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. ### Observatories | Armagh | Kew | |--------|-----| | Cape of Good Hope | Liverpool | | Dublin | Madras | | Edinburgh | Oxford (Radcliffe) | | Greenwich | | ### Institutions | Barbadoes | Library and Museum | |-----------|--------------------| | Calcutta | Asiatic Society | | Cambridge | Geological Museum | | Cambridge | Philosophical Society | | Cape Town | South African Library | | Dublin | Royal Dublin Society | | Dublin | Royal Irish Academy | | Edinburgh | Royal Society | | London | Admiralty Library | | London | Chemical Society | | London | Entomological Society | | London | Geological Society | | London | Geological Survey of Great Britain | | London | Horticultural Society | | London | Institute of British Architects | | London | Institution of Civil Engineers | | London | Linnean Society | | London | London Institution | | London | Queen's Library | | London | Royal Asiatic Society | | London | Royal Astronomical Society | | London | Royal College of Physicians | | London | Royal Geographical Society | | London | Royal Institution of Great Britain | | London | Royal Medical and Chirurgical Society | | London | Royal Society of Literature | | London | Society of Antiquaries | | London | Society of Arts | | London | The Treasury Library | | London | United Service Museum | | London | Zoological Society | | Malta | Public Library | | Manchester | Literary and Philosophical Society | | Oxford | Ashmolean Society | | Oxford | Radcliffe Library | | Swansea | Royal Institution | | Sydney | University Library | | Woolwich | Royal Artillery Library | ### Belgium | Brussels | Académie Royale de Médecine | |----------|-----------------------------| | Brussels | Royal Academy of Sciences | ### Denmark | Altona | Royal Observatory | |---------|-------------------| | Copenhagen | Royal Society of Sciences | ### France | Montpellier | Academy of Sciences | |--------------|--------------------| | Paris | Academy of Sciences | | Paris | Dépôt de la Marine | | Paris | École des Mines | | Paris | Geographical Society | | Paris | Geological Society | | Paris | Jardin des Plantes | | Paris | Société d'Encouragement pour l'Industrie Nationale | | Toulouse | Academy of Sciences | ### Germany | Berlin | Royal Academy of Sciences | |--------|---------------------------| | Berlin | Society of Experimental Philosophy | | Jena | Cassarcan 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 | | 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 | | Turin | 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 | | Philadelphia | American Philosophical Society | | Washington | Smithsonian Institution | | Washington | 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 | |------------------------|---------------------------------------------------| | Altoma | University | | Armagh | Academy | | Berlin | Academy | | Breslau | American Academy of Sciences | | Brussels | Bowdoin College | | Cadiz | Trinity College Library | | Cambridge | Harvard University | | Cape of Good Hope | University | | Coimbra | University | | Copenhagen | Royal Society | | Dorpat | University | | Dublin | University | | Edinburgh | Board of Ordnance | | Helsingfors | Queen's Library | | Königsberg | Royal Institution | | Madras | Royal Society | | Mannheim | Savilian Library | | Marseille | Academy of Sciences | | Milan | Board of Longitude | | Munich | Dépôt de la Marine | | Oxford | Hungarian Academy | | Palermo | American Philosophical Society | | Paris | University | | Seeberg | Imperial Academy | | Trevandrum | Royal Academy of Sciences | | Tübingen | Royal Society | | Turin | College | | Vienna | Twickenham | | Wilna | London | | 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** - **Cambridge, United States** Prof. J. Lovering. - **Christiania** C. Hansteen. - **Gotha** P. A. Hansen. - **Heidelberg** M. Tiedemann. - **Kew** B. Stewart. - **Kremsmünster** P. A. Reslhuber. - **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. - **House of Commons, Library.