon some of the Phenomena of Combustion. By Dr. E. Frankland, F.R.S. . . . . . . . . . . . . . . . . . . . 629\n\nERRATUM.\n\nPage 259 (seven lines from the bottom), upwards of 80 years, Females, Minimum, Encephalon, for 15·25 read 35·25.\nLIST OF ILLUSTRATIONS.\n\nPlates VI. VII. VIII.—Mr. S. J. A. Salter on the Structure and Growth of the Tooth of *Echinus*.\n\nPlates IX. X. XI.—Mr. B. Stewart on the Great Magnetic Disturbance of August 28 to September 7, 1859.\n\nPlates XII. XIII. XIV. XV.—Mr. J. B. Lawes, Dr. Gilbert, and Dr. Pugh on the Sources of the Nitrogen of Vegetation, &c.\n\nPlates XVI. XVII.—Mr. Lubbock on the Generative Organs, and on the Formation of the Egg in the Annulosa.\n\nPlates XVIII. XIX.—Dr. E. Frankland on the Influence of Atmospheric Pressure upon some of the Phenomena of Combustion.\nCONTENTS.\n\nXXVII. Account of Experiments made at Holyhead (North Wales) to ascertain the Transit-Velocity of Waves, analogous to Earthquake Waves, through the Local Rock Formations. By Robert Mallet, C.E., F.R.S. ........................................... page 655\n\nXXVIII. On the Construction of Specula of Six-feet Aperture; and a selection from the Observations of Nebulæ made with them. By the Earl of Rosse, K.P., &c., F.R.S. .................................................................................................................. 681\n\nXXIX. On the Elimination of Urea and Urinary Water, in relation to the Period of the Day, Season, Exertion, Food, Prison Discipline, Weight of Body, and other influences acting in the Cycle of the Year. By Edward Smith, M.D., LL.B., F.R.S., Assistant Physician to the Hospital for Consumption and Diseases of the Chest, Brompton, Corresponding Fellow of the Academy of Sciences and Arts of Montpellier, and of the Natural History Society of Montreal, &c. .................................................................................................................. 747\n\nIndex .................................................................................................................................................................................. 835\n\nAPPENDIX.\n\nPresents ........................................................................................................................................................................ [ 1 ]\nLIST OF ILLUSTRATIONS.\n\nPlates XX. XXI. XXII. XXIII.—Mr. Mallet on the Transit-Velocity of Earthquake Waves.\n\nPlates XXIV. XXV. XXVI. XXVII. XXVIII. XXIX. XXX. XXXI.—The Earl of Rosse on the Construction of Specula of 6-feet Aperture.\n\nPlates XXXII. XXXIII. XXXIV. XXXV. XXXVI.—Dr. Smith on the Elimination of Urea and Urinary Water.\nADJUDICATION of the Medals of the Royal Society for the year 1861 by the President and Council.\n\nThe Copley Medal to Professor Louis Agassiz, of Cambridge, Massachusetts, Foreign Member of the Royal Society, for his Researches in Palaeontology and other branches of science, and particularly for his great works the \"Poissons Fossiles,\" and \"Les Poissons du vieux Grès Rouge d'Ecosse.\"\n\nA Royal Medal to Dr. William B. Carpenter, F.R.S., for his Researches on the Foraminifera, contained in four Memoirs in the Philosophical Transactions, his investigations into the Structure of Shell, his observations on the embryonic Development of Purpura, and his various other writings in Physiology and Comparative Anatomy.\n\nA Royal Medal to Professor James Joseph Sylvester, F.R.S., for his various Memoirs and Researches in Mathematical science.\n\nThe Bakerian Lecture was delivered by Professor J. Tyndall, F.R.S.: it was entitled \"On the Absorption and Radiation of Heat by Gases and Vapours, and on the Physical Connexion of Radiation, Absorption, and Conduction.\"\n\nThe Croonian Lecture was delivered by Charles Edouard Brown-Séquard, Esq., F.R.S.: it was entitled \"On the Relations between Muscular Irritability, Cadaveric Rigidity, and Putrefaction.\"\nCONTENTS\n\nOF VOL. 151.\n\nI. THE BAKERIAN LECTURE.—On the Absorption and Radiation of Heat by Gases and Vapours, and on the Physical Connexion of Radiation, Absorption, and Conduction.