TRANSACTIONS OF SECTION A. 423 
shortest ever made on such an occasion, for it occupies only half a page of the report, 
and took, I should say, some three or four minutes to deliver. It would be to the 
advantage of the business of the meeting, and to my own great relief, if I had the 
courage to follow so attractive a precedent ; but I fear that the tradition which 
has since established itself is too strong for me to break without presumption. 
I will turn, therefore, to a theme which, I think, naturally presents itself—viz., 
a consideration of the place occupied by Stokes in the development of Mathe- 
matical Physics. It is not proposed to attempt an examination or appreciation 
of his own individual achievements; this has lately been done by more than one 
hand, and in the most authoritative manner. But it is part of the greatness 
of the man that his work can be reviewed from more than one standpoint. 
What I wish to direct attention to on this occasion is the historical or evolu- 
tionary relation in which he stands to predecessors and followers in the above 
field. 
The early years of Stokes’s life were the closing years of a mighty generation 
of mathematicians and mathematical physicists. When he came to manhood, 
Lagrange, Laplace, Poisson, Fourier, Fresnel, Ampére, had but lately passed 
away. Cauchy alone of this race of giants was still alive and productive. It is 
upon these men that we must look as the immediate intellectual ancestors of 
Stokes, for, although Gauss and IF. Neumann were in their full vigour, the 
interaction of German and English science was at that time not very great. It is 
noteworthy, however, that the development. of the modern German school of 
mathematical physics, represented by Helmholtz and Kirchhoff, in linear 
succession to Neumann, ran in many respects closely parallel to the work of Stokes 
and his followers. 
When the foundations of Analytical Dynamics had been laid by Euler and 
d’Alembert, the first important application was naturally to the problems of 
Gravitational Astronomy; this formed, of course, the chief work of Laplace, 
Lagrange, and others. Afterwards came the theoretical study of Elasticity, 
Conduction of Heat, Statical Electricity, and Magnetism, The investigations in 
Elasticity were undertaken mainly in relation to Physical Optics, with the hope 
of finding a material medium capable of conveying transverse vibrations, and of 
accounting 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 trans- 
ferred from Astronomy ; as, for instance, in the conception of a solid body as made 
up of discrete particles 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 were 
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 endeavoured to make out, in any given class of phenomena, 
how much can be recognised 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 investigations 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 