** - **King's College.** - **Royal Society.** - **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 Influence of Temperature on the Electric Conducting Power of Metals. By Augustus Matthiessen, F.R.S., and Moritz von Bose . . . . . page 1 II. On the Aquiferous and Oviducal System in the Lamellibranchiate Mollusks. By George Rolleston, Esq., M.D., F.L.S., Linacre Professor of Anatomy; and C. Robertson, Esq., Demonstrator of Anatomy, Oxford. Communicated by Dr. Acland . . . . . . . . . . . . . . . . 29 III. On the Contact of Curves. By William Spottiswoode, M.A., F.R.S. . . 41 IV. On Larixinic Acid, a crystallizable volatile principle found in the Bark of the Larch Tree (Pinus Larix, Linn.). By Dr. John Stenhouse, F.R.S. . . . 53 V. On the Absorption and Radiation of Heat by Gaseous Matter.—Second Memoir. 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, &c.; Professor of Natural Philosophy in the Royal Institution . . 59 VI. On the Calculus of Symbols. By William Spottiswoode, M.A., F.R.S. . . 99 VII. On the Theory of the Polyedra. By the Rev. Thomas P. Kirkman, M.A., F.R.S., Honorary Member of the Literary and Philosophical Societies of Manchester and Liverpool . . . . . . . . . . . . . . . . . . 121 VIII. On a New Series of Organic Compounds containing Boron. By Dr. E. Frankland, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 IX. On the Posterior Lobes of the Cerebrum of the Quadrumania. By William Henry Flower, F.R.C.S., Assistant-Surgeon to, and Demonstrator of Anatomy at, the Middlesex Hospital. Communicated by Dr. Sharpey, Sec. R.S. . . . . . . 185 X. On Magnetic Calms and Earth-Currents. By Charles V. Walker, Esq., F.R.S., F.R.A.S. . . . . . . . . . . . . . . . . . . . . . . . . . . 203 XI. On the Spectrum of Carbon. By John Attfield, Esq., F.C.S., Director of the Laboratory of the Pharmaceutical Society; lately Demonstrator of Chemistry at St. Bartholomew’s Hospital. Communicated by Dr. Frankland, F.R.S. . . 221 XII. On the Theory of Probabilities. By George Boole, F.R.S., Professor of Mathematics in Queen’s College, Cork . . . . . . . . . . . . . . . . . . . . 225 XIII. On the Calculus of Symbols.—Second Memoir. By W. H. L. Russell, Esq., A.B. Communicated by Arthur Cayley, Esq., F.R.S. . . . . . . . . . . . . . . . 253 MDCCCLXII. XIV. On the Calculus of Functions. By W. H. L. Russell, Esq., A.B. Communicated by Arthur Cayley, Esq., F.R.S. ........................................... page 265 XV. On the Difference in the Magnetic Properties of Hot-Rolled and Cold-Rolled Malleable Iron, as regards the power of receiving and retaining Induced Magnetism of Subpermanent Character. By George Biddell Airy, Astronomer Royal .................................................. 273 XVI. On the Relations of the Vomer, Ethmoid, and Intermaxillary Bones. By John Cleland, M.D., Demonstrator of Anatomy in the University of Edinburgh. Communicated by Professor Huxley, F.R.S. ............................................................ 289 XVII. On the Properties of Electro-deposited Antimony (concluded). By G. Gore, Esq. Communicated by Professor Stokes, Sec. R.S. .............................................. 323 XVIII. The Bakerian Lecture.—On the Total Solar Eclipse of July 18th, 1860, observed at Rivabellosa, near Miranda de Ebro, in Spain. By Warren De La Rue, Esq., Ph.D., F.R.S., Hon. Sec. Royal Astron. Soc., Treas. Chem. Soc. &c. ......................................................... 