\nBy JOHN TYNDALL, Esq., F.R.S., Member of the Academies and Societies of Holland, Geneva, Göttingen, Zürich, Halle, Marburg, Breslau, la Société Philomatique of Paris, &c.; Professor of Natural Philosophy in the Royal Institution, and in the Government School of Mines . . . . . . . . . . page 1\n\nII. On an Extension of ARBOGAST'S Method of Derivations. By ARTHUR CAYLEY, Esq., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . 37\n\nIII. On the Equation for the Product of the Differences of all but one of the Roots of a given Equation. By ARTHUR CAYLEY, Esq., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . 45\n\nIV. On the Synthesis of Succinic and Pyrotartaric Acids. By MAXWELL SIMPSON, M.B. Communicated by Dr. Frankland, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61\n\nV. On the Calculus of Symbols, with Applications to the Theory of Differential Equations. By W. H. L. RUSSELL, Esq., A.B. Communicated by ARTHUR CAYLEY, Esq., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69\n\nVI. On the Properties of Liquid Carbonic Acid. By G. GORE, Esq. Communicated by Professor TYNDALL, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83\n\nVII. On Magnetic Storms and Earth-Currents. By CHARLES V. WALKER, Esq., F.R.S., F.R.A.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89\n\nVIII. On the Surface-condensation of Steam. By J. P. JOULE, LL.D., F.R.S., President of the Literary and Philosophical Society of Manchester, &c. . . . . . 133\n\nIX. On the Effect produced on the Deviations of the Compass by the Length and Arrangement of the Compass-Needles; and on a New Mode of correcting the Quadrantal\nDeviation. By Archibald Smith, Esq., M.A., F.R.S., late Fellow of Trinity College, Cambridge; and Frederick John Evans, Esq., R.N., Superintendent of the Compass Department of Her Majesty's Navy ........................................... page 161\n\nX. Liquid Diffusion applied to Analysis. By Thomas Graham, F.R.S., Master of the Mint ................................................................. 183\n\nXI. On the Porism of the in-and-circumscribed Polygon. By Arthur Cayley, Esq., F.R.S. .................................................................................. 225\n\nXII. Tables of the Weights of the Human Body and Internal Organs in the Sane and Insane of both Sexes at various Ages, arranged from 2614 post-mortem examinations. By Robert Boyd, M.D., F.R.C.P.L., Physician to the Somerset County Lunatic Asylum. Communicated by Dr. Sharpey, Sec. R.S. ........................................................................................................... 241\n\nXIII. On a New Auxiliary Equation in the Theory of Equations of the Fifth Order. By Arthur Cayley, Esq., F.R.S. .................................................................................. 263\n\nXIV. A Seventh Memoir on Quantics. By Arthur Cayley, Esq., F.R.S. ........................................................................................................... 277\n\nXV. On Systems of Linear Indeterminate Equations and Congruences. By Henry J. Stephen Smith, M.A., Fellow and Mathematical Lecturer of Balliol College, Oxford. Communicated by J. J. Sylvester, Esq., F.R.S. ........................................................................................................... 293\n\nXVI. On the Method of Symmetric Products, and on Certain Circular Functions connected with that Method. By the Rev. Robert Harley, F.R.A.S., Corresponding Member of the Literary and Philosophical Society of Manchester. Communicated by A. Cayley, Esq., F.R.S. ........................................................................................................... 327\n\nXVII. On the Double Tangents of a Curve of the Fourth Order. By Arthur Cayley, Esq., F.R.S. ........................................................................................................... 357\n\nXVIII. Electro-Physiological Researches.—Eleventh Series. On the Secondary Electromotor Power of Nerves, and its Application to the Explanation of certain Electro-Physiological Phenomena. By Signor Carlo Matteucci. Communicated by General Sabine, Treas. and V.P.R.S. ........................................................................................................... 