CLERK MAXWELL'S
ELECTROMAGNETIC THEORY
The Rede Lecture for 1923
BY
H. A. LORENTZ
CAMBRIDGE
AT THE UNIVERSITY PRESS
1923
CLERK MAXWELL'S
ELECTROMAGNETIC THEORY
WHEN I had the honour to be invited to deliver a lecture in the Rede Foundation, I thought I might perhaps present to you a brief review of the electromagnetic theory of your great physicist James Clerk Maxwell. The choice seemed the more appropriate as it is now exactly fifty years ago that the work which raised him at once to the very first rank of investigators of all ages, the Treatise on Electricity and Magnetism, was published. In this work it was proved beyond all doubt that electric and magnetic actions can be conceived as being transmitted through a medium and the theory was crowned by the wonderful revelation that light is an electromagnetic phenomenon.
Maxwell's theory was also a great simplification. Indeed, before his time there was much uncertainty and confusion in this part of physics and many contending theories were in the field. In electrodynamics, for instance, we had the laws of Ampère and Grassmann for the actions between elements of current, and, when we went further, we found the speculations of Weber, Riemann and Clausius about the mutual actions of particles of electricity. In connexion with these theories there was a good deal of discussion on the phenomena that were to be expected in the case of closed and in that of open circuits. It was thought in those days that the current in a wire by means of which a metallic conductor is charged, ends on that conductor, and even the discharge current of a condenser was considered not to be closed; there was a gap in the circuit, because we had no idea that something is going on in the insulating layer between the coatings.
In optics we had no less trouble. It is true that the general principles of the undulatory theory of light had been firmly established and physicists were justly proud of the success that had been achieved in the explanation of interference and diffraction, double refraction and polarization. Yet, when we tried to penetrate somewhat deeper, we were confronted with serious difficulties. When we wanted to account for the different optical properties of various substances, of air and water for instance, we had the choice between two assumptions. Fresnel had sought the cause of the difference in an inequality of the density of the ether in 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 right value for the ratio between the amplitude of the reflected and that of the incident light. You know that in this problem two principal cases must be distinguished, the vibrations being normal to the plane of incidence in the one case and parallel to that plane in the other. The two values for the ratio in question are