io8 



NA TURE 



[December 5, 1901 



and externally compensated substances. The phase rule has 

 also been applied with complete success by van 't MolT to the 

 elucidation of the formation of oceanic salt deposits. In fact, 

 Willard Gibbs's generalisation is applicable to all cases of 

 reversible chemical interchange, and consequently to chemical 

 change generally. 



Royal Medal. 

 Prof. William Edward Ayrloii, F.R.S. 



A Royal Medal is given to Prof. William Edward Ayrton, 

 F.R.S. , for his contributions to electrical science. 



The services rendered by Prof, .\yrton to science daring the 

 last twenty-seven years may be roughly grouped under two heads. 

 He has carried out a large number of researches in pure physics, 

 and he has taken a very prominent part in the development of 

 the application of electricity to industr)', which has been so 

 remarkable a feature of the closing years of the nineteenth 

 century. It is not here necessary to refer particularly to his 

 researches, invention and inspiration under the second head. 

 At all times he has been doing service under both heads. From 

 1873 'o 'S7S, in Japan ; from 1879 to 18S4, at Finsbury ; and 

 from 1884 to the present time, at the Central College, Ken- 

 sington, he has acted as professor of physics ; he has arranged 

 large laboratories, and through his own example in research he 

 has inspired many students, who are now carrying out investiga- 

 tions of their own. 



A large number of papers contributed, sometimes alone and 

 sometimes in partnership with others, to the Royal Society 

 Proceedings and Transactions and other scientific publications, 

 while belonging to the second group above mentioned, have 

 greatly assisted in pure physics. 



It is not out of place to quote a published remark of the late 

 Prof. Clerk Maxwell in reference to the work of Prof. Ayrton 

 and a colleague in Japan, that they had moved the centre of 

 gravity of electrical science greatly eastward. 



Royal Medal. 

 Dr. VVilliani Thomas Blanford, F. R. S. 



The other Royal Medal is conferred upon Dr. William 

 Thomas Blanford, F.R.S., for his work in connection with 

 the " Geographical Distribution of Animals." 



Dr. W. T. Blanford received his scientific education at the 

 Royal School of Mines, and, after special instruction in the 

 methods of geological surveying under Prof, (afterwards -Sir 

 Andrew) Ramsay on the English Geological Survey, proceeded 

 in 1855 to take up a post on the Geological Survey of India. 



Between the years 1855 and 1 868, when he was engaged in 

 surveying difierent parts of India and Burma, he published a 

 number of valuable papers on Indian geology, and upon 

 malacology and other branches of natural history, based on 

 observations made during his travels as a geological surveyor. 



In 1S6S he was appointed to accompany the expeditionary 

 force under Lord Napier to Abyssinia in the capacity of 

 naturalist, and his observations on the geology and fauna of the 

 country are published in a number of communications to 

 scientific journals and in his work, "Observations on the 

 Geology and Zoology of Abyssinia," published in 1S70. 



Between 186S and 1872, Dr. Blanford returned to his work 

 on the Geological Survey of India, and as the result of his 

 labours in Sind, Cutch, the Deccan and other parts of the 

 country, a number of memoirs dealing with geology, malaco- 

 logy and ornithology were published by him. In 1872 he was 

 selected to act as naturalist to the Persian Boundary Commission 

 and the results of his observations appeared in a work, 

 "Eastern Persia, vol. ii.. Zoology and Geology," which was 

 published in 1876. 



Returning to India, he not only carried on the usual survey 

 work, but, in conjunction with Mr. H. B. Medlicott, prepared 

 the important " Manual of the Geology of India," 3 vols., 1879. 

 In this work a most valuable summary of the geological 

 observations which had been made upon all parts of the Indian 

 Empire is given, with a discussion of the age and relationships 

 of the formations of that vast district. 



Since his return from India, in 1SS2, Dr. Blanford has been 

 continuously engaged in zoological and geological researches. 

