August 25, 1905.1 



SCIENCE. 



245 



as well as monographs on particular topics ; 

 Avhat seems to me to be lacking is some com- 

 prehensive and comparative survey of the 

 whole range. The history of any of the 

 natural sciences, like the history of human 

 activity, is not merely an encyclopaedic 

 record of past facts; it reveals both the 

 spirit and the wealth which the past has 

 bequeathed to the present, and which, in 

 due course, the present will influence before 

 transmission to the future. Perhaps all 

 our physicists are too busy to spare the 

 labor needed for the production of a com- 

 prehensive history; yet I cannot help 

 thinking that such a contribution to the 

 subject would be of great value, not to 

 physicists alone. 



But, as you hear me thus referring to 

 astronomy and to physics, some of you 

 may think of the old Roman proverb which 

 made the cobbler not to look above his last ; 

 so I take the opportunity of referring very 

 hriefly to my own subject. One of the 

 features of the century has been the con- 

 tinued development of mathematics. As a 

 means of calculation the subject was de- 

 veloped as widely during the earlier portion 

 of the century as during the preceding 

 century; it soon began to show signs of 

 emergence as an independent science, and 

 the later part of the century has witnessed 

 the emancipation of pure mathematics. It 

 w'as pointed out, in connection with the 

 growth of theoretical astronomy, that 

 mathematics developed in the direction of 

 its application to that subject. AA^hen the 

 wonderful school of French physicists, 

 composed of Monge, Carnot, Fourier, Pois- 

 son, Poinsot, Ampere and Fresnel (to men- 

 tion only some names), together with Gauss, 

 Kirchhoff and von Helmholtz in Germany, 

 and Ivory, Green, Stokes, Maxwell and others 

 in England, applied their mathematics to 

 various branches of physics, for the most 

 part its development was that of an ancil- 



lary subject. The result is the superb body 

 of knowledge that may be summarized un- 

 der the title of ' mathematical physics ' ; 

 but the final interest is the interest of 

 physics, though the construction has been 

 the service of mathematics. Moreover, 

 this tendency was deliberate, and was 

 avowed in no uncertain tone. Thus Fourier 

 could praise the utility of mathematics by 

 declaring that ' there was no language more 

 universal or simpler, more free from errors 

 or obscurity, more worthy of expressing 

 the unchanging relations of natural enti- 

 ties ' ; in a burst of enthusiasm he declares 

 that, from the point of view he had indi- 

 cated, ' mathematical analysis is as wide 

 as nature herself, ' and ' it increases and 

 grows incessantly stronger amid all the 

 changes and errors of the human mind.' 

 Mathematicians might almost blush with 

 conscious pleasure at such a laudation of 

 their subject from such a quarter, though 

 it errs by both excess and defect ; but the 

 exultation of spirit need not last long. The 

 same authority, when officially expounding 

 to the French Academy the work of Jacobi 

 and of Abel upon elliptic functions, ex- 

 pressed his chilling opinion (it had nothing 

 to do with the case) that 'the questions of 

 natural philosophy, which have the mathe- 

 mathical study of all important phenomena 

 for their aim, are also a worthy and princi- 

 pal subject for the meditations of geometers. 

 It is to be desired that those persons who are 

 best fitted to improve the science of calcu- 

 lation should direct their labors to these im- 

 portant applications.' Abel was soon to 

 pass beyond the range of admonition ; but 

 Jacobi, in a private letter to Legendre, pro- 

 tested that the scope of the science was 

 npt to be limited to the explanation of 

 natural phenomena. I have not quoted 

 these ex-tracts by way of even hint of re- 

 proach against the author of such a wonder- 

 ful creation as Fourier's analytical theory 



