PHILOSOPHICAL

TRANSACTION S

OF THE

ROYAL SOCIETY OF LONDON.

S e r ie s A.

CONTAINING PAPERS OF A MATHEMATICAL OR PHYSICAL CHARACTER,

VOL. 194.

LONDON:

PRINTED BY HARRISON AND SONS, ST. MARTIN’S LANE, W.C. |3rintm in (irbinnrg to fin Hlajfstg. 1900. [ iK ]

CONTENTS.

(A)

VOL. 194.

List of Illustrations...... page v Advertisement ...... vii List of Institutions entitled to receive the Philosophical Transactions or Proceedings of the Royal Society...... ix

I. An Experimental Investigation of the Thermodynamical Properties of Super­ heated Steam.— On the Cooling of Saturated Steam by Free Expansion. By J ohn H . G r in d l e y , B.Sc ., Wh.Sc.Exhibition (1851) late Fellow of the Victoria University. Communicated by Professor O sborne R ey n o ld s, F.R.S...... page 1

II. A Comparison of Platinum and Gas Thincluding a Determination of the Boiling-Point of Sulphur on the Nitrogen Scale. An Account of Experi­ ments made in the Laboratory of the Bureau International des Poids et Mesures at Sevres. By J oh n A l le n H a r k e r , D.S c., formerly Bishop Berkeley Fellow of Owens College, , Research Assistant at Observatory, and P ie r r e C h a p p u is , Ph.D., Savant Attache au Bureau International des Poids et Mesures, Sevres. Communicated by the Keiv Observatory C om m ittee...... 37

III. On the Propagation of Earthquake Motion to Great Distances. By II. D. O l d h a m , Geological Survey of India. Communicated by Sir R obert S. B a l l , F.R.S...... 135 a 2 # [ *v ] IV. Impact with a Liquid Surface studied the aid of Instantaneous Photography By A. M. W o r t h i n g t o n , M . A . , F.R.Sand R. S . C o l e , M.A. . . . 175

V. Gold-Aluminium Alloys. By C. T. H ey c o c k , and F. H . N e v il l e , F-R-S...... 201

VI. B a k e r i a n L e c t u r e .— The Specific Heats o f Metals, and the Relation of Specific Heat to Atomic Weight. By W. A. T il d e n , I).S c., , Professor of Chemistry in the Royal College of Science, London. an Appendix by Professor J oh n P e r r y , F.R.S...... 233

VII. On the Association o f Attributes inwith Illustrations from the Material o f the Childhood Society, B y G. U d n y Y u l e , formerly Assistant Professor o f Applied Mathematics, University College, London. Communicated by Professor K a r l P e a r so n , F.R.S...... 257

VIII. The Ionization o f Dilute Solutions at the Freezing Point. By W. C. D. W h e t h a m , M.A., Fellow of Trinity College. Cambridge. Communicated by E. H. G r i f f i t h s , F.R.S...... 321

IX. Combinatorial Analysis.— The Foundations of a New Theory. By Major P. A. M a c M a h o n , D.Sc., F . R . S ...... 361

Index to Volume . 387 [ V ]

LIST OF ILLUSTRATIONS.

Plate 1.—Drs. J. A. H a r k e r and P. C h a p p u is on a Comparison of Platinum and Gas Thermometers, including a Determination of the Boiling-Point of Sulphur on the Nitrogen Scale. An Account of Experiments made in the Laboratory of the Bureau International des Poids et Mesures at Sevres.

Plates 2-3.—Messrs. A. M. W o rth in g to n and R. S. C ole on Impact with a Liquid Surface studied by the aid of Instantaneous Photography.—Paper II.

Plates 4 -5 .—Messrs. C. T. H eycock and F. H . N evtlle on Gold-Aluminium Alloys. Vll

ADVERTISEMENT.

T h e 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 Boyal 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, [ viii J 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. [ i* 1

1 9 0 0 .

L is t o f I nstitutions e n t i t l e d t o r e c e i v e t h e P hilosophical T ransactions o r

P r o c e e d in g s o f t h e R o y a l S o c ie t y .