333 XIX. On a New Method of Approximation applicable to Elliptic and Ultra-elliptic Functions.—Second Memoir. By Charles W. Merrifield. Communicated by W. Spottiswoode, Esq., F.R.S. ......................................................... 417 XX. On Simultaneous Differential Equations of the First Order in which the Number of the Variables exceeds by more than one the Number of the Equations. By George Boole, F.R.S., Professor of Mathematics in Queen's College, Cork ......................................................... 437 XXI. (I.) On the Dicynodont Reptilia, with a Description of some Fossil Remains brought by H.R.H. Prince Alfred from South Africa, November 1860. (II.) On the Pelvis of the Dicynodon. (III.) Notice of a Skull and parts of the Skeleton of Rhynchosaurus articeps. By Professor Owen, F.R.S. &c. ......................................................... 455 XXII. On the Differential Coefficients and Determinants of Lines, and their Application to Analytical Mechanics. By A. Cohen, Esq. Communicated by Professor Stokes, Sec. R.S. ......................................................... 469 XXIII. A Supplement to Two Papers published in the Transactions of the Royal Society, "On the Science connected with Human Mortality;" the one published in 1820, and the other in 1825. By Benjamin Gompertz, F.R.S., F.R.A.S. &c. ......................................................... 511 XXIV. On Tschirnhausen's Transformation. By Arthur Cayley, Esq., F.R.S. ......................................................... 561 ERRATA. Page 163, lines 2, 9, 13 (art. XLVII.), erase the word "non-polar." — — line 7, for because read when. LIST OF ILLUSTRATIONS. Plate I.—Professor Tyndall on the Absorption and Radiation of Heat by Gaseous Matter. Plates II. III.—Mr. William Henry Flower on the Posterior Lobes of the Cerebrum of the Quadrumania. Plates IV. V.—Dr. John Cleland on the Relations of the Vomer, Ethmoid, and Intermaxillary Bones. Plates VI. to XVIII.—Mr. Warren De La Rue on the Total Solar Eclipse of July 18, 1860, observed at Rivabellosa, near Miranda de Ebro, in Spain. Plates XIX. to XXV.—Professor Owen on the Dicynodont Reptilia, with a Description of some Fossil Remains brought by H.R.H. Prince Alfred from South Africa, November 1860. CONTENTS. XXV. On the Thermal Effects of Fluids in Motion.—Part IV. By J. P. Joule, LL.D., F.R.S. &c., and Professor W. Thomson, A.M., LL.D., F.R.S. &c. . . page 579 XXVI. On the Law of Expansion of Superheated Steam. By William Fairbairn, Esq., LL.D., F.R.S., and Thomas Tate, Esq. . . . . . . . . . . . . . . . . . 591 XXVII. On the Long Spectrum of Electric Light. By G. G. Stokes, M.A., D.C.L., Sec. R.S., Lucasian Professor of Mathematics in the University of Cambridge . . . . . . . . . . 599 XXVIII. On the Nature of the Forces concerned in producing the greater Magnetic Disturbances. By Balfour Stewart, M.A., F.R.S. . . . . . . . . . . . . . . . . . 621 XXIX. On the Analytical Theory of the Conic. By Arthur Cayley, F.R.S. . . . . . . . . . . 639 XXX. Appendix to the Account of the Earthquake-Wave Experiments made at Holyhead. By Robert Mallet, C.E., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . 663 XXXI. On the Theory of the Motion of Glaciers. By William Hopkins, Esq., St. Peter's College, Cambridge, M.A., F.R.S. &c. . . . . . . . . . . . . . . . . . 677 XXXII. On the Anatomy and Physiology of the Spongiadæ.—Part II. By J. S. Bowerbank, LL.D., F.R.S., F.L.S. &c. . . . . . . . . . . . . . . . . . . . . . . 