363\n\nXIX. On Liquid Transpiration in relation to Chemical Composition. By Thomas Graham, F.R.S., Master of the Mint ........................................................................................................... 373\n\nXX. On the Structure and Growth of the Tooth of Echinus. By S. James A. Salter, M.B. Lond., F.L.S., F.G.S. Communicated by Thomas Bell, Esq., F.R.S. ........................................................................................................... 387\n\nXXI. On Fermat's Theorem of the Polygonal Numbers.—Part I. By Sir Frederick Pollock, F.R.S., Lord Chief Baron, &c. &c. ........................................................................................................... 409\n\nXXII. On the Great Magnetic Disturbance which extended from August 28 to September 7, 1859, as recorded by Photography at the Kew Observatory. By Balfour Stewart, A.M. ........................................................................................................... 423\nXXIII. On the Sources of the Nitrogen of Vegetation; with special reference to the Question whether Plants assimilate Free or uncombined Nitrogen. By John Bennet Lawes, F.R.S., F.C.S., Joseph Henry Gilbert, Ph.D., F.R.S., F.C.S., and Evan Pugh, Ph.D., F.C.S. . . . . . . . . . . . . . . . . . . . . . . . . 431\n\nXXIV. On the Indian Arc of Meridian. By the Venerable J. H. Pratt, M.A., Archdeacon of Calcutta. Communicated by Professor Stokes, Sec. R.S. . . . . . . . . . . . . . . . . . . 579\n\nXXV. Notes on the Generative Organs, and on the Formation of the Egg in the Annulosa. By John Lubbock, Esq., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595\n\nXXVI. On the Influence of Atmospheric Pressure upon some of the Phenomena of Combustion. By Dr. E. Frankland, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629\n\nXXVII. Account of Experiments made at Holyhead (North Wales) to ascertain the Transit-Velocity of Waves analogous to Earthquake Waves, through the Local Rock Formations. By Robert Mallet, C.E., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655\n\nXXVIII. On the Construction of Specula of Six-feet Aperture; and a selection from the Observations of Nebulae made with them. By the Earl of Rosse, K.P., &c., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681\n\nXXIX. On the Elimination of Urea and Urinary Water, in relation to the Period of the Day, Season, Exertion, Food, Prison Discipline, Weight of Body, and other influences acting in the Cycle of the Year. By Edward Smith, M.D., LL.B., F.R.S., Assistant-Physician to the Hospital for Consumption and Diseases of the Chest, Brompton, Corresponding Fellow of the Academy of Sciences and Arts of Montpellier, and of the Natural History Society of Montreal, &c. . . . . . . . . . . . . . 747\n\nIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835\n\nAPPENDIX.\n\nPresents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [ 1 ]\n\nERRATUM.\n\nPage 259 (seven lines from the bottom), upwards of 80 years, Females, Minimum, Encephalon, for 15:25 read 35:25.\nLIST OF ILLUSTRATIONS.\n\nPlate I.—Professor Tyndall on the Absorption and Radiation of Heat by Gases and Vapours.\n\nPlates II. III. IV.—Mr. C. V. Walker on Magnetic Storms and Earth-Currents.\n\nPlate V.—Messrs. Smith and Evans on the Effect of the Length of the Compass Needle on the Deviations of the Compass.\n\nPlates VI. VII. VIII.—Mr. S. J. A. Salter on the Structure and Growth of the Tooth of Echinus.\n\nPlates IX. X. XI.—Mr. B. Stewart on the Great Magnetic Disturbance of August 28 to September 7, 1859.\n\nPlates XII. XIII. XIV. XV.—Mr. J. B. Lawes, Dr. Gilbert, and Dr. Pugh on the Sources of the Nitrogen of Vegetation, &c.\n\nPlates XVI. XVII.—Mr. Lubbock on the Generative Organs, and on the Formation of the Egg in the Annulosa.\n\nPlates XVIII. XIX.—Dr. E. Frankland on the Influence of Atmospheric Pressure upon some of the Phenomena of Combustion.\n\nPlates XX. XXI. XXII. XXIII.—Mr. Mallet on the Transit-Velocity of Earthquake Waves.\n\nPlates XXIV. XXV. XXVI. XXVII. XXVIII. XXIX. XXX. XXXI.—The Earl of Rosse on the Construction of Specula of 6-feet Aperture.\n\nPlates XXXII. XXXIII. XXXIV. XXXV. 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