pressed force is best defined in terms of the energy which it communicates to the system; thus, if e be an impressed electric force, the energy communicated to unit volume of the electromagnetic system in unit time is e × the electric current. In order that this equation may be true, it is necessary to regard the electric current in a moving medium as composed of the conduction-current, displacement-current, convectioncurrent, and also of the term curl [D.w], whose presence in the equation we have already noticed. This may be called the current of dielectric convection. Thus the total current is
,
![{\displaystyle \mathbf {S} =\mathbf {\dot {D}} ={\boldsymbol {\iota }}+\rho \mathbf {w} +{\text{curl}}[\mathbf {D.w} ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1bf431f80a5b5627c1b81c090a09d8b467b7b9f5)
where ρw denotes the conduction-current; and the equation connecting current with magnetic force is
,
where h0, denotes the impressed magnetic forces other than that induced by motion of the medium.
We must now consider the advances which were effected during the period following the publication of Maxwell's Treatise in some of the special problems of electricity and optics.
We have seen[1] that Maxwell accounted for the rotation of the plane of polarization of light in a medium subjected to a magnetic field K by adding to the kinetic energy of the aether, which is represented by 12ρė2, a term 12σ(ė. curl ∂e/∂θ, where σ is a magneto-optic constant characteristic of the substance through which the light is transmitted, and ∂/∂θ stands for Kx∂/∂x + Ky∂/∂y + Kz∂/∂z. This theory was developed further in 1879 by FitzGerald,[2] who brought it into closer connexion with the electromagnetic theory of light by identifying the curl of the displacement e of the aethereal particles with the electric displacement; the derivate of e with respect to the time then corresponds to the magnetic force. Being thus in possession of a definitely electromagnetic theory of the magnetic rotation of
