Front Matter

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. - Cape of Good Hope. - Dublin. - Edinburgh. - Greenwich. - Madras. - Oxford (Radcliffe). **Institutions.** - Barbadoes ........ Library and Museum. - Calcutta .......... Asiatic Society. - Geological Museum. - Cambridge ......... Philosophical Society. - 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. - Medical and Chirurgical Society. - Queen's Library. - Royal Asiatic Society. - Royal Astronomical Society. - Royal College of Physicians. - Royal Geographical Society. - Royal Institution of Great Britain. - 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. - Woolwich ......... Royal Artillery Library. **Belgium.** - Brussels .......... Royal Academy of Sciences. **Denmark.** - Altona ........... Royal Observatory. - Copenhagen ....... Royal Society of Sciences. **France.** - Paris ............ Academy of Sciences. - Dépôt de la Marine. - Ecole des Mines. - Entomological Society. - Geographical Society. - Paris ............ Geological Society. - Jardin des Plantes. - Toulouse ........ Academy of Sciences. **Germany.** - Berlin ........... Royal Academy of Sciences. - Society of Experimental Philosophy. - Bonn ............ Cesarean Acad. of Naturalists. - Frankfort ........ Natural History Society. - Giessen .......... University. - Göttingen ........ University. - Leipzig .......... Royal Saxon Society of Sciences. - Mannheim ........ Observatory. - Munich ........... Royal Academy of Sciences. - Vienna ........... Imperial Academy of Sciences. - Würzburg ......... Physico-Medical Society. **Italy.** - Milan ........... Institute of Sciences, Letters and Arts. - Modena .......... Italian Society of Sciences. - Naples .......... Institute of Sciences. - Rome ........... The Academy de' Nuovi Lincei. - The Collegio Romano. - Turin ........... Royal Academy of Sciences. **Netherlands.** - Amsterdam ....... Royal Institute. - Haarlem .......... Dutch Society of Sciences. - Rotterdam ........ Batavian Society of Experimental Philosophy. **Portugal.** - Lisbon ........... Royal Academy of Sciences. **Russia.** - Moscow .......... Imperial Society of Naturalists. - Pulkowa .......... Observatory. - St. Petersburgh .. Imperial Academy of Sciences. **Spain.** - Cadiz ........... Observatory. - Madrid .......... Royal Academy of Sciences. **Sweden and Norway.** - Drontheim ....... Royal Society of Sciences. - Stockholm ....... Royal Academy of Sciences. **Switzerland.** - Geneva .......... Société de Phys. et d'Hist. Naturelle. **United States.** - Albany .......... New York State Library. - Boston .......... American Academy of Sciences. - Cambridge ....... Harvard University. - Philadelphia ..... 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 | | Marseilles | Oxford Savilian Library | | Milan | Paris Academy of Sciences | | Munich | Board of Longitude | | Oxford | Dépôt de la Marine | | Palermo | Philadelphia American Philosophical Society | | Paris | St. Andrews University | | Seeberg | St. Petersburg Imperial Academy | | Trevandrum | Stockholm Royal Academy of Sciences | | Tübingen | Upsal Royal Society | | Turin | Waterville (U.S.) College | | Individuals | |-------------| | Christie, S. H., Esq. Twickenham | | Lubbock, Sir John William, Bart. London | | Lowndes Professor of Astronomy Cambridge | | Plumian Professor of Astronomy | | President of the Royal Society London | | Smyth, Rear-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 - Cairo - Cambridge, United States - Christiania - Gotha - Heidelberg - Kew - Kremsmünster - Leipsic - Marburg - Prague - Stockholm - Toronto - Upsal - Washington ### Institutions - Bombay - Bonn - Bowditch Library - Cambridge - Cherckow - Falmouth - London - Oxford - Paris - St. Bernard - Washington - Woolwich ### Individuals - Bache, Dr. A. D. - Barlow, P. W., Esq. - Ballot, Dr. Buys - Demidoff, Prince Anatole de - Dovè, Prof. H. W. - Erman, Dr. Adolph - Fox, R. W., Esq. - Gilliss, Lt. J. M., U.S. Navy - Harris, Sir W. Snow - Howard, Luke, Esq. - Humboldt, Baron von - Kaemtz, Prof. L. F. - Kreil, Prof. K. - Kupffer, A. T. - Lloyd, Rev. Dr. - Loomis, Professor - Lovering, Professor - Melvill, Sir J. C. - Pegado, Dr. - Phillips, John, Esq. - Quetelet, A. - Reid, Col. Sir W., R.E. - Riddell, Lieut.