Front Matter

ADVERTISEMENT. The 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. But 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. It 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 thanks, 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. The 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. A 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. Observatories. | Armagh | Kew | |--------|-----| | Cape of Good Hope | Liverpool | | Dublin | Madras | | Edinburgh | Oxford (Radcliffe) | | Greenwich | | Institutions. | Barbadoes | Library and Museum. | |-----------|---------------------| | Calcutta | Asiatic Society. | | | Geological Museum. | | Cambridge | Philosophical Society. | | Cape Town | South African Library. | | Dublin | Royal Dublin Society. | | | Royal Irish Academy. | | Edinburgh | Royal Society. | | London | Admiralty Library. | | | Chemical Society. | | | Entomological Society. | | | Geological Society. | | | Geological Survey of Great Britain. | | | Horticultural Society. | | | Institute of British Architects. | | | Institution of Civil Engineers. | | | Linnean Society. | | | London Institution. | | | Queen's Library. | | | Royal Asiatic Society. | | | Royal Astronomical Society. | | | Royal College of Physicians. | | | Royal Geographical Society. | | | Royal Institution of Great Britain. | | | Royal Medical and Chirurgical Society. | | | Royal Society of Literature. | | | Society of Antiquaries. | | | Society of Arts. | | | The Treasury Library. | | | United Service Museum. | | | Zoological Society. | | Malta | Public Library. | | Manchester | Literary and Philosophical Society. | | Oxford | Ashmolean Society. | | | Radcliffe Library. | | Swansea | Royal Institution. | | Sydney | University Library. | | Woolwich | Royal Artillery Library. | Belgium. | Brussels | Académie Royale de Médecine. | | | Royal Academy of Sciences. | Denmark. | Altona | Royal Observatory. | | Copenhagen | Royal Society of Sciences. | France. | Montpellier | Academy of Sciences. | | | Faculté de Médecine. | | Paris | Academy of Sciences. | | | Dépôt de la Marine. | | | École des Mines. | | | Geographical Society. | | | Geological Society. | | | Jardin des Plantes. | | | Société d'Encouragement pour l'Industrie Nationale. | | Toulouse | Academy of Sciences. | Germany. | Berlin | Royal Academy of Sciences. | | | Society of Experimental Philosophy. | | Jena | Cesarean Acad. of Naturalists. | | Frankfort | Natural History Society. | | Giessen | University. | | Göttingen | University. | | Hamburg | Naturwissenschaftlicher-Verein. | | Königsberg | Königlichen Physikalisch Ökonomischen Gesellschaft. | | Leipzig | Royal Saxon Society of Sciences. | | Mannheim | Observatory. | | Munich | Royal Academy of Sciences. | | Prague | Bohemian Society of Sciences. | | Vienna | Imperial Academy of Sciences. | | | Geologische Reichsanstalt. | | Würzburg | Physico-Medical Society. | Hungary. | Pesth | Hungarian Academy of Sciences. | Italy. | Catanea | Accademia Gioenia di Scienze Naturali. | | Milan | Institute of Sciences, Letters and Arts. | | Modena | Italian Society of Sciences. | | Naples | Institute of Sciences. | | Palermo | Academy of Sciences and Letters. | | Rome | Academy de' Nuovi Lincei. | | | Collegio Romano. | | Turin | Royal Academy of Sciences. | | Venice | Institute of Sciences, Letters, and Arts. | Java. | Batavia | Batavian Society of Sciences. | Netherlands. | Amsterdam | Royal Institute. | | Haarlem | Dutch Society of Sciences. | | Rotterdam | Batavian Society of Experimental Philosophy. | Portugal. | Lisbon | Royal Academy of Sciences. | Russia. | Kazan | Imperial University. | | Moscow | Imperial Society of Naturalists. | | Pulkowa | Observatory. | | St. Petersburg | Imperial Academy of Sciences. | Spain. | Cadiz | Observatory. | | Madrid | Royal Academy of Sciences. | Sweden and Norway. | Christiania | Royal University. | | Drontheim | Royal Society of Sciences. | | Gottenburg | Kongl. Vetenskaps och Vitterhets Samhälle. | | Stockholm | Royal Academy of Sciences. | Switzerland. | Bern | Allg. Schweizerischen Gesellschaft. | | Geneva | Société de Phys. et d'Hist. Naturelle. | Transylvania. | Klausenburg | Society of the Transylvanian Museum. | United States. | Albany | New York State Library. | | Boston | American Academy of Sciences. | | Newhaven (Conn.) | The Editors of the American Journal. | | Cambridge | Harvard University. | | Philadelphia | Academy of Natural Sciences. | | | American Philosophical Society. | | Washington | Smithsonian Institution. | | | Observatory. | The fifty Foreign