** PHILOSOPHICAL TRANSACTIONS OP THE ROYAL SOCIETY OE LONDON. S e r ie s A CONTAINING PAPERS OF A MATHEMATICAL OR PHYSICAL CHARACTER. FOR THE YEAR 1897. VOL. 189. LONDON: PRINTED BY HARRISON AND SONS, ST. MARTIN’S LANE, W.C., printers in (©rbinarg to fjtr Hiajtstg. 1897. 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 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, [ iv ] upon any subject, either of Nature or Art, that conies 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. 1897 L ist of I nstitutions e n t it l e d to r e c e iv e t h e P hilosophical T ransactions or P ro ceed in g s of t h e R o y a l S o ciety. Institutions marked a arc entitled to receive Philosophical Transactions, Series A, and Proceedings. „ „ b „ ,, „ „ Series 11, and Proceedings. ., ab ,, „ „ ,, Series A and 11, and Proceedings. ,, „ p „ „ Proceedings only. America (Central). Austria (continued). Mexico. Briinn. p. Sociedad Cientifica “ Antonio Alzate.” ab. Naturforschender Verein. America (North). (See U nited S tates and Canada.) Gratz. America (South). ab. Naturwissenschaftlicher Verein fur Steier- Bnenos Ayres. mark. ab. Museo National. Innsbruck. Caracas. ab. Das Ferdinandeum. B. University Library. p. Naturwissenschaftlich - Medicinischer Coi’dova. Verein. ab. Academia National de Ciencias. Prague. Demerara. ab. Konigliche Bohmische Gesellschaft dor p. Royal Agricultural and Commercial Wi ssenschaf ten. Society, British Guiana. Trieste. La Plata. b. Museo di Storia Naturale. b. Museo de La Plata. p. Societa Adriatica di Scienze Naturali. Rio de Janeiro. p.Observatorio. Vienna. Australia. p. Anthropologische Gesellschaft. ab. Kaiserliche Akademie der Wissenschaften. Adelaide. p. K.K. Geographische Gesellschaft. p.Royal Society of South Australia. ar.. K.K. Geologische Reichsanstalt. Brisbane. B, K.K. Naturhistorisches Hof-Museum. p. Royal Society of Queensland. b. K.K. Zoologisch-Botanische Gesellschaft. Melbourne. p. Oesterreichisclie Gesellschaft fiir Meteoro- p. Observatory. logie. p. Royal Society of Victoria. a. Von Kuffner’sche Stern'warte. ab. University Library. Belgium. Sydney. Brussels. p. Australian Museum. B. Academie Royale de Medecine. p. Geological Survey. ab. Academie Royale des Sciences. p. Linnean Society of New South Wales. B. Musee Royal d’Histoire Naturelle de ab. Royal Society of New South Wales. Belgique. ab. University Library. p. Observatoire Royal. Austria. p. Societe Beige de Geologie, de Paleonto- A gram. logie, et d’Hydrologie. p. Jugoslavenska Akademija Znanosti i Um- p. Societe Malacologique de Belgique. jetnosti. Ghent. p. Societas Historico-Naturalis Croatica. ab. University. MDCCCXC VII.— A. b [ Vi ] Belgium (continued). England and Wales (continued). Liege. Cooper’s Hill. ab. Societe des Sciences. ab. Royal Indian Engineering College. p. Societe Geologique de Belgique. Dudley. Louvain. p. Dudley and Midland Geological and b. Laboratoire de Microscopie et de Biologie Scientific Society. Cellulaire, Essex. AB. Universite. p. Essex Field Club. Canada. Falmouth. Hamilton. p. Royal Cornwall Polytechnic Society. p. Hamilton Association. Greenwich. Montreal. a . Royal Observatory. AB. McGill University. Kew. p. Natural History Society. b. Royal Gardens. Ottawa. Leeds. ab. Geological Survey of Canada. p. Philosophical Society. ab. Royal Society of Canada. ab. Yorkshire College. Toronto. Liverpool. p. Astronomical and Physical Society. ab. Free Public Library. p. Canadian Institute. p. Literary and Philosophical Society. ab. University. a. Observatory. Cape of Good Hope. ab. University College. a. Observatory. London. ab. South African Librai’y. ab. Admiralty. Ceylon. p. Anthropological Institute. Colombo. ab. British Museum (Nat. Hist.). b. Museum. AB. Chemical Society. China. A. City and Guilds of London Institute. Shanghai. p. “ Electrician,” Editor of the. p. China Branch of the Royal Asiatic Society. b. Entomological Society. Denmark. ab. Geological Society. Copenhagen. ab. Geological Survey of Great Britain. ab. Kongelige Danske Videnskabernes Selskab. p. Geologists’ Association. Egypt. ab. Guildhall Library. Alexandria. A. Institution of Civil Engineers. ab. Bibliotheque Municipale. p. Institution of Electrical Engineers. England and Wales. a. Institution of Mechanical Engineers. Aberystwith. A. Institution of Naval Architects. ab. University College. p. Iron and Steel Institute. Bangor. ab. King’s College. ab. University College of North Wales. b. Linnean Society. Birmingham. ab. London Institution. ab. Free Central Library. p. London Library. ab. Mason College. A. Mathematical Society. p. Philosophical Society. p. Meteorological Office. Bolton. p. Odontological Society. p. Public Library. p. Pharmaceutical Society. Bristol. p. Physical Society. p. Merchant Venturers’ School. p. Quekett Microscopical Club. ab. University College. p. Royal Agricultural Society. Cambridge. a. Royal Astronomical Society. ab. Philosophical Society. b. Royal College of Physicians. p. Union Society. B. Royal College of Surgeons. [ vii ] England and Wales (continued). England and Wales (continued). London (continued). Stonyhurst. p. Royal Engineers (for Libraries abroad, six p. The College. copies). Swansea. ab. Royal Engineers. Head Quarters Library. AB. Royal Institution. p. Royal Geographical Society. Woolwich. p. Royal Horticultural Society. ab. Royal Artillery Library. ab. Royal Institution of Great Britain. Finland. B. Royal Medical and Chirurgical Society. Helsingfors. p. Royal Meteorological Society. p. Societas pro Fauna et Flora Fennica. p. Royal Microscopical Society. ab. Societe des Sciences. p. Royal Statistical Society. France. ab. Royal United Service Institution. Bordeaux. ab. Society of Arts. p. Academie des Sciences. p. Society of Biblical Archaeology. p. Faculte des Sciences. p. Society of Chemical Industry (London p. Societe de Medecine et de Chirurgie. Section). p. Societe des Sciences Physiques et p. Standard Weights and Measures Depart­ Naturelles. ment. Caen. ab. The Queen’s Library. p .Societe Linneenne de Normandie. ab. The War Office. Cherbourg. ab. University College. p. Societe des Sciences Naturelles. p. Victoria Institute. Dijon. B. Zoological Society. p. Academie des Sciences. Manchester. Lille. ab. Free Library. p. Faculte des Sciences. ab. Literary and Philosophical Society. Lyons. p. Geological Society. ab. Academie des Sciences, Belles-Lettres et Arts. ab. Owens College. ab. Universite. Netley. Marseilles. p. Royal Victoria Hospital. ab. Faculte des Sciences. Newcastle. Montpellier. AB. Free Library. ab. Academie des Sciences et Lettres. p. North of England Institute of Mining and B. Faculte de Medecine. Mechanical Engineers. Nantes. p. Society of Chemical Industry (Newcastle p. Societe des Sciences Naturelles de l’Ouest Section). de la France. Norwich. Paris. p. Norfolk and Norwich Literary Institution. ab. Academie