Furthermore, Maxwell had considered more especially the case of matter at rest in the ether, and it was necessary to investigate the general case of matter in motion. This extension of Maxwell’s theory, known as the electrodynamics of moving bodies, was attempted by Hertz, who assumed that matter in motion through the ether would drag the ether along with it in its interior—a hypothesis not so radical, but somewhat in line with that of Stokes. So long as conductors were contemplated, Hertz’s hypothesis seemed to be in accord with experiment; but when we came to consider dielectrics in motion, Hertz’s anticipations were contradicted. Fizeau’s experiment in particular, proving that the velocity of running water did not compound with the velocity of the light in stagnant water, was incompatible with Hertz’s hypothesis of a total drag. Also, in an experiment of a totally different nature, dealing with the motion of a dielectric through a magnetic field, Wilson proved the existence of the same partial drag, given once again by Fresnel’s convection coefficient. It appeared, therefore, that Fresnel’s convection coefficient was a fact which would have to be fitted into any theoretical scheme of the electrodynamics of moving dielectrics. Now, Fresnel’s partial drag hypothesis, though seemingly confirmed by experiment, had yet to be accounted for theoretically, and this appeared impossible so long as we remained in such utter ignorance of the ultimate constitution of dielectrics and of matter in general. At this stage Lorentz started his theoretical investigations which were to lead him to a refinement of Maxwell’s equations, extending their application to cases where matter was present, either at rest or in motion through the ether. As we have mentioned, Maxwell’s equations [Pg 130] had proved themselves incapable of accounting for dispersion. It appeared necessary to conceive of some structure for dielectrics which would act selectively, imposing different degrees of retardation on light waves of different frequencies. Lorentz achieved this result by assuming that electricity was atomic and that matter was constituted by more or less complicated groupings of these electric atoms or electrons. In the case of dielectrics or non-conductors such as glass, the electrons were assumed to be tied down to their atoms by elastic forces. When disturbed they would vibrate with some characteristic frequency depending on the magnitude of the elastic forces which held them in place. If, then, a wave of light were transmitted through the transparent dielectric, the electrons would be set into forced vibration and the retarding effect these vibrations would impose on the incident light would depend on the relative frequencies of the incident light and of the natural frequencies of the electrons. In this way it was possible to obtain a mathematical interpretation of dispersion.