Front Matter

PHILOSOPHICAL TRANSACTIONS, OF THE ROYAL SOCIETY OF LONDON. FOR THE YEAR MDCCCXVI. PART I. LONDON, PRINTED BY W. BULMER AND CO. CLEVELAND-ROW, ST. JAMES'S; AND SOLD BY G. AND W. NICOL, PALL-MALL, BOOKSELLERS TO HIS MAJESTY, AND PRINTERS TO THE ROYAL SOCIETY. MDCCCXVI. 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 judgment 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 receive them, are to be considered in no other light than as a matter of civility, in return for the respect shewn 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. I. On the fire-damp of coal mines, and on methods of lighting the mines so as to prevent its explosion. By Sir H. Davy, LL. D. F. R. S. V. P. R. I. p. 1 II. An account of an invention for giving light in explosive mixtures of fire-damp in coal mines, by consuming the fire-damp. By Sir Humphry Davy, LL. D. F. R. S. V. P. R. I. p. 23 III. On the developement of exponential functions; together with several new theorems relating to finite differences. By John Frederick W. Herschel, Esq. F. R. S. p. 45 IV. On new properties of heat, as exhibited in its propagation along plates of glass. By David Brewster, LL. D. F. R. S. Lond. and Edin. In a Letter addressed to the Right Hon. Sir Joseph Banks, Bart. G. C. B. P. R. S. p. 46 V. Farther experiments on the combustion of explosive mixtures confined by wire-gauze, with some observations on flame. By Sir H. Davy, LL. D. F. R. S. V. P. R. I. p. 115 VI. Some observations and experiments made on the Torpedo of the Cape of Good Hope in the year 1812. By John T. Todd, late surgeon of His Majesty's ship Lion. Communicated by Sir Everard Home, Bart. V. P. R. S. p. 120 VII. Direct and expeditious methods of calculating the excentric from the mean anomaly of a planet. By the Reverend Abram Robertson, D. D. F. R. S. Savilian Professor of Astronomy in the University of Oxford, and Radcliffian Observer. Communicated by the Right Hon. Sir Joseph Banks, Bart. G. C. B. P. R. S. p. 127 VIII. Demonstrations of the late Dr. Maskelyne's formulae for finding the longitude and latitude of a celestial object from its right ascension and declination; and for finding its right ascension and declination from its longitude and latitude, the obliquity of the ecliptic being given in both cases. By the Rev. Abram Robertson, D.D. F.R.S. Savilian Professor of Astronomy in the University of Oxford, and Radcliffian Observer. Communicated by the Right Honourable Sir Joseph Banks, Bart. G.C.B. P.R.S. p. 138 IX. Some account of the feet of those animals whose progressive motion can be carried on in opposition to gravity. By Sir Everard Home, Bart. V. P. R. S. p. 149 X. On the communication of the structure of doubly refracting crystals to glass, muriate of soda, fluor spar, and other substances, by mechanical compression and dilatation. By David Brewster, LL.D. F.R.S. Lond. and Edin. In a letter addressed to the Right Hon. Sir Joseph Banks, Bart. G.C.B. P.R.S. p. 156 APPENDIX. Meteorological Journal kept at the Apartments of the Royal Society, by Order of the President and Council. The President and Council of the Royal Society adjudged the Medal on Sir Godfrey Copley's Donation, for the year 1815, to David Brewster, LL.D., for his Paper on the Polarisation of Light by Reflection, printed in the Philosophical Transactions; And the Gold and Silver Medals on Count Rumford's Donation, to William Charles Wells, M.D. for his Essay on Dew, published in the course of the preceding year. CONTENTS. XI. An essay towards the calculus of functions. Part II. By C. Babbage, Esq. Communicated by W. H. Wollaston, M.D. Sec. R.S. - - - - 179 XII. Experiments and observations to prove that the beneficial effects of many medicines are produced through the medium of the circulating blood, more particularly that of the colchicum autumnale upon the gout. By Sir Everard Home, Bart. V.P.R.S. Communicated by the Society for improving animal chemistry. - - - - - 257 XIII. An appendix to a paper on the effects of the colchicum autumnale on gout. By Sir Everard Home, Bart. V.P.R.S. 262 XIV. On the cutting diamond. By W. H. Wollaston, M.D. Sec. R.S. - - - - 265 XV. An account of the discovery of a mass of native iron in Brasil. By A. F. Mornay, Esq. in a letter to W. H. Wollaston, M.D. Sec. R.S. - - - - 270 XVI. Observations and experiments on the mass of native iron found in Brasil. By W. H. Wollaston, M.D. Sec. R.S. 281 XVII. On ice found in the bottoms of rivers. By T. A. Knight, Esq. F.R.S. In a letter addressed to the Right Hon. Sir Joseph Banks, Bart. G.C.B. P.R.S. - 286 XVIII. On the action of detached leaves of plants. By T. A. Knight, Esq. F.R.S. In a letter addressed to the Right Hon. Sir Joseph Banks, Bart. G.C.B. P.R.S. 289 XIX. On the manufacture of the sulphate of magnesia at Monte della Guardia, near Genoa. By H. Holland, M. D. F. R. S. XX. On the formation of fat in the intestine of the tadpole, and on the use of the yolk in the formation of the embryo in the egg. By Sir Everard Home, Bart. V. P. R. S. XXI. On the structure of the crystalline lens in fishes and quadrupeds, as ascertained by its action on polarised light. By David Brewster, LL.D. F. R. S. Lond. and Edin. In a Letter addressed to the Right Hon. Sir Joseph Banks, Bart. G. C. B. P. R. S. XXII. Some farther account of the fossil remains of an animal, of which a description was given to the Society in 1814. By Sir Everard Home, Bart. V. P. R. S. XXIII. Farther observations on the feet of animals whose progressive motion can be carried on against gravity. By Sir Everard Home, Bart. V. P. R. S. XXIV. A new demonstration of the binomial theorem. By Thomas Knight, Esq. Communicated by W. H. Wollaston, M. D. Sec. R. S. XXV. On the fluents of irrational functions. By Edward Ffrench Bromhead, Esq. M. A. Communicated by J. F. W. Herschel, Esq. F. R. S.