Page:Zur Elektrodynamik bewegter Systeme I.djvu/2

${\begin{cases}{\mathsf {P}}\{cH-[wE]\}=J+{\frac {\partial D}{\partial t}}+\Gamma (D)w-P[wD]\\{\mathsf {P}}(cE)=-{\frac {\partial B}{\partial t}}\\\Gamma (D)=\rho ;\ \Gamma (B)=0\\D=E+P;\ B=H+M\end{cases}}$.

(L)

Here, P = rotation, $\Gamma$ = divergence, $c$ is the speed of light in vacuum, $w$ the velocity of matter; $E$ and $H$ the electric and magnetic field intensity; $D$ and $B$ the electric polarization and magnetic induction (recently denoted as electric and magnetic excitation); $P$ and $M$ the electric and magnetic moment of unit volume (recently denoted as polarization); $J$ the electric current (by conduction).

To be able to apply equations (L), is is obviously necessary to represent J, P, M as functions of E and H. With this postulate the mentioned paper ends.

For our purposes is is only required, that one can give the form of the functions for arbitrary $w$, when they are known for $w=0$. In this connection, the papers given so far by Lorentz (including the article in the Mathematical encyclopedia) only gave assumptions that are near at hand according to the author's own opinion;^[1] those are also connected to magnitudes only, which are proportional to the first power of the ratio of the body's velocity and the speed of light. A comparison between both theories was, in a strict sense, only possible in the single case, where J, P and M have no considerable values, i.e., with respect to the propagation of light in moving gases. Here, it is actually carried out.^[2] In addition is was near at hand in the cases where only the first power of ${\tfrac {w}{c}}$ was of relevance (although it was connected with some uncertainty).

The recent paper of Lorentz^[3], however, brings a series of new assumptions on electrons, molecules, and the forces acting on them, which lead to a very specific answer to the questions stated above, as far as the whole considered system has a common velocity of translation $w$.

1. See Math. Enc. V. 2, p. 215 ff.
2. See § 7. below.
3. Kon. Akad. van Wetensch. te Amsterdam Dl. XII, p. 986 (23. April 1904). Only this Dutch edition was accessible to me.