747 XXXIII. On the Oxidation and Disoxidation effected by the Alkaline Peroxides. By B. C. Brodie, F.R.S., Professor of Chemistry in the University of Oxford . . . . . . . 837 XXXIV. On the Photographic Transparency of various Bodies, and on the Photographic Effects of Metallic and other Spectra obtained by means of the Electric Spark. By W. A. Miller, M.D., LL.D., Treas. & V.P.R.S., Professor of Chemistry in King's College, London . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 861 XXXV. Further Observations on the Distribution of Nerves to the Elementary Fibres of Striped Muscle. By Lionel S. Beale, M.B., F.R.S., Professor of Physiology and of General and Morbid Anatomy in King's College, London; Physician to King's College Hospital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 889 XXXVI. Researches on the Development of the Spinal Cord in Man, Mammalia, and Birds. By J. Lockhart Clarke, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . .. 911 XXXVII. On Spectra of Electric Light, as modified by the Nature of the Electrodes and the Media of Discharge. By the Rev. T. R. Robinson, D.D., F.R.S. &c. . . 939 XXXVIII. Experimental Researches on the Transmission of Electric Signals through Submarine Cables.—Part I. Laws of Transmission through various lengths of one Cable. By Fleeming Jenkin, Esq. Communicated by C. Wheatstone, Esq., F.R.S. XXXIX. The Lignites and Clays of Bovey Tracey, Devonshire. By William Pengelly, F.G.S. Communicated by Sir Charles Lyell, F.R.S. XL. On the Fossil Flora of Bovey Tracey. By Dr. Oswald Heer, Professor of Botany, and Director of the Botanical Gardens in Zurich Communicated by Sir C. Lyell XLI. On the Anatomy and Physiology of the Spongiadae.—Part III. On the Generic Characters, the Specific Characters, and on the Method of Examination. By J. S. Bowerbank, LL.D., F.R.S., F.L.S. &c. Index APPENDIX. Presents ERRATA. Page 588, line 10 from bottom, cancel \( p \) at the end of the formula, which should be \[ v \frac{Ct}{p} - \frac{3}{4} AJK \left( \frac{273-t}{t} \right)^2. \] — 755, 7 lines from bottom, for Plate A. read Plate XXVII. — 864, 8 lines from bottom of text, for fig. 2 read fig. 3. — — 6 lines from bottom of text, for fig. 3 read fig. 2. — 869, 13 lines from bottom of text, for more read less. LIST OF ILLUSTRATIONS. Plate XXVI.—Dr. J. P. Joule and Professor W. Thomson on the Thermal Effects of Fluids in Motion. Plates XXVII. to XXXVI.—Dr. J. S. Bowerbank on the Anatomy and Physiology of the Spongiadæ. Plates XXXVII. XXXVIII.—Professor B. C. Brodie on the Oxidation and Disoxidation effected by the Alkaline Peroxides. Plates XXXIX. XL.—Professor W. A. Miller on the Photographic Transparency of various Bodies. Plates XLI. to XLIV.—Professor Beale on the Distribution of Nerves to the Elementary Fibres of Striped Muscle. Plates XLV. to XLVIII.—Mr. J. Lockhart Clarke on the Development of the Spinal Cord in Man, Mammalia, and Birds. Plates XLIX. to LI.—Mr. F. Jenkin, Experimental Researches on the Transmission of Electric Signals through Submarine Cables. Plates LII. to LIV.—Mr. Pengelly on the Lignites and Clays of Bovey Tracey, Devonshire. Plates LV. to LXXI.—Dr. Heer on the Fossil Flora of Bovey Tracey. Plates LXXII. to LXXIV.