Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/385

content of Maxwell's theory for bodies at rest, proceeded^[1] to extend the equations to the case in which material bodies are in motion in the field.

In a really comprehensive and correct theory, as Hertz remarked, a distinction should be drawn between the quantities which specify the state of the aether at every point, and those which specify the state of the ponderable matter entangled with it. This anticipation has been fulfilled by later investigators; but Hertz considered that the time was not ripe for such a complete theory, and preferred, like Maxwell, to assume that the state of the compound system—matter plus aether—can be specified in the same way when the matter moves as when it is at rest; or, as Hertz himself expressed it, that "the aether contained within ponderable bodies moves with them."

Maxwell's own hypothesis with regard to moving systems^[2] amounted merely to a modification in the equation

$\mathbf {\dot {B}} =-{\text{curl }}\mathbf {E}$,

which represents the law that the electromotive force in a closed circuit is measured by the rate of decrease in the number of lines of magnetic induction which pass through the circuit. This law is true whether the circuit is at rest or in motion; but in the latter case, the E in the equation must be taken to be the electromotive force in a stationary circuit whose position momentarily coincides with that of the moving circuit; and since an electromotive force [w. B] is generated in matter by its motion with velocity w in a magnetic field B, we see that E is connected with the electromotive force E′ in the moving ponderable body by the equation

$\mathbf {E} ^{\prime }=\mathbf {E} +[\mathbf {w.B} ]$

so that the equation of electromagnetic induction in the moving body is

$\mathbf {\dot {B}} =-{\text{curl }}\mathbf {E} ^{\prime }+{\text{curl }}[\mathbf {w.B} ]$

1. Ann. d. Phys. xli (1890), p. 369; Electric Waves (English ed.), p. 241. The propagation of light through a moving dielectric bad been discussed previously, on the basis of Maxwell's equations for moving bodies, by J.J. Thomason, Phil. Mag. ix (1880), p. 284; Proc. Camb. Phil. Soc. v (1885), p. 250.
2. Cf. p. 288.