-Colonel, R.A. - Sabine, Major-General, R.A. - Sonftenberg, Baron von - Vernon, G. V., Esq. - Wartmann, Professor Elie - Younghusband, Capt., R.A. (Twelve copies for distribution to the Russian Mag. and Met. Obs.) - Dublin - New York University - Cambridge, U.S. - East India House - Lisbon - Oxford - Brussels - Malta - Woolwich - London - Prague - Manchester - Geneva - Woolwich CONTENTS. I. On the Evidence of the existence of the Decennial Inequality in the Solar-diurnal Magnetic Variations, and its non-existence in the Lunar-diurnal Variation, of the Declination at Hobarton. By Major-General Edward Sabine, of the Royal Artillery, Treas. and V.P. of the Royal Society . . . . . . . . . . . . . . . . . page 1 II. On the Stability of Loose Earth. By W. J. Macquorn Rankine, F.R.S. . . . . . . . . 9 III. On the Geometrical Isomorphism of Crystals. By Henry James Brooke, F.R.S., Hon. M.C.P.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 IV. On the Equation of Laplace's Functions, &c. By W. F. Donkin, M.A., F.R.S., F.R.A.S., Savilian Professor of Astronomy in the University of Oxford . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 V. Researches on Organo-metallic Bodies.—Third Memoir. On a New Series of Organic Acids containing Nitrogen. By E. Frankland, Ph.D., F.R.S., Professor of Chemistry in Owens College, Manchester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 VI. An account of the Two Methods of Reproduction in Daphnia, and of the Structure of the Ephippium. By John Lubbock, Esq., F.G.S. Communicated by Charles Darwin, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 VII. On the Scelidotherium (Scelidotherium leptocephalum, Owen). By Professor Owen, F.R.S. &c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 VIII. On the Structure and Development of the Cysticercus cellulosae, as found in the Muscles of the Pig. By George Rainey, M.R.C.S., Lecturer on Anatomy and Demonstrator of Practical and Microscopical Anatomy at St. Thomas's Hospital. Communicated by R. D. Thomson, M.D., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 IX. Electro-Physiological Researches. Physical and Chemical Phenomena of Muscular Contraction.—Tenth Series. Part I. By Carlo Matteucci, Professor in the University of Pisa. Communicated by Michael Faraday, Esq., D.C.L., F.R.S. &c. 129 X. The Bakerian Lecture.—Experimental Relations of Gold (and other Metals) to Light. By Michael Faraday, Esq., D.C.L., F.R.S., Fullerian Prof. Chem. Royal Institution, Foreign Associate of the Acad. Sciences, Paris, Ord. Boruss. pour le Mérite, Eq., Memb. Royal and Imp. Acad. of Sciences, Petersburgh, Florence, Copenhagen, Berlin, Göttingen, Modena, Stockholm, Munich, Bruxelles, Vienna, Bologna, Commander of the Legion of Honour, &c. &c. . . . . . . . . . . . page 145 XI. On Autopolar Polyedra. By the Rev. Thomas P. Kirkman, A.M., F.R.S., Rector of Croft with Southworth. Communicated by Arthur Cayley, Esq., F.R.S. . . 183 XII. On the K-partitions of the R-gon and R-ace. By the Rev. Thomas P. Kirkman, A.M., F.R.S., Rector of Croft with Southworth. Communicated by Arthur Cayley, Esq., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 XIII. A Memoir upon Caustics. By Arthur Cayley, Esq. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 LIST OF ILLUSTRATIONS. Plate I.—Major-General Sabine on the Decennial Magnetic Inequality at Hobarton. Plates II. III. IV. V.—Mr. H. J. Brooke on the Geometrical Isomorphism of Crystals. Plates VI. VII.—Mr. John Lubbock on Two Methods of Reproduction in *Daphnia*, and on the Structure of the Ephippium. Plates VIII. IX.—Professor Owen on the Scelidotheres. Plates X. XI.—Mr. George Rainey on the Structure and Development of the *Cysti-cercus cellulosae*, as found in the Muscles of the Pig. Plates XII. XIII. XIV.—The Rev. Thomas P. Kirkman on Autopolar Polyedra. CONTENTS. XIV. On the Dioecious Character of the Rotifera. By Philip Henry Gosse. Communicated by Thomas Bell, F.R.S., P.L.S., F.G.S., Professor of Zoology in King's College .................................................. page 313 XV. On the Structure and Motion of Glaciers. By John Tyndall, F.R.S., Professor of Natural Philosophy, Royal Institution; and Thomas H. Huxley, F.R.S., Fullerian Professor of Physiology, Royal Institution ................................................................. 327 XVI. Description of the Fatal Membranes and Placenta of the Elephant (Elephas Indicus, Cuv.), with Remarks on the value of placental characters in the classification of the Mammalia. By Professor Owen, F.R.S. ........................................................................................................... 347 XVII. Photo-chemical Researches.—Part I. Measurement of the Chemical Action of Light. By Robert Bunsen, Professor of Chemistry at the University of Heidelberg, and Henry Enfield Roscoe, B.A., Ph.D., Professor of Chemistry at Owens College, Manchester. Communicated by Professor Stokes, Sec. R.S. ........................................................................................................... 355 XVIII. Photo-chemical Researches.—Part II. Phenomena of Photo-chemical Induction. By Professor Bunsen, Professor of Chemistry at the University of Heidelberg, and Henry Enfield Roscoe, B.A., Ph.D., Professor of Chemistry at Owens College, Manchester. Communicated by Professor Stokes, Sec. R.S. ........................................................................................................... 381 XIX. On the Immediate Principles of Human Excrements in the Healthy State. By W. Marcet, M.D., F.C.S., Assistant Physician to the Westminster Hospital. Communicated by H. Bence Jones, M.D., F.R.S. ........................................................................................................... 403 XX. A Memoir on Curves of the Third Order. By A. Cayley, Esq., F.R.S. ........................................................................................................... 415 XXI. On some of the Products of the Destructive Distillation of Boghead Coal.—Part I. By C. Greville Williams, Lecturer on Chemistry in the Normal College, Swansea. Communicated by Dr. Sharpey, Sec. R.S. ........................................................................................................... 447 XXII. On an Element of Strength in Beams subjected to Transverse Strain, named by the author "The Resistance of Flexure."—Second Paper. By William Henry Barlow, Esq., F.R.S. &c. ........................................................................................................... 463 XXIII. A Memoir on the Symmetric Functions of the Roots of an Equation. By Arthur Cayley, Esq., F.R.S. ................. page 489 XXIV. On Hourly Observations of the Magnetic Declination made by Captain Rochfort Maguire, R.N., and the Officers of H.M.S. 'Plover', in 1852, 1853 and 1854, at Point Barrow, on the shores of the Polar Sea. By Major-General Edward Sabine, R.A., D.C.L., Treas. and Vice-President ..................... 