Institutions marked a are entitled to receive Philosophical Transactions, Series A, and Proceedings. „ „ b „ „ „ „ Series B, and Proceedings. „ „ ab „ „ „ „ Series A and B, 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- Buenos Ayres. mark. ab. Museo Nacional. Innsbruck. Caracas. ab. Das Ferdinandeum. b. University Library p. Naturwissenschaftlich - Medicinischer Cordova. Verein. ab. Academia Nacional de Ciencias. Prague. Demerara. AB. Konigliche Bohmische Gesellschaft der p. Royal Agricultural and Commercial W issenschaf 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. p. Antbropologische Gesellschaft. Australia. ab. Kaiserliche Akademie der Wissenschaften. Adelaide. p. K.K. Geographische Gesellschaft. p. Royal Society of South Australia. ab. K.K. Geologische Reichsanstalt. Brisbane. b. K.K. Naturhistorisches Hof-Museum. p. Royal Society of Queensland. b. K.K. Zoologisch-Botanische Gesellschaft. Melbourne. p. Oesterreichische Gesellschaft fur Meteoro- p. Observatory. logie. p. Royal Society of Victoria. a. Von Kuffner’sche Sternwarte. 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. is. 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- Agram. logie, et d’Hydrologie. p. Jugoslavenska Akademija Znanosti i Um- p. Societe Malacologique de Belgique. jetnosti. Ghent. p. Societas Historico-Naturalis Croatica. ab. University. VOL. CXCIV.— A. b [ xi ] England and Wales (continued). England and Wales (continued). London (continued). Oxford. p. London Library. p. Ashmolean Society. A. Mathematical Society. ab. Radcliffe Library. p. Meteorological Office. A. Radcliffe Observatory. p. Odontological Society. Penzance. p. Pharmaceutical Society. p. Geological Society of Cornwall. p. Physical Society. Plymouth. p. Quekett Microscopical Club. B. Marine Biological Association. p. Royal Agricultural Society. p. Plymouth Institution. Richmond. a. Royal Astronomical Society. B. Royal College of Physicians. a. “ Kew ” Observatory. B. Royal College of Surgeons. Salford. p. Royal Engineers (for Libraries abroad, six p. Royal Museum and Libraiy. copies). Stonyhurst. ab. Royal Engineers. Head Quarters Library. p. The College. p. Royal Geographical Society. Swansea. p. Royal Horticultural Society. AB. Royal Institution. Woolwich. p. Royal Institute of British Architecis. ab. Royal Artillery Library. ab. Royal Institution of Great Britain. Finland. b. Royal Medical and Chirurgical Society. p. Royal Meteorological Society. Helsingfors. p. Royal Microscopical Society. p. Societas pro Fauna et Flora Fenuica. p. Royal Statistical Society. ab. Societe des Sciences. France. ab. Royal United Service Institution. Bordeaux. ab. Society of Arts. p. Society of Biblical Archeology. p. Academie des Sciences. p. Society of Chemical Industry (London p. Faculte des Sciences. Section). p. Societe de Medecine et de Chirurgie. p. Standard Weights and Measures Depart­ p. Societe des Sciences Physiques et ment. Naturelles. 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 etArts. 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’Onest Section). de la France. Paris. Norwich. ab. Academie des Sciences de l’lnstitut. p. Norfolk and Norwich Literary Institution. p. Association Fran^aise pour l’Avancement Nottingham. des Sciences. ab. Free Public Library. p. Bureau des Longitudes. b 2 [ xii 1