Members of the Royal Society. A 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. | Observatories | Institutions | |--------------------|--------------------------------------------------| | Altona | Aberdeen University | | Armagh | Berlin Academy | | Berlin | Bologna Academy | | Breslau | Boston American Academy of Sciences | | Brussels | Brunswick, U.S. Bowdoin College | | Cadiz | Cambridge Trinity College Library | | Cambridge | Cambridge, U.S. Harvard University | | Cape of Good Hope | Dublin University | | Coimbra | Edinburgh University | | Copenhagen | Royal Society | | Dorpat | Glasgow University | | Dublin | Göttingen University | | Edinburgh | Leyden University | | Helsingfors | London Board of Ordnance | | Königsberg | Queen's Library | | Madras | Royal Institution | | Mannheim | Royal Society | | Marseille | Oxford Savilian Library | | Milan | Paris Academy of Sciences | | Munich | Board of Longitude | | Oxford | Dépôt de la Marine | | Palermo | Pesth Hungarian Academy | | Paris | Philadelphia American Philosophical Society | | Seeberg | St. Andrews University | | Tübingen | St. Petersburg Imperial Academy | | Turin | Stockholm Royal Academy of Sciences | | Vienna | Upsal Royal Society | | Wilna | Waterville, Maine (U.S.) College | | Individuals | | |--------------------|--------------------------------------------------| | Christie, S. H., Esq. | Twickenham. | | Lubbock, Sir John William, Bart. | London. | | Lowndes' Professor of Astronomy | Cambridge. | | Plumian Professor of Astronomy | Cambridge. | | President of the Royal Society | London. | | Smyth, Vice-Admiral W. H. | Aylesbury. | | South, Sir James | Kensington. | | The Earl of Rosse | Parsonstown. | A List of Observatories, Institutions and Individuals, entitled to receive a Copy of the Magnetical and Meteorological Observations made at the Royal Observatory, Greenwich. ### Observatories - **Bombay** ................. Lieut. P. W. Mitcheson. - **Cambridge, United States** .... Prof. J. Lovering. - **Christiania** ............. C. Hansteen. - **Gotha** .................. P. A. Hansen. - **Heidelberg** .............. M. Tiedemann. - **Kew** .................... B. Stewart. - **Kremsmünster** .......... P. A. Reshuber. - **Leipzig** ................ Professor Möbius. - **Lisbon** .................. Señor da Silveira. - **Marburg** ................ Professor Gerling. - **Prague** .................. K. Jelinek. - **Stockholm** ............... Professor H. Selander. - **Toronto** ................ Professor Kingston. - **Upsal** ................... Professor Svanberg. - **Washington** ............. Capt. Gilliss. ### Institutions - **Bombay** ................ Geographical Society. - **Bonn** .................... University. - **Boston, U.S.** ........... The Public Library (late Bowditch). - **Cambridge** .............. Philosophical Society. - **Cherkow** ................. University. - **Falmouth** ............... Royal Cornwall Polytechnic Society. - **London** .................. House of Lords, Library. - **London** .................. House of Commons, Library. - **London** .................. King's College. - **London** .................. Royal Society. - **London** .................. University College, Library. - **Oxford** .................. Radcliffe Observatory. - **Paris** .................... Meteorological Society. - **St. Bernard** ............. Convent. - **Washington** ............. Smithsonian Institution. - **Woolwich** ............... Office of Mag. and Met. Publication. ### Individuals - **Bache, Dr. A. D.** ........ Washington. - **Buys Ballot, Dr.** ........ Utrecht. - **Dove, Prof. H. W.** ........ Berlin. - **Erman, Dr. Adolph** ...... Berlin. - **Fox, R. W., Esq.** ........ Falmouth. - **Harris, Sir W. Snow** ..... Plymouth. - **Howard, Luke, Esq.** ...... Tottenham. - **Kaemtz, Prof. L. F.** ...... Dorpat. - **Kreil, Prof. K.** .......... Vienna. - **Kupffer, A. T.** .......... St. Petersburg. *(Twelve copies for distribution to the Russian Mag. and Met. Obs.)* - **Lloyd, Rev. Dr.** .......... Dublin. - **Loomis, Prof. E.** .......... Yale College, Newhaven (Conn.). - **Phillips, Prof. John** ...... Oxford. - **Quetelet, A.** ............. Brussels. - **Sabine, Major-General, R.A.** London. - **Señor de Souza** .......... Coimbra. - **Vernon, G. V., Esq.** ...... Manchester. - **Wartmann, Prof. Elie** ..... Geneva. - **Younghusband, Col., R.A.