497 XXV. Researches on Silica. By Colonel Philip Yorke, F.R.S. .......... 533 XXVI. On the Fructification of certain Sphaeriaceous Fungi. By Frederick Currey, M.A., F.L.S. Communicated by W. J. Hooker, M.D., F.R.S. .......... 543 XXVII. Researches on a New Class of Alcohols. By Augustus William Hofmann, LL.D., F.R.S., and Augustus Cahours, F.C.S. ................. 555 XXVIII. Researches on the Phosphorus-Bases. By Augustus William Hofmann, LL.D., F.R.S., and Augustus Cahours, F.C.S. ................. 575 XXIX. Photo-chemical Researches.—Part III. Optical and Chemical Extinction of the Chemical Rays. By Robert Bunsen, Professor of Chemistry at the University of Heidelberg, and Henry Enfield Roscoe, B.A., Ph.D., Professor of Chemistry at Owens College, Manchester. Communicated by Professor Stokes, Sec. R.S. 601 LIST OF ILLUSTRATIONS. Plate XV.—Mr. P. H. Gosse on the Dioecious Character of the Rotifera. Plate XVI.—Professor Owen on the Foetal Membranes and Placenta of the Elephant. Plates XVII. XVIII. XIX. XX. XXI. XXII.—Professor Bunsen and Dr. H. E. Roscoe’s Photo-chemical Researches.—Parts I. II. Plate XXIII.—Dr. Marcet on the Immediate Principles of Human Excrements. Plates XXIV. XXV. XXVI.—Mr. F. Currey on the Fructification of certain Sphaeriaceous Fungi. Plate XXVII.—Professor Bunsen and Dr. H. E. Roscoe’s Photo-chemical Researches.—Part III. CONTENTS. XXX. Account of the Construction of the New National Standard of Length, and of its principal Copies. By G. B. Airy, Esq., Astronomer Royal . . . . page 621 XXXI. Memoir on the Resultant of a System of two Equations. By Arthur Cayley, Esq., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703 XXXII. On the Symmetric Functions of the Roots of certain Systems of two Equations. By Arthur Cayley, Esq., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717 XXXIII. A Memoir on the Conditions for the Existence of given Systems of Equalities among the Roots of an Equation. By Arthur Cayley, Esq., F.R.S. . . . . . 727 XXXIV. Tables of the Sturmian Functions for Equations of the Second, Third, Fourth, and Fifth Degrees. By Arthur Cayley, Esq., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733 XXXV. On some of the Products of the Destructive Distillation of Boghead Coal.—Part II. By C. Greville Williams, Lecturer on Chemistry in the Normal College, Swansea. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737 XXXVI. On the Comparison of Transcendents, with certain applications to the Theory of Definite Integrals. By George Boole, Esq., Professor of Mathematics in the Queen’s University. Communicated by Professor W. F. Donkin, F.R.S. . . . . 745 XXXVII. Experimental Researches on the Conductive Powers of various Substances, with the application of the Results to the Problem of Terrestrial Temperature. By W. Hopkins, Esq., M.A., F.R.S., of St. Peter’s College, Cambridge . . . . 805 XXXVIII. Experimental Researches on the Strength of Pillars of Cast Iron, from various Parts of the Kingdom. By Eaton Hodgkinson, Esq., F.R.S., F.G.S., Hon. Mem. Inst. Civ. E., Hon. Mem. Soc. Ing. Civ. Paris, and Professor of the Mechanical Principles of Engineering in University College, London . . . . 851 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 901 APPENDIX. Presents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [ 1 ] LIST OF ILLUSTRATIONS. Plates XXVIII. XXIX. XXX.—Mr. Airy’s Account of the Construction of the New National Standard of Length, and of its principal Copies. Plates XXXI. XXXII. XXXIII.