Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/300

ment-current corresponds to ∂B/∂t, and may therefore have a value different from zero even in free aether.

It may be remarked in passing that the term displacement, which was thus introduced, and which has been retained in the later development of the theory, is perhaps not well chosen; what in the early models of the aether was represented as an actual displacement, has in later investigations been conceived of as a change of structure rather than of position in the elements of the aether.

Maxwell supposed the electromotive force acting on the electric particles to be connected with the displacement D which accompanies it, by an equation of the form

$={\frac {1}{4\pi c_{1}^{2}}}\mathbf {E}$,

where c₁ denotes a constant which depends on the elastic properties of the cells. The displacement-current Ḋ must now be inserted in the relation which connects the current with the magnetic force; and thus we obtain the equation

$\mathrm {curl} \ \mathbf {H} =4\pi \mathbf {s}$,

where the vector S, which is called the total current, is the sum of the convection-current i and the displacement-current Ḋ. By performing the operation div on both sides of this equation, it is seen that the total current is a circuital vector, In the model, the total current is represented by the total motion of the rolling particles; and this is conditioned by the rotations of the vortices in such a way as to impose the kinematic relation

$\mathrm {div} \ \mathbf {S} =0$.

Having obtained the equations of motion of his system of vortices and particles, Maxwell proceeded to determine the rate of propagation of disturbances through it. He considered in particular the case in which the substance represented is a dielectric, so that the conduction-current is zero. If, moreover,