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SCIENCE. 



[N. S. Vol. XXII. No. 556. 



of heat ; his estimate could have been justi- 

 fied on a merely historical review of the 

 circumstances of his own time and of past 

 times ; and I am not sure that his estimate 

 has not its exponents at the present day. 

 But all history shows that new discoveries 

 and new methods can spread to issues wider 

 than those of their origins, and that it is 

 almost a duty of human intelligence to 

 recognize this possibility in the domain of 

 progressive studies. The fact is that mathe- 

 matical physics and pure mathematics have 

 given much to each other in the past and 

 will give much to each other in the future ; 

 in doing so, they will take harmonized ac- 

 tion in furthering the progress of knowl- 

 edge. But neither science must pretend to 

 absorb the activity of the other. It is al- 

 most an irony of circumstance that a theo- 

 rem, initiated by Fourier in the treatise 

 just mentioned, has given rise to a vast 

 amount of discussion and attention, which, 

 while of supreme value in the development 

 of one branch of pure mathematics, have 

 hitherto offered little, if anything, by way 

 of added explanation of natural phe- 

 nomena. 



The century that has gone has witnessed 

 a wonderful development of pure mathe- 

 matics. The bead-roll of names in that 

 science— Gauss; Abel, Jacobi; Cauchy, 

 Riemann, Weierstrass, Hermite ; Cayley, 

 Sylvester ; Lobatchewsky, Lie — will on only 

 the merest recollection of the work with 

 which their names are associated show that 

 an age has been reached where the develop- 

 ment of human thought is deemed as worthy 

 a scientific occupation of the human mind 

 as the most profound study of the phe- 

 nomena of the material universe. 



The last feature of the century that will 

 be mentioned has been the increase in the 

 number of subjects, apparently dissimilar 

 from one another, which are now being 

 made to use mathematics to some extent. 



Perhaps the most surprising is the appli- 

 cation of mathematics to the domain of 

 pure thought; this was effected by George 

 Boole in his treatise ' Laws of Thought,' 

 published in 1854 ; and though the develop- 

 ments have passed considerably beyond 

 Boole's researches, his work is one of those 

 classics that mark a new departure. Polit- 

 ical economy, on the initiative of Cournot 

 and Jevons, has begun to employ symbols 

 and to develop the graphical methods; but 

 there the present use seems to be one of 

 suggestive record and ., expression, rather 

 than of positive construction. Chemistry, 

 in a modern spirit, is stretching out into 

 mathematical theories; Willard Gibbs, in 

 his memoir on the equilibrium of chemical 

 systems, has led the way; and, though his 

 way is a path which chemists find strewn 

 with the thorns of analysis, his work has 

 rendered, incidentally, a real service in co- 

 ordinating experimental results belonging 

 to physics and to chemistry. A new and 

 generalized theory of statistics is being con- 

 structed ; and a school has grown up which 

 is applying them to biological phenomena. 

 Its activity, however, has not yet met with 

 the sympathetic good- will of all the pure 

 biologists ; and those who remember the 

 quality of the discussion that took place last 

 year at Cambridge between the biometri- 

 cians and some of the biologists will agree 

 that, if the new school should languish, it 

 will not be for want of the tonic of 

 criticism. 



If I have dealt with the past history of 

 some of the sciences with which our section 

 is concerned, and have chosen particular 

 epochs in that history with the aim of con- 

 centrating your attention upon them, you 

 will hardly expect me to plunge into the 

 future. Being neither a prophet nor the 

 son of a prophet, not being possessed of the 

 knowledge which enabled Halley to don the 

 prophet's mantle with confidence, I shall 