—Mr. Hodgkinson’s Experimental Researches on the Strength of Pillars of Cast Iron. I. On the Evidence of the existence of the Decennial Inequality in the Solar-diurnal Magnetic Variations, and its non-existence in the Lunar-diurnal Variation, of the Declination at Hobarton. By Major-General Edward Sabine, of the Royal Artillery, Treas. and V.P. of the Royal Society .......................................................... page 1 II. On the Stability of Loose Earth. By W. J. Macquorn Rankine, F.R.S. ......................................................... 9 III. On the Geometrical Isomorphism of Crystals. By Henry James Brooke, F.R.S., Hon. M.C.P.S. .............................................................. 29 IV. On the Equation of Laplace's Functions, &c. By W. F. Donkin, M.A., F.R.S., F.R.A.S., Savilian Professor of Astronomy in the University of Oxford ........... 43 V. Researches on Organo-metallic Bodies.—Third Memoir. On a New Series of Organic Acids containing Nitrogen. By E. Frankland, Ph.D., F.R.S., Professor of Chemistry in Owens College, Manchester ............................................................................. 59 VI. An account of the Two Methods of Reproduction in Daphnia, and of the Structure of the Ephippium. By John Lubbock, Esq., F.G.S. Communicated by Charles Darwin, F.R.S. .......................................................... 79 VII. On the Scelidothere (Scelidotherium leptocephalum, Owen). By Professor Owen, F.R.S. &c. ........................................................................ 101 VIII. On the Structure and Development of the Cysticercus cellulose, as found in the Muscles of the Pig. By George Rainey, M.R.C.S., Lecturer on Anatomy and Demonstrator of Practical and Microscopical Anatomy at St. Thomas's Hospital. Communicated by R. D. Thomson, M.D., F.R.S. .................................................. 111 IX. Electro-Physiological Researches. Physical and Chemical Phenomena of Muscular Contraction.—Tenth Series. Part I. By Carlo Matteucci, Professor in the University of Pisa. Communicated by Michael Faraday, Esq., D.C.L., F.R.S. &c. .................................................. 129 X. The Bakerian Lecture.—Experimental Relations of Gold (and other Metals) to Light. By Michael Faraday, Esq., D.C.L., F.R.S., Fullerian Prof. Chem. Royal Institution, Foreign Associate of the Acad. Sciences, Paris, Ord. Boruss. pour le Mériche, Esq., Memb. Royal and Imp. Acadd. of Sciences, Petersburgh, Florence, Copenhagen, Berlin, Göttingen, Modena, Stockholm, Munich, Bruxelles, Vienna, Bologna, Commander of the Legion of Honour, &c. &c. .................................. page 145 XI. On Autopolar Polyedra. By the Rev. Thomas P. Kirkman, A.M., F.R.S., Rector of Croft with Southworth. Communicated by Arthur Cayley, Esq., F.R.S. .................................. 183 XII. On the K-partitions of the R-gon and R-ace. By the Rev. Thomas P. Kirkman, A.M., F.R.S., Rector of Croft with Southworth. Communicated by Arthur Cayley, Esq., F.R.S. .................................. 217 XIII. A Memoir upon Caustics. By Arthur Cayley, Esq. .................................. 273 XIV. On the Diaecious Character of the Rotifera. By Philip Henry Gosse. Communicated by Thomas Bell, F.R.S., P.L.S., F.G.S., Professor of Zoology in King's College .................................. 313 XV. On the Structure and Motion of Glaciers. By John Tyndall, F.R.S., Professor of Natural Philosophy, Royal Institution; and Thomas H. Huxley, F.R.S., Fullerian Professor of Physiology, Royal Institution .................................. 327 XVI. Description of the Fatal Membranes and Placenta of the Elephant (Elephas Indicus, Cuv.), with Remarks on the value of placentary characters in the classification of the Mammalia. By Professor Owen, F.R.S. .................................. 347 XVII. Photo-chemical Researches.