Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/448

 which vanishes by virtue of the principle of conservation of electricity. Thus

or the total current is a circuital vector, Equations (I) to (V) are the fundamental equations of Lorentz' theory of electrons.

We have now to consider the relation by which the polarization of dielectrics is determined. If the dielectric is moving with velocity, the ponderomotive force on unit electric charge moving with it is (as in all theories)

In order to connect with, it is necessary to consider the motion of the corpuscles. Let denote tho charge and  the mass of a corpuscle,  its displacement from its position of equilibrium,  the restitutive force which retains it in the vicinity of this point; then the equations of motion of the corpuscle are

and similar equations in and. When the corpuscle is set in motion by light of frequency passing through the medium, the displacements and forces will be periodic functions of —say,

Substituting these values in the equations of motion, we obtain

Thus, if denote the number of polarizable molecules per unit volume, the polarization is determined by the equation

In the particular case in which the dielectric is at rest, this equation gives

But, as we have seen bears to  the ratio, where