Page:Zur Elektrodynamik bewegter Systeme I.djvu/3

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§ 2. We want to derive the sought relations, and introduce them into (L).[1] Here, we want to presuppose that all bodies are "non-magnetizable", i.e., generally . Furthermore, we want to pass to relative coordinates, and denote the corresponding derivatives with respect to time by , so that generally we have

.

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

(L1)

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

1. By a translation, every body suffers a deformation, so that length with components goes over to with components , where

(1)

Following Lorentz, this shall be denoted by the symbol

. (2)

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

(3)
  1. The now following derivations are using the same mathematical operations, by which Lorentz was led to his assumptions. As to the details of the calculations, it shall be referred to Lorentz l.c.