—Part I. Measurement of the Chemical Action of Light. By Robert Bunsen, Professor of Chemistry at the University of Heidelberg, and Henry Enfield Roscoe, B.A., Ph.D., Professor of Chemistry at Owens College, Manchester. Communicated by Professor Stokes, Sec. R.S. .................................. 355 XVIII. Photo-chemical Researches.—Part II. Phenomena of Photo-chemical Induction. By Robert Bunsen, Professor of Chemistry at the University of Heidelberg, and Henry Enfield Roscoe, B.A., Ph.D., Professor of Chemistry at Owens College, Manchester. Communicated by Professor Stokes, Sec. R.S. .................................. 381 XIX. On the Immediate Principles of Human Excrements in the Healthy State. By W. Marcet, M.D., F.C.S., Assistant Physician to the Westminster Hospital. Communicated by H. Bence Jones, M.D., F.R.S. .................................. 403 XX. A Memoir on Curves of the Third Order. By A. Cayley, Esq., F.R.S. .................................. 415 XXI. On some of the Products of the Destructive Distillation of Boghead Coal.—Part I. By C. Greville Williams, Lecturer on Chemistry in the Normal College, Swansea. Communicated by Dr. Sharpey, Sec. R.S. .................................. 447 XXII. On an Element of Strength in Beams subjected to Transverse Strain, named by the author "The Resistance of Flexure."—Second Paper. By William Henry Barlow, Esq., F.R.S. &c. .................................. 463 XXIII. A Memoir on the Symmetric Functions of the Roots of an Equation. By Arthur Cayley, Esq., F.R.S. ........................................... page 489 XXIV. On Hourly Observations of the Magnetic Declination made by Captain Rochfort Maguire, R.N., and the Officers of H.M.S. 'Plover,' in 1852, 1853 and 1854, at Point Barrow, on the shores of the Polar Sea. By Major-General Edward Sabine, R.A., D.C.L., Treas. and Vice-President .................................................. 497 XXV. Researches on Silica. By Colonel Philip Yorke, F.R.S. .................................................. 533 XXVI. On the Fructification of certain Sphaeriaceous Fungi. By Frederick Currey, M.A., F.L.S. Communicated by W. J. Hooker, M.D., F.R.S. .................................................. 543 XXVII. Researches on a New Class of Alcohols. By Augustus William Hofmann, LL.D., F.R.S., and Augustus Cahours, F.C.S. .................................................. 555 XXVIII. Researches on the Phosphorus-Bases. By Augustus William Hofmann, LL.D., F.R.S., and Augustus Cahours, F.C.S. .................................................. 575 XXIX. Photo-chemical Researches.—Part III. Optical and Chemical Extinction of the Chemical Rays. By Robert Bunsen, Professor of Chemistry at the University of Heidelberg, and Henry Enfield Roscoe, B.A., Ph.D., Professor of Chemistry at Owens College, Manchester. Communicated by Professor Stokes, Sec. R.S. .................................................. 601 XXX. Account of the Construction of the New National Standard of Length, and of its principal Copies. By G. B. Airy, Esq., Astronomer Royal .................................................. 621 XXXI. Memoir on the Resultant of a System of two Equations. By Arthur Cayley, Esq., F.R.S. .................................................. 703 XXXII. On the Symmetric Functions of the Roots of certain Systems of two Equations. By Arthur Cayley, Esq., F.R.S. .................................................. 717 XXXIII. A Memoir on the Conditions for the Existence of given Systems of Equalities among the Roots of an Equation. By Arthur Cayley, Esq., F.R.S. .................................................. 727 XXXIV. Tables of the Sturmian Functions for Equations of the Second, Third, Fourth, and Fifth Degrees. By Arthur Cayley, Esq., F.R.S. .................................................. 