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Page:Popular Science Monthly Volume 65.djvu/513

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MATHEMATICAL PHYSICS.

ing that it will in due course engage the attention of the section, and that we may look forward to interesting and stimulating discussions, in which we trust the many distinguished foreign physicists who honor us by their presence will take an active part.

It is, I believe, not an unknown thing for your president to look up the records of previous meetings in search of inspiration, and possibly of an example. I have myself not had to look very far, for I found that when the British Association last met in Cambridge, in the year 1862, this section was presided over by Stokes, and moreover that the address which he gave was probably the 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, in the first instance, to a theme which, I think, naturally presents itself—viz., a consideration of the place occupied by Stokes in the development of mathematical 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 specially wish to direct attention to on this occasion is the historical or evolutionary 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, Ampère had but recently 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 F. Neumann were alive and flourishing, 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 Kirchoff, 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 mate-