—Dr. J. S. Bowerbank on the Anatomy and Physiology of the Spongiadæ. ADJUDICATION of the Medals of the Royal Society for the year 1862 by the President and Council. The Copley Medal to Thomas Graham, Esq., F.R.S., for three Memoirs on the Diffusion of Liquids, published in the Philosophical Transactions for 1850 and 1851; for a Memoir on Osmotic Force in the Philosophical Transactions for 1854; and particularly for a Paper on Liquid Diffusion applied to Analysis, including a distinction of Compounds into Colloids and Crystalloids, published in the Philosophical Transactions for 1861. The Rumford Medal to Professor Kirchhoff, of Heidelberg, for his Researches on the fixed Lines of the Solar Spectrum, and on the inversion of the bright lines in the Spectra of artificial light. A Royal Medal to the Rev. Dr. T. R. Robinson, F.R.S., of Armagh, for the Armagh Catalogue of 5345 Stars, deduced from observations made at the Armagh Observatory, from the year 1826 up to 1854; for his Papers on the Construction of Astronomical Instruments, in the Memoirs of the Astronomical Society, and his Paper on Electro-Magnets, in the Transactions of the Royal Irish Academy. A Royal Medal to Professor Alexander W. Williamson, F.R.S., for his Researches on the Compound Ethers, and his subsequent communications in Organic Chemistry. The Bakerian Lecture was delivered by Warren De La Rue, Esq., F.R.S.: it was entitled "On the Total Solar Eclipse of July 18th, 1860, observed at Rivabellosa, near Miranda de Ebro, in Spain." The Croonian Lecture was delivered by Professor A. Kölliker, For. Memb. R.S.: it was entitled "On the Termination of Nerves in Muscles, as observed in the Frog; and on the Disposition of the Nerves in the Frog's Heart." CONTENTS OF VOL. 152. I. On the Influence of Temperature on the Electric Conducting Power of Metals. By Augustus Matthiessen, F.R.S., and Moritz von Bose . . . . . 1 II. On the Aquiferous and Oviducal System in the Lamellibranchiate Mollusks. By George Rolleston, Esq., M.D., F.L.S., Linacre Professor of Anatomy; and C. Robertson, Esq., Demonstrator of Anatomy, Oxford. Communicated by Dr. Acland . . . . . 29 III. On the Contact of Curves. By William Spottiswoode, M.A., F.R.S. . . . 41 IV. On Larixinic Acid, a crystallizable volatile principle found in the Bark of the Larch Tree (Pinus Larix, Linn.). By Dr. John Stenhouse, F.R.S. . . . 53 V. On the Absorption and Radiation of Heat by Gaseous Matter.—Second Memoir. 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, &c.; Professor of Natural Philosophy in the Royal Institution . . . 59 VI. On the Calculus of Symbols. By William Spottiswoode, M.A., F.R.S. . . . 99 VII. On the Theory of the Polyedra. By the Rev. Thomas P. Kirkman, M.A., F.R.S., Honorary Member of the Literary and Philosophical Societies of Manchester and Liverpool . . . . . . . . . . . . . . . . . . 121 VIII. On a New Series of Organic Compounds containing Boron. By Dr. E. Frankland, F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 IX. On the Posterior Lobes of the Cerebrum of the Quadrupeds. By William Henry Flower, F.R.C.S., Assistant-Surgeon to, and Demonstrator of Anatomy at, the Middlesex Hospital. Communicated by Dr. Sharpey, Sec. R.S. . . . . . . . 185 X. On Magnetic Calms and Earth-Currents. By Charles V. Walker, Esq., F.R.S., F.R.A.S. . . . . . . . . . . . . . . . . . . . . . . . . . . 203 XI. On the Spectrum of Carbon. By John Attfield, Esq., F.C.S., Director of the Laboratory of the Pharmaceutical Society; lately Demonstrator of Chemistry at St. Bartholomew's Hospital. Communicated by Dr. Frankland, F.R.S. page 221 XII. On the Theory of Probabilities. By George Boole, F.R.S., Professor of Mathematics in Queen's College, Cork .............. 225 XIII. On the Calculus of Symbols.—Second Memoir. By W. H. L. Russell, Esq., A.B. Communicated by Arthur Cayley, Esq., F.R.S. .................. 253 XIV. On the Calculus of Functions. By W. H. L. Russell, Esq., A.B. Communicated by Arthur Cayley, Esq., F.R.S. .................. 