733 XXXV. On some of the Products of the Destructive Distillation of Boghead Coal.—Part II. By C. Greville Williams, Lecturer on Chemistry in the Normal College, Swansea .................................................. 737 XXXVI. On the Comparison of Transcendents, with certain applications to the Theory of Definite Integrals. By George Boole, Esq., Professor of Mathematics in the Queen's University. Communicated by Professor W. F. Donkin, F.R.S. .................................................. 745 XXXVII. Experimental Researches on the Conductive Powers of various Substances, with the application of the Results to the Problem of Terrestrial Temperature. By W. Hopkins, Esq., M.A., F.R.S., of St. Peter’s College, Cambridge. XXXVIII. Experimental Researches on the Strength of Pillars of Cast Iron, from various Parts of the Kingdom. By Eaton Hodgkinson, Esq., F.R.S., F.G.S., Hon. Mem. Inst. Civ. E., Hon. Mem. Soc. Ing. Civ. Paris, and Professor of the Mechanical Principles of Engineering in University College, London. Index ............................................................................. 901 APPENDIX. Presents .......................................................................... [1] ERRATUM. At page 98 of the Volume for 1855, in Archdeacon Pratt’s paper “On the Attraction of the Himalayas on the Plumb-Line in India,” lines 7 and 5 from the bottom, read \[ a = -0.00019203 + 0.0059576 u - 0.0014564 v \] and \[ = (0.9980797 + 0.0059576 u - 0.0014564 v). \] This correction affects none of the results of the paper. LIST OF ILLUSTRATIONS. Plate I.—Major-General SABINE on the Decennial Magnetic Inequality at Hobarton. Plates II. III. IV. V.—Mr. H. J. BROOKE on the Geometrical Isomorphism of Crystals. Plates VI. VII.—Mr. JOHN LUBBOCK on Two Methods of Reproduction in *Daphnia*, and on the Structure of the Ephippium. Plates VIII. IX.—Professor OWEN on the Scelidothere. Plates X. XI.—Mr. GEORGE RAINEY on the Structure and Development of the *Cysticercus cellulosae*, as found in the Muscles of the Pig. Plates XII. XIII. XIV.—The Rev. THOMAS P. KIRKMAN on Autopolar Polyedra. Plate XV.—Mr. P. H. GOSSE on the Dioecious Character of the Rotifera. Plate XVI.—Professor OWEN on the Fœtal Membranes and Placenta of the Elephant. Plates XVII. XVIII. XIX. XX. XXI. XXII.—Professor BUNSEN and Dr. H. E. ROSCOE’s Photo-chemical Researches.—Parts I. II. Plate XXIII.—Dr. MARCET on the Immediate Principles of Human Excrements. Plates XXIV. XXV. XXVI.—Mr. F. CURREY on the Fructification of certain Sphaeraceous Fungi. Plate XXVII.—Professor BUNSEN and Dr. H. E. ROSCOE’s Photo-chemical Researches.—Part III. Plates XXVIII. XXIX. XXX.—Mr. AIRY’s Account of the Construction of the New National Standard of Length, and of its principal Copies. Plates XXXI. XXXII. XXXIII.—Mr. HODGKINSON’s Experimental Researches on the Strength of Pillars of Cast Iron. ADJUDICATION of the Medals of the Royal Society for the year 1857 by the President and Council. The Copley Medal to Michel Eugène Chevreul, for his Researches in Organic Chemistry, particularly on the Composition of the Fats, and for Researches on the Contrast of Colours. A Royal Medal to Dr. Edward Frankland, for the Isolation of the Organic Radicals of the Alcohols, and for his Researches on the Metallic Derivatives of Alcohol. A Royal Medal to Dr. John Lindley, for his numerous Researches and Works on all branches of Scientific Botany, and especially for his "Vegetable Kingdom" and his "Genera and Species of Orchideæ." The Bakerian Lecture was delivered by Michael Faraday, Esq., D.C.L., F.R.S., and entitled "Experimental Relations of Gold (and other Metals) to Light." The Croonian Lecture was delivered by James Paget, Esq., F.R.S., and entitled "On the Cause of the Rhythmic Motion of the Heart."