13. The next important theoretical contribution to our subject is implicitly contained in §§ 600, 601 of Maxwell's "Treatise on Electricity and Magnetism" (1872). It is there verified, by direct transformation, that the type of the equations of electromotive disturbance is the same whether they are, referred to axes of coordinates at rest in the aether or to axes which are in motion after the manner of a solid body. The principle is here involved, as FitzGerald[1] was the first to point out, and as was no doubt in Maxwell's own mind considering his recent occupation with the subject, that in treating of the electromotive disturbance which constitutes light we are permitted to make use of axes of coordinates which move along with the Earth without having to alter in any way the form of the analytical equations. This statement covers as a special case Bradley's law of astronomical aberration. It also directly includes in its entirety the principle of Arago and Fresnel that the laws of geometrical optics are not affected by the Earth's motion: it ought therefore to involve as a consequence Fresnel's expression for the change of velocity of radiation produced by motion of the material medium which it traverses. The latter question was examined directly from Maxwell's analytical equations by J. J. Thomson[2] with a result different from Fresnel's, namely, that the acceleration of velocity is always half that of the moving material medium, being the same for all kinds of matter. This discrepancy is one of several which indicate that for extremely rapid disturbances like optical waves, the analytical scheme of Maxwell does not sufficiently take into account the influence of the material medium on the propagation. A contradiction of some kind is also suggested by the circumstance that Maxwell's theorem does too much by making the optical properties independent of uniform velocity of rotation of the material medium, as well as of uniform velocity of translation; we shall see (§ 23) that the possibility of exact independence in both respects is negatived by the general nature of rays. The necessary amendment of the scheme of Maxwell has been independently arrived at by more than one writer, but somewhat earliest in point of time
