Page:BatemanElectrodynamical.djvu/34

 These equations are of the form

{{MathForm2|(I)|$$\left.\begin{array}{lll} \mathsf{curl}\ H=\frac{\partial D}{\partial t}+s, & & \mathsf{div}\ D=\rho\\ \\\mathsf{curl}\ E=-\frac{\partial B}{\partial t}, & & \mathsf{div}\ B=0\end{array}\right\} $$}}

where the vectors E, H, D, B denote the electric force, magnetic force, electric displacement, and magnetic induction respectively, s denotes the current and &rho; the volume density of electricity. The equations differ from those used by Lorentz by the fact that the vector H - [Pw] occurring in Lorentz's equations is replaced here by the vector H. It should be remarked that Frank has obtained Minkowski's equations by a process of averaging in the case of non-magnetic bodies.

We shall suppose that the electric polarisation P and the magnetic polarisation Q are connected with D, E, B, and H by the formulae

$P=D-E,\ Q=B-H.$

The electrodynamical equations (I) can be replaced by the two integral equations

These equations are unaltered in form by a transformation from (x, y, z, t) to (x', y', z', t') if

where &theta; and &phi; are constants.