265 XV. On the Difference in the Magnetic Properties of Hot-Rolled and Cold-Rolled Malleable Iron, as regards the power of receiving and retaining Induced Magnetism of Subpermanent Character. By George Biddell Airy, Astronomer Royal 273 XVI. On the Relations of the Vomer, Ethmoid, and Intermaxillary Bones. By John Cleland, M.D., Demonstrator of Anatomy in the University of Edinburgh. Communicated by Professor Huxley, F.R.S. .................. 289 XVII. On the Properties of Electro-deposited Antimony (concluded). By G. Gore, Esq. Communicated by Professor Stokes, Sec. R.S. .................. 323 XVIII. The Bakerian Lecture.—On the Total Solar Eclipse of July 18th, 1860, observed at Rivabellosa, near Miranda de Ebro, in Spain. By Warren De La Rue, Esq., Ph.D., F.R.S., Hon. Sec. Royal Astron. Soc., Treas. Chem. Soc. &c. 333 XIX. On a New Method of Approximation applicable to Elliptic and Ultra-elliptic Functions.—Second Memoir. By Charles W. Merrifield. Communicated by W. Spottiswoode, Esq., F.R.S. .................. 417 XX. On Simultaneous Differential Equations of the First Order in which the Number of the Variables exceeds by more than one the Number of the Equations. By George Boole, F.R.S., Professor of Mathematics in Queen's College, Cork .......... 437 XXI. (I.) On the Dicynodont Reptilia, with a Description of some Fossil Remains brought by H.R.H. Prince Alfred from South Africa, November 1860. (II.) On the Pelvis of the Dicynodon. (III.) Notice of a Skull and parts of the Skeleton of Rhinchosaurus anticeps. By Professor Owen, F.R.S. &c. ............ 455 XXII. On the Differential Coefficients and Determinants of Lines, and their Application to Analytical Mechanics. By A. Cohen, Esq. Communicated by Professor Stokes, Sec. R.S. .................. 469 XXIII. A Supplement to Two Papers published in the Transactions of the Royal Society, “On the Science connected with Human Mortality;” the one published in 1820, and the other in 1825. By Benjamin Gompertz, F.R.S., F.R.A.S. &c. ............ 511 XXIV. On Tschirnhausen's Transformation. By Arthur Cayley, Esq., F.R.S. .......... page 561 XXV. On the Thermal Effects of Fluids in Motion.—Part IV. By J. P. Joule, LL.D., F.R.S. &c., and Professor W. Thomson, A.M., LL.D., F.R.S. &c. ...... 579 XXVI. On the Law of Expansion of Superheated Steam. By William Fairbairn, Esq., LL.D., F.R.S., and Thomas Tate, Esq. ...................... 591 XXVII. On the Long Spectrum of Electric Light. By G. G. Stokes, M.A., D.C.L., Sec. R.S., Lucasian Professor of Mathematics in the University of Cambridge 599 XXVIII. On the Nature of the Forces concerned in producing the greater Magnetic Disturbances. By Balfour Stewart, M.A., F.R.S. ................. 621 XXIX. On the Analytical Theory of the Conic. By Arthur Cayley, F.R.S. ....... 639 XXX. Appendix to the Account of the Earthquake-Wave Experiments made at Holyhead. By Robert Mallet, C.E., F.R.S. ....................... 663 XXXI. On the Theory of the Motion of Glaciers. By William Hopkins, Esq., St. Peter's College, Cambridge, M.A., F.R.S. &c. ............... 677 XXXII. On the Anatomy and Physiology of the Spongiae.—Part II. By J. S. Bowerbank, LL.D., F.R.S., F.L.S. &c. ...................... 747 XXXIII. On the Oxidation and Disoxidation effected by the Alkaline Peroxides. By B. C. Brodie, F.R.S., Professor of Chemistry in the University of Oxford . 837 XXXIV. On the Photographic Transparency of various Bodies, and on the Photographic Effects of Metallic and other Spectra obtained by means of the Electric Spark. By W. A. Miller, M.D., LL.D., Treas. & V.P.R.S., Professor of Chemistry in King's College, London . . . . . . . . . . . . . . . . . . . . . 861 XXXV. Further Observations on the Distribution of Nerves to the Elementary Fibres of Striped Muscle. By Lionel S. Beale, M.B., F.R.S., Professor of Physiology and of General and Morbid Anatomy in King's College, London; Physician to King's College Hospital ................. 