Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/386

Maxwell made no change in the other electromagnetic equations, which therefore retained the customary forms

$\mathbf {D} =\epsilon \mathbf {E} ^{\prime }/4\pi c^{2},\qquad {\text{div }}\mathbf {D} =0,\qquad 4\pi ({\boldsymbol {\iota }}+\mathbf {\dot {D}} )={\text{curl }}\mathbf {H}$,

Hertz, however, impressed by the duality of electric and magnetic phenomena, modified the last of these equations by assuming that a magnetic force 4π [D.w] is generated in a dielectric which moves with velocity w in an electric field; such a force would be the magnetic analogue of the electromotive force of induction. A term involving curl [D.w] is then introduced into the last equation.

The theory of Hertz resembles in many respects that of Heaviside,^[1] who likewise insisted much on the duplex nature of the electromagnetic field, and was in consequence disposed to accept the term involving curl [D.w] in the equations of moving media. Heaviside recognized more clearly than his predecessors the distinction between the force E′, which determines the flux D, and the force E, whose curl represents the electric current; and, in conformity with his principle of duality, he made a similar distinction between the magnetic force H′, which determines the flux B, and the force H, whose curl represents the "magnetic current" This distinction, as Heaviside showed, is of importance when the system is acted on by "impressed forces," such as voltaic electromotive forces, or permanent magnetization; these latter must be included in E′ and K′, since they help to give rise to the fluxes D and B; but they must not be included in E and H since their curls are not electric or magnetic currents; so that in general We have

$\mathbf {E} ^{\prime }=\mathbf {E} +\mathbf {e} ,\qquad \mathbf {H} ^{\prime }=+\mathbf {h}$,

where e and h denote the impressed forces.

Developing the theory by the aid of these conceptions, Heaviside was led to make a further modification, An im-

1. Heaviside's general theory was published in a series of papers in the Electrician, from 1885 onwards. His earlier work was republished in his Electrical Papers (2 vols., 1892), and his Electromagnetic Theory (2 vols., 1894). Mention may be specially made of a memoir in Phil. Trans. clxxxiii (1892), P. 423.