** Woolwich. CONTENTS. I. On the Relation of Radiant Heat to Aqueous Vapour. By John Tyndall, F.R.S., Member of the Academies and Societies of Holland, Geneva, Göttingen, Zürich, Halle, Marburg, Breslau, Upsala, la Société Philomathique of Paris, Cam. Phil. Soc. &c.; Professor of Natural Philosophy in the Royal Institution ............................................................................................................. . 1 II. On the Volumes of Pedal Surfaces. By T. A. Hirst, F.R.S. .........................................................................................................................................................................................................................................................................................13 III. On the Archeopteryx of von Meyer, with a description of the Fossil Remains of a Long-tailed species, from the Lithographic Stone of Solenhofen. By Professor Owen, F.R.S. &c. .........................................................................................................................................................................................................................................................................................33 IV. On the Strains in the Interior of Beams. By George Biddell Airy, F.R.S., Astronomer Royal .........................................................................................................................................................................................................................................................................................49 V. On the Reflexion of Polarized Light from Polished Surfaces, Transparent and Metallic. By the Rev. Samuel Haughton, M.A., F.R.S., Fellow of Trinity College, Dublin ...........................................................................................................................................................................................................................................................................81 VI. On the Exact Form of Waves near the Surface of Deep Water. By William John Macquorn Rankine, C.E., LL.D., F.R.SS. L. & E. .........................................................................................................................................................................................................................................................................................127 VII. Photo-chemical Researches.—Part V. On the Direct Measurement of the Chemical Action of Sunlight. By Robert Bunsen, For. Mem. R.S., Professor of Chemistry in the University of Heidelberg, and Henry E. Roscoe, B.A., Ph.D., Professor of Chemistry in Owens College, Manchester ...............................................................................................................................................................................................................................................................................139 VIII. On the Immunity enjoyed by the Stomach from being digested by its own Secretion during Life. By F. W. Payy, M.D. .......................................................................................................................................................................................................................................................................................161 IX. On Thallium. By William Crookes, Esq. Communicated by Professor G. G. Stokes, Sec. R.S. .........................................................................................................................................................................................................................................................................................173 X. On the Distribution of Surfaces of the Third Order into Species, in reference to the absence or presence of Singular Points, and the reality of their Lines. By Dr. Schlafli, Professor of Mathematics in the University of Berne. Communicated by Arthur Cayley, F.R.S. .......................................................................................................................................................................................................................................................................193 MDCCCLXIII. XI. On the Tides of the Arctic Seas. By the Rev. Samuel Haughton, M.A., F.R.S., Fellow of Trinity College, Dublin. Part I. On the Diurnal Tides of Port Leopold, North Somerset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . page 243 XII. Results of the Magnetic Observations at the Kew Observatory, from 1857 and 1858 to 1862 inclusive.—Nos. I. and II. By Major-General Edward Sabine, R.A., President of the Royal Society . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 XIII. On the Diurnal Inequalities of Terrestrial Magnetism, as deduced from observations made at the Royal Observatory, Greenwich, from 1841 to 1857. By George Biddell Airy, F.R.S., Astronomer Royal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 XIV. Researches on the Refraction, Dispersion, and Sensitiveness of Liquids. By J. H. Gladstone, Ph.D., F.R.S., and the Rev. T. P. Dale, M.A., F.R.A.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 XV. Researches into the Chemical Constitution of Narcotine, and of its Products of Decomposition.—Part I. By Augustus Matthiessen, F.R.S., Lecturer on Chemistry in St. Mary's Hospital, London, and G. C. Foster, B.A., Lecturer on Natural Philosophy in Anderson's University, Glasgow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 LIST OF ILLUSTRATIONS. Plates I. to IV.—Professor Owen on the Archeopteryx. Plates V. to VII.—Mr. G. B. Airy on the Strains in the Interior of Beams. Plate VIII.—Rev. S. Haughton on the Reflexion of Polarized Light from Polished Surfaces, Transparent and Metallic. Plate IX.—Professor Bunsen and Dr. H. E. Roscoe's Photo-chemical Researches. Plates X. to XII.—Rev. S. Haughton on the Tides of the Arctic Seas. Plates XIII. to XV.—Major-General Sabine on the Magnetic Observations at the Kew Observatory. Plates XVI. to XXIII.—Mr. G. B. Airy on the Diurnal Inequalities of Terrestrial Magnetism. XVI. On the Influence of Temperature on the Electric Conducting-Power of Thallium and Iron. By A. Matthiessen, F.R.S., Lecturer on Chemistry in St. Mary's Hospital, and C. Vogt, Ph.D. XVII. On the Molecular Mobility of Gases. By Thomas Graham, F.R.S., Master of the Mint XVIII. On the Peroxides of the Radicals of the Organic Acids. By Sir B. C. Brodie, Bart., F.R.S., Professor of Chemistry in the University of Oxford XIX. An Account of Experiments on the Change of the Elastic Force of a Constant Volume of Atmospheric Air, between 32° F. and 212° F., and also on the Temperature of the Melting-point of Mercury. By Balfour Stewart, M.A., F.R.S. XX. On some Compounds and Derivatives of Glyoxylic Acid. By Henry Debus, Ph.D., F.R.S. XXI. On Skew Surfaces, otherwise Scrolls. By Arthur Cayley, F.R.S. XXII. On the Differential Equations of Dynamics. A sequel to a Paper on Simultaneous Differential Equations. By George Boole, F.R.S., Professor of Mathematics in Queen's College, Cork XXIII. On the Nature of the Sun's Magnetic Action upon the Earth. By Charles Chambers. Communicated by General Sabine, P.R.S. XXIV. On the Calculus of Symbols.—Third Memoir. By W. H. L. Russell, Esq., A.B. Communicated by A. Cayley, F.R.S. XXV. Numerical Elements of Indian Meteorology. By Hermann de Schlagintweit, Ph.D., LL.D., Corr. Memb. Acad. Munich, Madrid, Lisbon, &c. Communicated by Major-General Sabine, P.R.S. XXVI. On the Structure and formation of the so-called Apolar, Unipolar, and Bipolar Nerve-cells of the Frog. By Lionel S. Beale, F.R.S., M.B., Fellow of the Royal College of Physicians; Professor of Physiology and of General and Morbid Anatomy in King's College, London; Physician to King's College Hospital, &c. XXVII. On the Rigidity of the Earth. By W. Thomson, LL.D., F.R.S., Professor of Natural Philosophy in the University of Glasgow .................................................. page 573 XXVIII. Dynamical Problems regarding Elastic Spheroidal Shells and Spheroids of Incompressible Liquid. By Professor W. Thomson, LL.D., F.R.S. ............................................. 583 XXIX. First Analysis of One Hundred and Seventy-seven Magnetic Storms, registered by the Magnetic Instruments in the Royal Observatory, Greenwich, from 1841 to 1857. By George Biddell Airy, Astronomer Royal ............................................................................................................................ 617 XXX. Results of hourly Observations of the Magnetic Declination made by Sir Francis Leopold M'Clinstock, and the Officers of the Yacht 'Fox,' at Port Kennedy, in the Arctic Sea, in the Winter of 1858–59; and a Comparison of these Results with those obtained by Captain Rochfort Maguire, and the Officers of Her Majesty's Ship 'Plover,' in 1852, 1853, and 1854, at Point Barrow. By Major-General Edward Sabine, R.A., President of the Royal Society .................................................................................................................................................................................. 649 Index ........................................................................................................................................................................ 