France (continued). Germany (continued). Paris (continued). Emden. a. Bureau International des Poids et Mesures. p. Raturforschende Gesellschaft. p. Commission des Annales des Pouts et Erlangen. Chaussees. ab. Physikalisch-Medicinische Societal. p. Conservatoire des Arts et Metiers. Frankfurt-am-Main. p.Cosmos (M. l ’A bbe V alette). ab. Senckenbergische Raturforschende Gesell­ ab. Depot de la Marine. schaft. ab. lilcole des Mines. p. Zoologische Gesellschaft. ab. Ecole Normale Superieure. Frankfurt-am-Oder. ab. Ccole Polytechnique. p. Raturwissenschaftlicher Yerein. ab. Faculte des Sciences de la Sorbonne. Freiburg-i m-Breisgau. B. Institut Pasteur. ab. Universitat. ab. Jardin des Plantes. Giessen. p. L’Electricien. ab. Grossherzogliche Universitat. A. L’Observatoire. p. Revue Scientifique (Mons. H. de V arigny). Gorlitz. p. Societe de Biologie. p. Raturforschende Gesellschaft. ab. Societe d’Encouragement pour ^Industrie Gottingen. Rationale. ab. Konigliche Gesellschaft der Wissenschaf ten. ab. Societe de Geographie. Halle. p. Societe de Physique. ab. Kaiserliche Leopoldino - Carolinische B. Societe Entomologique. Deutsche Akademie der Raturforscher. AB. Societe Geologique. p. Raturwissenschaftlicher Yerein fiir Sach­ p. Societe Mathematique. sen und Thiiringen. p. Societe Meteorologique de France. Hamburg. Toulouse. p. Raturhistorisches Museum. ab. Academie des Sciences. ab. Raturwissenschaftlicher Yerein. a. Faculte des Sciences. Heidelberg. Germany. p. Raturhistorisch-Medizinischer Yerein. Berlin. ab. Universitat. a. Deutsche Chemische Gesellschaft. Jena. a. Die Sternwarte. ab. Medicinisch-Raturwissenschaftliche Gesell­ p. Gesellschaft fur Erdkunde. schaft. ab. Konigliche Preussische Akademie der Karlsruhe. W issenschaften. a. Grossherzogliche Sternwarte. a. Physikalische Gesellschaft. p. Technische Hochschule. Bonn. Kiel. p. Raturwissenschaftlicher Verein fiir ab. Universitat. Schleswig-Holstein. Bremen. A. Astronomische Rachrichten. p. Raturwissenschaftlicher Yerein. ab. Universitat. Breslau. p. Schlesische Gesellschaft fiir Y aterliindische Konigsberg. Kultur. AB. Konigliche Physikalisch - Okonomische Gesellschaft. Brunswick. Leipsic. p. Verein fiir Raturwissenscliaft. p. Annalen der Physik und Chemie. Charlottenburg. ab. Konigliche Sachsische Gesellschaft der a. Physikalisch-Technische Reichsanstalt. W issenschaften. Danzig. Magdeburg. ab. Raturforschende Gesellschaft. p. Raturwissenschaftlicher Yerein. Dresden. Marburg. p. Verein fiir Erdkunde. AB. Universitat. [ xiii ] Germany (continued). Ireland. Munich. Armagh. ab. Kbnigliche Bayerische Akademie der A. Observatory. Wissenschaf ten. Belfast. p. Zeitschrift fiir Biologie. ab. Queen’s College. Miinster. Cork. ab. Konigliche Theologische und Philo- p. Philosophical Society. sophische Akademie. ab. Queen’s College. Potsdam. Dublin. A. As trophy sikalisches Observatorium. A. Observatory. Rostock. ab. National Library of Ireland. ab. Universitat. b. Royal College of Surgeons in Ireland. Strasburg. ab. Royal Dublin Society. AB. Universitat. ab. Royal Irish Academy. Tubingen. Galway. AB. Universitat. ab. Queen’s College. W iirzburg. Italy. ab. Physikalisch-Medicinische Gesellschaft. Acireale. Greece. p. Accademia di Scienze, Lettere ed Arti. Athens. Bologna. A. Rational Observatory. ab. Accademia delle Scienze dell’ Istituto. Catania. Holland. (See N etherlands.) ab. Accademia Gioenia di Scienze Naturali. Hungary. Florence. Buda-pest. p. Biblioteca