889 XXXVI. Researches on the Development of the Spinal Cord in Man, Mammalia, and Birds. By J. Lockhart Clarke, F.R.S. .......................... 911 XXXVII. On Spectra of Electric Light, as modified by the Nature of the Electrodes and the Media of Discharge. By the Rev. T. R. Robinson, D.D., F.R.S. &c. . . . . . . . . . . . . . . . . . . . . . 939 XXXVIII. Experimental Researches on the Transmission of Electric Signals through Submarine Cables.—Part I. Laws of Transmission through various lengths of one Cable. By Fleeming Jenkin, Esq. Communicated by C. Wheatstone, Esq., F.R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . 987 XXXIX. The Lignites and Clays of Bovey Tracey, Devonshire. By William Pengelly, F.G.S. Communicated by Sir Charles Lyell, F.R.S. ........... page 1019 XL. On the Fossil Flora of Bovey Tracey. By Dr. Oswald Heer, Professor of Botany, and Director of the Botanical Gardens in Zürich. Communicated by Sir C. Lyell .......................................................... 1039 XLI. On the Anatomy and Physiology of the Spongiadæ.—Part III. On the Generic Characters, the Specific Characters, and on the Method of Examination. By J. S. Bowerbank, LL.D., F.R.S., F.L.S. &c. .................................................................. 1087 Index ........................................................................... 1137 APPENDIX. Presents .................................................................................. [ 1 ] ERRATA. Page 163, lines 2, 9, 13 (art. XLVII.), erase the word "non-polar." — line 7, for because read when. — 588, line 10 from bottom, cancel \( p \) at the end of the formula, which should be \[ v \frac{C_{\theta}}{p} = \frac{1}{3} AJK \left( \frac{273-7}{t} \right)^2. \] — 755, 7 lines from bottom, for Plate A. read Plate XXVII. — 864, 8 lines from bottom of text, for fig. 2 read fig. 2. — 6 lines from bottom of text, for fig. 3 read fig. 2. Page 869, 13 lines from bottom of text, for more read less. LIST OF ILLUSTRATIONS. Plate I.—Professor Tyndall on the Absorption and Radiation of Heat by Gaseous Matter. Plates II. III.—Mr. William Henry Flower on the Posterior Lobes of the Cerebrum of the Quadrumania. Plates IV. V.—Dr. John Cleland on the Relations of the Vomer, Ethmoid, and Intermaxillary Bones. Plates VI. to XVIII.—Mr. Warren De La Rue on the Total Solar Eclipse of July 18, 1860, observed at Rivabellosa, near Miranda de Ebro, in Spain. Plates XIX. to XXV.—Professor Owen on the Dicynodont Reptilia, with a Description of some Fossil Remains brought by H.R.H. Prince Alfred from South Africa, November 1860. Plate XXVI.—Dr. J. P. Joule and Professor W. Thomson on the Thermal Effects of Fluids in Motion. Plates XXVII. to XXXVI.—Dr. J. S. Bowerbank on the Anatomy and Physiology of the Spongiadæ. Plates XXXVII. XXXVIII.—Professor B. C. Brodie on the Oxidation and Disoxidation effected by the Alkaline Peroxides. Plates XXXIX. XL.—Professor W. A. Miller on the Photographic Transparency of various Bodies. Plates XLI. to XLIV.—Professor Beale on the Distribution of Nerves to the Elementary Fibres of Striped Muscle. Plates XLV. to XLVIII.—Mr. J. Lockhart Clarke on the Development of the Spinal Cord in Man, Mammalia, and Birds. Plates XLIX. to LI.—Mr. F. Jenkin, Experimental Researches on the Transmission of Electric Signals through Submarine Cables. Plates LII. to LIV.—Mr. Pengelly on the Lignites and Clays of Bovey Tracey, Devonshire. Plates LV. to LXXI.—Dr. Heer on the Fossil Flora of Bovey Tracey. Plates LXXII. to LXXIV.—Dr. J. S. Bowerbank on the Anatomy and Physiology of the Spongiadæ.