5io POPULAR SCIENCE MONTHLY. 



rial medium capable of conveying transverse vibrations, and of ac- 

 counting also for the various phenomena of reflection, refraction and 

 double refraction. It has often been pointed out, as characteristic of 

 the French school referred to, that their physical speculations were 

 largely influenced by ideas transferred from astronomy; as, for in- 

 stance, in the conception of a solid body as made up of discrete par- 

 ticles acting on one another at a distance with forces in the lines joining 

 them, which formed the basis of most of their work on elasticity and 

 optics. The difficulty of carrying out these ideas in a logical manner 

 was enormous, and the strict course of mathematical deduction had to 

 be replaced by more or less precarious assumptions. The detailed 

 study of the geometry of a continuous deformable medium which was 

 instituted by Cauchy was a first step towards liberating the theory from 

 arbitrary and unnecessary hypothesis; but it was reserved for Green, 

 the immediate predecessor of Stokes among English mathematicians, 

 to carry out this process completely and independently, with the help 

 of Lagrange's general dynamical methods, which here found their first 

 application to questions of physics outside the ordinary dynamics of 

 rigid bodies and fluids. The modern school of English physicists, 

 since the time of Green and Stokes, have consistently endeavored to 

 make out, in any given class of phenomena, how much can be recog- 

 nized as a manifestation of general dynamical principles, independent 

 of the particular mechanism which may be at work. One of the most 

 striking examples of this was the identification by Maxwell of the laws 

 of electromagnetism with the dynamical equations of Lagrange. It 

 would, however, be going too far to claim this tendency as the exclusive 

 characteristic of English physicists; for example, the elastic investiga- 

 tions of Green and Stokes have their parallel in the independent though 

 later work of Kirchhoff ; and the beautiful theory of dynamical systems 

 with latent motion which we owe to Lord Kelvin stands in a very 

 similar relation to the work of Helmholtz and Hertz. 



But perhaps the most important and characteristic feature in the 

 mathematical work of the later school is its increasing relation to and 

 association with experiment. In the days when the chief applications 

 of mathematics were to the problems of gravitational astronomy, the 

 mathematician might well take his materials at second hand; and in 

 some respects the division of labor was, and still may be, of advantage. 

 The same thing holds in a measure of the problems of ordinary dynam- 

 ics, where some practical knowledge of the subject matter is within the 

 reach of every one. But when we pass to the more recondite phe- 

 nomena of physical optics, acoustics and electricity, it hardly needs 

 the demonstrations which have involuntarily been given to show that 

 the theoretical treatment must tend to degenerate into the pursuit of 

 mere academic subtleties unless it is constantly vivified by direct con- 