Nazionale Centrale. p. Konigl. Ungarische Geologische Anstalt. ab. Museo Botanico. ab. A Magyar Tudos Tarsasag. Die Ungarische p. Reale Istituto di Studi Superiori. Akademie der Wissenschaf ten. Genoa. Hermannstadt. p. Societa Ligustica di Scienze Naturali e p. Siebenbiirgischer Verein fur die Natur- Geograficho. wissenschaften. Milan. Klausenburg. ab. Reale Istituto Lombardo di Scienze, ab. Az Erdelyi Muzeum. Das Siebenburgische Lettere ed Arti. Museum. ab. Societa Italiana di Scienze Naturali. S chemnitz. Modena. p. K. Ungarische Berg- und Forst-Akademie, p. Le Stazioni Sperimentali Agrarie Italiane. India. Naples. Bombay. p. Societa di Naturalisti. ab. Societa Reale, Accademia delle Scienze. ab. Elphinstone College. p. Royal Asiatic Society (Bombay Branch). b. Stazione Zoologica (D r. D ohrn). Padua. Calcutta. p. University. ab. Asiatic Society of Bengal. Palermo. ab. Geological Museum. A. Circolo Matematico. p. Great Trigonometrical Survey of India. AB. Consiglio di Perfezionamento (Societa di ab. Indian Museum. Scienze Naturali ed Economiche). p. The Meteorological Reporter to the A. Reale Osservatorio. Government of India. Pisa. Madras. p. 11 Nuovo Cimento. b. Central Museum. p. Societa Toscana di Scienze Naturali. A. Observatory. Rome. Roorkee. p. Accademia Pontificia de’ Nuovi Lincei. p. Roorkee College. p. Rassegna delle Scienze Geologiche in Italia. [ XIV 1 Italy (continued). Norway. Home (continued). Bergen. a. Reale Ufficio Centrale di Meteorologia e di ab. Bergenske Museum. Geodinamica, Collegio Romano. Christiania. ab. Reale Accademia dei Lincei. ab. Kongelige Norske Frederiks Universitet. p. R. Comitato Geologico d’ Italia. Tromsoe. a. Specola Vaticana. p. Museum. ab. Societa Italiana delle Scienze. Trondhjem. Siena. ab. Kongelige Norske Videnskabers Sclskab. p. Reale Accademia dei Fisiocritici. Portugal. Turin. Coimbra. p. Laboratorio di Fisiologia. ab. Universidade. ab. Reale Accademia delle Scienze. Lisbon. Venice. ab. Academia Real das Sciencias. p. Ateneo Veneto. p. Sec^ao dos Trabalhos Geologicos de Portugal. ab. Reale Istitnto Veneto di Scienze, Lettere Oporto. ed Arti. p. Annaes de Sciencias Naturaes. Japan. Russia. Tokio. Dorpat. AB. Imperial University. ab. Universite. p. Asiatic Society of Japan. Irkutsk. Java. p. Societe Imperiale Russe de Geograph ie Buitenzorg. (Section de la Siberie Orientale). p. Jardin Botanique. Kazan. Luxembourg. ab. Imperatorsky Kazansky Universitet. Luxembourg. p. Societe Physico-Matliematique. p. Societe des Sciences Naturelles. Kharkoff. Malta. p. Section Medicale de la Societe des Sciences p. Public Library. Experimentales, Universite de Kharkoff. Mauritius. Kieff. p. Societe des Naturalistes. p. Royal Society of Arts and Sciences. Kronstadt. Netherlands. p. Marine Observatory. Amsterdam. Moscow. ab. Koninklijke Akademie van Wetenscliappen. ab. Le Musee Public. p. K. Zoologiscb Genootschap ‘ Natura Artis b. Societe Imperiale des Naturalistes. Magistral Odessa. Delft. p. Societe des Naturalistes de la Nouvellc- p. Ecole Polytechnique. Russie. Haarlem. Pulkowa. ab. Hollandscbe Maatschappij der Weten- A. Nikolai Haupt-Sternwarte. schappen. St. Petersburg. p. Musee Teyier. ab. Academie Imperiale des Sciences. Leyden. b. Archives des Sciences Biologiques. ab. University. ab. Comite Geologique. Rotterdam. ab. Ministere de la Marine. ab. Bataafsch Genootschap der Proefonder- A. Observatoire Physique Central. vindelijlce Wijsbegeerte. Scotland. Utrecht. Aberdeen. ab. Provinciaal