665 APPENDIX. Presents ........................................................................................................................................... [ 1 ] LIST OF ILLUSTRATIONS. Plate XXIV.—Mr. Balfour Stewart on Experiments with an Air-Thermometer. Plates XXV. to XXVII.—Mr. C. Chambers on the Nature of the Sun's Magnetic Action upon the Earth. Plates XXVIII. to XXXII.—Dr. H. de Schlagintweit on the Numerical Elements of Indian Meteorology. Plates XXXIII. to XL.—Professor Beale on the Structure of the so-called Apolar, Unipolar, and Bipolar Nerve-cells of the Frog. Plate XLI.—Major-General Sabine on the Results of hourly Observations of the Magnetic Declination at Port Kennedy. ADJUDICATION of the MEDALS of the ROYAL SOCIETY for the year 1863 by the PRESIDENT and COUNCIL. The Copley Medal to the Rev. Adam Sedgwick, F.R.S., for his original observations and discoveries in the Geology of the Palaeozoic Series of Rocks, and more especially for his determination of the characters of the Devonian System, by observations of the order of Superposition of the Killas Rocks and their Fossils, in Devonshire. A Royal Medal to the Rev. Miles J. Berkeley, for his Researches in Cryptogamic Botany, especially Mycology. A Royal Medal to John P. Gassiot, Esq., F.R.S., for his Researches on the Voltaic Battery and Current, and on the Discharge of Electricity through Attenuated Media. The Bakerian Lecture was delivered by Henry Clifton Sorby, F.R.S.: it was entitled, "On the Direct Correlation of Mechanical and Chemical Forces." The Croonian Lecture was delivered by Professor Joseph Lister, F.R.S.: it was entitled, "On the Coagulation of the Blood." ## CONTENTS OF VOL. 153. | I. | On the Relation of Radiant Heat to Aqueous Vapour. By John Tyndall, F.R.S., Member of the Academies and Societies of Holland, Geneva, Göttingen, Zürich, Halle, Marburg, Breslau, Upsala, la Société Philomathique of Paris, Cam. Phil. Soc. &c.; Professor of Natural Philosophy in the Royal Institution | |---|---| | II. | On the Volumes of Pedal Surfaces. By T. A. Hirst, F.R.S. | | III. | On the Archeopteryx of von Meyer, with a description of the Fossil Remains of a Long-tailed species, from the Lithographic Stone of Solenhofen. By Professor Owen, F.R.S. &c. | | IV. | On the Strains in the Interior of Beams. By George Biddell Airy, F.R.S., Astronomer Royal | | V. | On the Reflexion of Polarized Light from Polished Surfaces, Transparent and Metallic. By the Rev. Samuel Haughton, M.A., F.R.S., Fellow of Trinity College, Dublin | | VI. | On the Exact Form of Waves near the Surface of Deep Water. By William John Macquorn Rankine, C.E., LL.D., F.R.S.S. L. & E. | | VII. | Photo-chemical Researches.—Part V. On the Direct Measurement of the Chemical Action of Sunlight. By Robert Bunsen, For. Mem. R.S., Professor of Chemistry in the University of Heidelberg, and Henry E. Roscoe, B.A., Ph.D., Professor of Chemistry in Owens College, Manchester | | VIII. | On the Immunity enjoyed by the Stomach from being digested by its own Secretion during Life. By F. W. Pavy, M.D. | | IX. | On Thallium. By William Crookes, Esq. Communicated by Professor G. G. Stokes, Sec. R.S. | X. On the Distribution of Surfaces of the Third Order into Species, in reference to the absence or presence of Singular Points, and the reality of their Lines. By Dr. Schläfli, Professor of Mathematics in the University of Berne. Communicated by Arthur Cayley, F.R.S. . . . . . . . . . . . . . . . . . . . . . . page 193 XI. On the Tides of the Arctic Seas. By the Rev. Samuel Haughton, M.A., F.R.S., Fellow of Trinity College, Dublin . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 XII. Results of the Magnetic Observations at the Kew Observatory, from 1857 and 1858 to 1862 inclusive.—Nos. I. and II. By Major-General Edward Sabine, R.A., President of the Royal Society . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 XIII. On the Diurnal Inequalities of Terrestrial Magnetism, as deduced from observations made at the Royal Observatory, Greenwich, from 1841 to 1857. By George Biddell Airy, F.R.S., Astronomer Royal . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 XIV. Researches on the Refraction, Dispersion, and Sensitiveness of Liquids. By J. H. Gladstone, Ph.D., F.R.S., and the Rev. T. P. Dale, M.A., F.R.A.S. . . . . . . . . . 317 XV. Researches into the Chemical Constitution of Narcotine, and of its Products of Decomposition.—Part I. By Augustus Matthiessen, F.R.S., Lecturer on Chemistry in St. Mary's Hospital, London, and G. C. Foster, B.A., Lecturer on Natural Philosophy in Anderson's University, Glasgow . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 XVI. On the Influence of Temperature on the Electric Conducting-Power of Thallium and Iron. By A. Matthiessen, F.R.S., Lecturer on Chemistry in St. Mary's Hospital, and C. Vogt, Ph.D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 XVII. On the Molecular Mobility of Gases. By Thomas Graham, F.R.S., Master of the Mint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 XVIII. On the Peroxides of the Radicals of the Organic Acids. By Sir B. C. Brodie, Bart., F.R.S., Professor of Chemistry in the University of Oxford . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 XIX. An Account of Experiments on the Change of the Elastic Force of a Constant Volume of Atmospheric Air, between 32° F. and 212° F., and also on the Temperature of the Melting-point of Mercury. By Balfour Stewart, M.A., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 XX. On some Compounds and Derivatives of Glyoxylie Acid. By Henry Debus, Ph.D., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 XXI. On Skew Surfaces, otherwise Scrolls. By Arthur Cayley, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 XXII. On the Differential Equations of Dynamics. A sequel to a Paper on Simultaneous Differential Equations. By George Boole, F.R.S., Professor of Mathematics in Queen's College, Cork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 XXIII. *On the Nature of the Sun's Magnetic Action upon the Earth.* By Charles Chambers. Communicated by General Sabine, P.R.S. . . . . . . . . . page 503 XXIV. *On the Calculus of Symbols.—Third Memoir.* By W. H. L. Russell, Esq., A.B. Communicated by A. Cayley, F.R.S. . . . . . . . . . . . . . . . . . 517 XXV. *Numerical Elements of Indian Meteorology.* By Hermann de Schlagintweit, Ph.D., LL.D., Corr. Memb. Acad. Munich, Madrid, Lisbon, &c. Communicated by Major-General Sabine, P.R.S. . . . . . . . . . . . . . . . . . 525 XXVI. *On the Structure and formation of the so-called Apolar, Unipolar, and Bipolar Nerve-cells of the Frog.* By Lionel S. Beale, F.R.S., M.B., Fellow of the Royal College of Physicians; Professor of Physiology and of General and Morbid Anatomy in King's College, London; Physician to King's College Hospital, &c. . . . . . 543 XXVII. *On the Rigidity of the Earth.* By W. Thomson, LL.D., F.R.S., Professor of Natural Philosophy in the University of Glasgow . . . . . . . . . . . . 573 XXVIII. *Dynamical Problems regarding Elastic Spheroidal Shells and Spheroids of Incompressible Liquid.* By Professor W. Thomson, LL.D., F.R.S. . . . . . . . . 583 XXIX. *First Analysis of One Hundred and Seventy-seven Magnetic Storms, registered by the Magnetic Instruments in the Royal Observatory, Greenwich, from 1841 to 1857.* By George Biddell Airy, Astronomer Royal . . . . . . . . . . . . . . . . . 617 XXX. *Results of hourly Observations of the Magnetic Declination made by Sir Francis Leopold Mc Clintock, and the Officers of the Yacht 'Fox,' at Port Kennedy, in the Arctic Sea, in the Winter of 1858–59; and a Comparison of these Results with those obtained by Captain Rochfort Maguire, and the Officers of Her Majesty's Ship 'Plover,' in 1852, 1853, and 1854, at Point Barrow.* By Major-General Edward Sabine, R.A., President of the Royal Society . . . . . . . . 649 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 APPENDIX. Presents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [ 1 ] LIST OF ILLUSTRATIONS. Plates I. to IV.—Professor Owen on the Archeopteryx. Plates V. to VII.—Mr. G. B. Airy on the Strains in the Interior of Beams. Plate VIII.—Rev. S. Haughton on the Reflexion of Polarized Light from Polished Surfaces, Transparent and Metallic. Plate IX.—Professor Bunsen and Dr. H. E. Roscoe's Photo-chemical Researches. Plates X. to XII.—Rev. S. Haughton on the Tides of the Arctic Seas. Plates XIII. to XV.—Major-General Sabine on the Magnetic Observations at the Kew Observatory. Plates XVI. to XXIII.—Mr. G. B. Airy on the Diurnal Inequalities of Terrestrial Magnetism. Plate XXIV.—Mr. Balfour Stewart on Experiments with an Air-Thermometer. Plates XXV. to XXVII.—Mr. C. Chambers on the Nature of the Sun's Magnetic Action upon the Earth. Plates XXVIII. to XXXII.—Dr. H. de Schlagintweit on the Numerical Elements of Indian Meteorology. Plates XXXIII. to XL.—Professor Beale on the Structure of the so-called Apolar, Unipolar, and Bipolar Nerve-cells of the Frog. Plate XLI.—Major-General Sabine on the Results of hourly Observations of the Magnetic Declination at Port Kennedy.