CLERK MAXWELL'S
ELECTROMAGNETIC THEORY
The Rede Lecture for 1923
BY
CAMBRIDGE
AT THE UNIVERSITY PRESS
1923
CLERK MAXWELL'S
ELECTROMAGNETIC THEORY
WHEN I had the honour to be invited todeliver a lecture in the Rede Foundation, I thought I might perhapspresent to you a brief review of the electromagnetic theory of yourgreat physicist James Clerk Maxwell. The choice seemed the moreappropriate as it is now exactly fifty years ago that the work whichraised him at once to the very first rank of investigators of all ages,the Treatise on Electricity and Magnetism, was published. In this workit was proved beyond all doubt that electric and magnetic actions can beconceived as being transmitted through a medium and the theory wascrowned by the wonderful revelation that light is an electromagneticphenomenon.
Maxwell's theory was also a great simplification. Indeed, before histime there was much uncertainty and confusion in this part of physicsand many contending theories were in the field. In electrodynamics, forinstance, we had the laws of Ampère and Grassmann for the actionsbetween elements of current, and, when we went further, we found thespeculations of Weber, Riemann and Clausius about the mutual actions ofparticles of electricity. In connexion with these theories there was agood deal of discussion on the phenomena that were to be expected in thecase of closed and in that of open circuits. It was thought in thosedays that the current in a wire by means of which a metallic conductoris charged, ends on that conductor, and even the discharge current of acondenser was considered not to be closed; there was a gap in thecircuit, because we had no idea that something is going on in theinsulating layer between the coatings.
In optics we had no less trouble. It is true that the general principlesof the undulatory theory of light had been firmly established andphysicists were justly proud of the success that had been achieved inthe explanation of interference and diffraction, double refraction andpolarization. Yet, when we tried to penetrate somewhat deeper, we wereconfronted with serious difficulties. When we wanted to account for thedifferent optical properties of various substances, of air and water forinstance, we had the choice between two assumptions. Fresnel had soughtthe cause of the difference in an inequality of the density of the etherin the two substances, the elasticity being the same in both. F. E.Neumann, on the other hand, had supposed the densities to be the same,but the elasticities to be different. On either of these suppositions,and in no other way, it had been found possible to deduce the rightvalue for the ratio between the amplitude of the reflected and that ofthe incident light. You know that in this problem two principal casesmust be distinguished, the vibrations being normal to the plane ofincidence in the one case and parallel to that plane in the other. Thetwo values for the ratio in question are
sin (i - r) / sin (i + r)
and
tg (i - r) / tg (i + r),
if i is the angle of incidence and r the angle ofrefraction; and it is remarkable that, of the two rival theories, oneled