 His memoirs on the rocks of India .and Australia which 

 exhibit glacial conditions, and on kindred subjects, have been 

 most valuable contributions to geological science. Equally 

 important have been the two addresses on " Geological 

 Nomenclature" and "The Permanence or otherwise of Ocean 



NO. 1675, VOL. 65] 



Basins," which he delivered in his capacity of president of the 

 Geological Society in 1889 and 1890. In the last-mentioned 

 address he has laid down principles and established conclusions 

 which have given a new aspect to the study of the geographical 

 distribution of animals. 



" The Fauna of India," published under the authority of the 

 Secretary of State for India in Council (8 vols., concluded in 

 1898), was edited by Dr. Blanford, who has contributed three 

 volumes on birds and mammals. This work has been most 

 favourably received by the scientific public and is looked upon 

 .as the standard authority of Indian vertebrates. His contribu- 

 tions to this work constitute his special claim to a Royal Medal. 



Dr. Blanford is one of the few men who are regarded as an 

 authority on geology, pal.xontology and zoology, to each of 

 which branches of science he has largely contributed. 



Davy Medal. 

 Prof. George Downing Liveing, F.R.S. 



The Davy Medal is awarded to Prof. George Downing Live- 

 ing, F.R.S., for his contributions to spectroscopy. 



Prof. Liveing's papers on spectroscopic subjects have been 

 mainly published during the last quarter of a century in con- 

 junction with Prof. Dewar, and have appeared for the most part 

 in the Proceedings of the Royal Society. Tliey make up a 

 record of patient, accurate, conscientious labour, and, taken 

 together, constitute one of the most valuable contributions to 

 this department of chemical physics yet made by British 

 workers. 



Sylvester Medal. 

 Prof. Henri Poincan', Foreign Member, R. S. 



The Sylvester Medal, given this year for the first time, is 

 awarded to Prof. Henri Poincare, a Foreign Member of this 

 Society, for his many and important contributions to mathe- 

 matical science. 



Prof. Henri Poincare's mathematical writings display very 

 great originality, independence of thought and far sightedness. 

 The number of the memoirs and works which he has 

 published is extraordinary, and the wide range of subjects 

 in pure mathematics and its applications to astronomy 

 and physics which they cover is equally remarkable. The bond 

 of unity which connects his investigations is that nearly all 

 have a more or less intimate connection with the study of 

 ditTerential equations. He has dealt with the theories of linear 

 difterential equations, of ordinary nonlinear differential 

 equations and of partial differential equations, with striking 

 results in each theory ; and each is associated with a department 

 of his other important researches. 



In the theory of linear differential equations, Fuchs had 

 called attention to the substitutions by which different particular 

 integrals are interchanged at the critical points. The sub- 

 stitutions form a group, and (at any rate when the equation is 

 of the second order) there exist aulomorphic functions which 

 are unchanged by the operations of the group. M. Poincare 

 has constructed these functions and shown how by means of 

 them a complete integration of the linear differential equation 

 can be effected (.4cla Malhentatica, t. iv. ). He has devoted five 

 classical memoirs {.4cla Matlumalica, i., iii., iv., v.) to a pro- 

 found study of the aulomorphic functions and Fuchsian' and 

 Kleinian groups. Closely related to the same study are his 

 delicate researches as to the topology of loci in space of n 

 dimensions, and a number of contributions to the theory of 

 algebraic functions. 



In the theory of ordinary differential equations (not linear) he 

 has introduced a new method of dealing with the question of 

 the existence of a solution, and has shown how various methods 

 of approximating to a solution may be utilised for solving the 

 problem which gives rise to the differential equation. This lies 

 at the root of his investigations in connection with the equations 

 of dynamics and the special problem of gravitational astronomy 

 —that of « bodies. He has shown th.at G. W. Hill's periodic 

 solution of the problem of three bodies is one of an infiiiite 

 system. M. Poincare has also discussed from the point of view 

 of modern analysis the methods of solution in periodic series 

 which are associated with the name of Laplace and with the 

 problem of the stability of the solar system, and has been led to 

 give the first complete theory of series of the kind now called 

 " asymptotic " and to point out their uses in analysis. 



Mathematical physics requires the investigation of certain 