Genootschap van Kunsten en ab. University. W etenschappen. Edinburgh. New Zealand. p. Geological Society. Wellington. p. Royal College of Physicians (Research ab. New Zealand Institute. Laboratory). [ xv 1 Scotland (contiuucd). t I United States. Edinburgh (continued). Albany. p. Royal Medical Society. ab. New York State Library. A. Royal Observatory. Annapolis. p. Royal Physical Society. ab. Naval Academy. p. Royal Scottish Society of Arts. Austin. ab Royal Society. p. Texas Academy of Sciences. Glasgow. Baltimore. ab. Mitchell Free Library. ab. Johns Hopkins University. p. Natural History Society. Berkeley. p. Philosophical Society. p. University of California. Servia. Boston. Belgrade. ab. American Academy of Sciences. p. Academie Roy ale de Serbie. b. Boston Society of Natural History. I taly.) Sicily. (See a. Technological Institute. Spain. Brooklyn. Cadiz. ab. Brooklyn Library. a. Instituto y Observatorio de Marina de San Cambridge. Fernando. ab. Harvard University. Madrid. b. Museum of Comparative Zoology. p. Comision del Mapa Geologico de Espana, Chapel Hill (N.C.). ab. Real Academia de Ciencias. p, Elisha Mitchell Scientific Society. Sweden. Charleston. Gottenburg. p. Elliott Society of Science and Art of South ab. Kong].Vetenskaps och Vitterhets Samhalle. Carolina. Lund. Chicago. ab. Universitet. ab. Academy of Sciences. Stockholm. p. Astrophysical Journal. a. Acta Mathematica. p. Field Columbian Museum. ab. Kongliga Svenska Vetenskaps-Akademie. Davenport (Iowa). ab. Sveriges Geologiska Undersokning. Upsala. p. Academy of Natural Sciences. Granville (Ohio). ab. Universitet. Switzerland. p. Journal of Comparative Neurology. Basel. Ithaca (N.Y.). p. Naturforschende Gesellschaft. A. Journal of Physical Chemistry. Bern. p. Physical Review (Cornell University). ab. Allg. Schweizerische Gesellschaft. Lawrence. p. Naturforschende Gesellschaft. p. Kansas University. Geneva. Madison. ab. Societe de Physique et d’Histoire Naturelle. p. Wisconsin Academy of Sciences. ab. Institut National Genevois. Mount Hamilton (California). Lausanne. A. Lick Observatory. p. Societe Vaudoise des Sciences Naturelles. New Haven (Conn.). Neuchatel. ab. American Journal of Science. p. Societe des Sciences Naturelles. ab. Connecticut Academy of Arts and Sciences. Zurich. New York. ab. Das Schweizerische Polytechnikum. p. American Geographical Society. p. Naturforschende Gesellschaft. A. American Mathematical Society, p. Sternwarte. p. American Museum of Natural History Tasmania. AB. Columbia College Library, Hobart. p. New York Academy of Sciences, p. Royal Society of Tasmania. p. New York Medical Journal. [ xvi ]

United StatesJ(continued). United States (continued). Philadelphia. Washington. ab. Academy of Natural Sciences. ab. Patent Office. ab. American Philosophical Society. ab. Smithsonian Institution. p. Franklin Institute. ab. United States Coast Survey. p. Wagner Free Institute of Science. b. United States Commission of Fish and Rochester (N.Y.). Fisheries. p. Academy of Science. ab. United States Geological Survey. St. Louis. ab. United States Naval Observatory. p. Academy of Science. p. United States Department of Agriculture. Salem (Mass.). a. United States Department of Agriculture p. American Association for the Advance­ (Weather Bureau). ment of Science. West Point (N.Y.) ab. Essex Institute. ab. United States Military Academy. San Francisco. ab. California Academy of Sciences.