Page:Zur Elektrodynamik bewegter Systeme I.djvu/2



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 (including the article in the Mathematical encyclopedia) only gave assumptions that are near at hand according to the author's own opinion; 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. 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, 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 $$w$$.