December 9, 1869. Dr. WILLIAM ALLEN MILLER, Treasurer and Vice-President, in the Chair. It was announced from the Chair that the President had appointed the following Members of Council to be Vice-Presidents : The Treasurer. Mr. De la Rue. Sir Philip Egerton. Mr. Archibald Smith. Dr. W. W. Gull was admitted into the Society. The Presents received were laid on the Table, and thanks ordered for them, as follows: Transactions. : Albany-State of New York. Fiftieth and Fifty-first Annual Reports of the Trustees of the State Library. Twentieth Annual Report of the Regents of the University on the Condition of the State Cabinet of Natural History. Report of Dr. Peters on the Longitude of the Western Boundary Line of the State of New York. 8vo. New York 1868-69. The Regents of the University. Boston-American Academy of Arts and Sciences. Proceedings. Vol. VII. Sheets 44-66. 8vo. Boston 1868. The Academy. Boston Society of Natural History. Proceedings. Vol. XII. Sheets 1-17. Occasional Papers, I. (Entomological Correspondence of T. W. Harris.) 8vo. Boston 1868–69. The Society. Breslau-Schlesische Gesellschaft für vaterländische Cultur. Abhandlungen. Phil.-Hist. Abth. 1868. Heft II. 1869. Abth. für Naturwissenschaften und Medicin, 1868-69. Sechsundvierzigster Jahresbericht. 8vo. Breslau 1869. The Society. Cambridge, Mass.:-American Association for the Advancement of Science. Proceedings. Sixteenth Meeting held at Burlington, Vermont, August 1867. 8vo. Cambridge 1868. The Association. Harvard College. Forty-Second Annual Report of the President for the year 1867-68. Treasurer's Statement, 1868. Report of the Board of Overseers, 1869. A Catalogue of the Officers and Students for the year 1868-69. The New Catalogue of Harvard College Library, and other papers. 8vo. The College. Museum of Comparative Zoology. Annual Report of the Trustees, 1868. Bulletin, pp. 121-142. 8vo. Boston and Cambridge 1868-69. The Museum. Carácas-Sociedad de Ciencias Fisicas y Naturales. Vargasia: Boletin Transactions (continued). de la Sociedad. Num. 1-4. El Lago de Asfalto en la Isla de Trinidad, por A. Rojas. La Sumergida Isla de Atlantis, por el Dr. F. Unger, traducido por G. A. Ernst. Rede gehalten am Abend der Vorfeier des Humboldt-Festes 13. Sept. 1869 in der Ruine von Saboura Grande, von A. Ernst. 8vo. Carácas 1867-69. The Society. London:-Geological Survey of Great Britain. Memoirs. Reports on the Geology of Jamaica, by J. S. Sawkins. The Geology of the Carboniferous Limestone, Yoredale Rocks, and Millstone Grit of North Derbyshire and the adjoining parts of Yorkshire. The Triassic and Permian Rocks of the Midland Counties of England, by E. Hull. The Geology of part of the Yorkshire Coal-field. Mineral Statistics for 1868, by R. Hunt. Catalogue of the published Maps, Sections, Memoirs, and other Publications. 8vo. London 1869. The Survey. Royal Medical and Chirurgical Society. Medico Chirurgical Transactions. Vol. LII. 8vo. London 1869. The Society. New York. Lyceum of Natural History. Annals. Vol. IX. Nos. 1-4. 8vo. New York 1868. The Lyceum. United States Sanitary Commission. A Sketch of its purposes and its work. 12mo. Boston 1863. A Succinct Narrative of its works and purposes. 8vo. New York 1864. History of the Commission, by C. J. Stillé. 8vo. New York 1868. Memoirs, Statistical. 8vo. New York 1869. History of the Brooklyn and Long Island Fair, Feb. 22, 1864. 8vo. Brooklyn 1864. Memoir of the Great Central Fair held at Philadelphia, June 1864, by C. J. Stillé. 4to. Philadelphia 1864. A Record of the Metropolitan Fair held at New York in April 1864. 4to. New York 1867. The Commission. Philadelphia:-Forty-Ninth Annual Report of the Board of Controllers of Public Schools of the First School District of Penn'a for the year ending Dec. 31, 1867. 8vo. Philadelphia 1868. American Philosophical Society. Proceedings. Vol. X. 8vo. Philadelphia 1867-68. The Board. Nos. 78-80. The Society. Pisa-Memorie Valdarnesi. Vol. I.-IV. 8vo. Pisa 1835-55. San Francisco-California Academy of Sciences. C. Falconer, Esq. Proceedings. Vol. IV. The Academy. Inscriptions et BellesToulouse 1869. The Academy. Washington:-National Academy of Sciences. Letters of the President and Vice-President, 1867-68. 8vo. Washington. The Academy. Smithsonian Institution. Annual Report of the Board of Regents for the year 1867. 8vo. Washington 1868. The Institution. Chase (P. E.) Some Remarks on the Fall of Rain, as affected by the Moon. The Author. Smiles (R.) Memoir of the late Henry Booth, of the Liverpool and Manchester, and afterwards of the London and North-Western Railway. 8vo. London 1869. Miss Booth. Tuson (R. V.) A Pharmacopoeia, including the Outlines of Materia Medica and Therapeutics, for the use of Practitioners and Students of Veterinary Medicine. 12mo. London 1869. The following communications were read :— The Author. By J. NOR I. "Spectroscopic Observations of the Sun."-No. V. MAN LOCKYER, F.R.S. Received July 8, 1869. (See p. 74.) II. "Researches on Gaseous Spectra in relation to the Physical Constitution of the Sun, Stars, and Nebulæ."-Third Note. By E. FRANKLAND, F.R.S., and J. NORMAN LOCKYER, F.R.S. Received July 14, 1869. (See p. 79.) III. "On the successive Action of Sodium and Iodide of Ethyl on Acetic Ether." By J. ALFRED WANKLYN, F.C.S. &c. Communicated by Professor WILLIAMSON. Received July 16, 1869. (See p. 91.) IV. "On Linear Differential Equations." By W. H. L. RUSSELL, F.R.S. Received November 13, 1869. The condition that the linear differential equation When a, ß, y are none of them equal to zero, and p2y—py' +y"=0, Pr=p2B-{2y(r−1)+B'}p+ (r−1)y'+B', Q=p'a (2ẞr+a')p+yr(r−1)+ẞ'r+a", S,=a(r+1)(r+2). There will be (n+2) horizontal and (n+1) vertical rows, where n is the index of the highest power of x in the denominator of p. Similar methods will apply to the linear differential equation (a+ẞx+2x2) +(a' + ß'x + y2x2) d3u dx3 d2u da +(a"+ẞ"x+y"x2) du dx and the process admits of a very remarkable simplification. All linear differential equations of the second and third orders may be treated in the same way, and, I believe, all linear differential equations of every degree*. V. "Spectroscopic Observations of the Solar Prominences, being Extracts from a Letter addressed to Sir J. F. W. HERSCHEL, Bart., F.R.S., by Captain HERSCHEL, R.E., dated Bangalore, June 12th and 15th, 1869.'" Communicated by Sir J. HERSCHEL. Received July 19, 1869. (See p. 62.) * This investigation assumes that a+ßx+yx2 and the denominator of have no common factor.-W. H. L. R., Jan. 13, 1869. |