Page:Zur Elektrodynamik bewegter Systeme I.djvu/3

 § 2. We want to derive the sought relations, and introduce them into (L). Here, we want to presuppose that all bodies are "non-magnetizable", i.e., generally $$B=H$$. Furthermore, we want to pass to relative coordinates, and denote the corresponding derivatives with respect to time by $$\tfrac{d}{dt}$$, so that generally we have

If we choose the speed of light in vacuum as unity, then (L) becomes:

Here, the hypotheses of have to be supplemented. Let $$w$$ be parallel to $$x$$; then they read:

1. By a translation, every body suffers a deformation, so that length $$r_0$$ with components $$x_0\ y_0\ z_0$$ goes over to $$r$$ with components $$x=\tfrac{x_{0}}{k},\ y=y_{0},\ z=z_{0}$$, where

Following, this shall be denoted by the symbol

2. When the distribution of electricity $$e$$ upon the material element is invariantly given, then all forces $$F_0$$ upon given particles are suffering a change by the translation, which is represented by the same symbolism