Friedrich Kottler

“ The nature of this reference system can only be determined in § 8. Here it is sufficient, that the three family parameter of or remain unchanged during this motion, while and experience the same increase . Thus during the transport of the potentials and fields to these four generalized coordinates, it has to be shown that these potentials and fields at the reference-point do not depend on .
In the following, we will only give the formulas for the potentials and the differentiation formulas stated in § 5, by which the (rather complicated) expressions for the field emerge from the potentials. ”

“ If we now go on to consider special motions of a pointlike electron, we have to (by thinking about the metric nature of the relativity principle) study the metrically preferred world lines in advance. ”

“ For the vectors arising in the Wiechert formulas
[2]
one finds:
as well as
and eventually
( has the parameter line !)
Thus we have by § 4 (15) :
I. Potentials in :
[3]
Note, that only appears in the relation , from which one can conclude that the increase of and by each, leaves the potentials unchanged. Furthermore by § 4 (18) :
II. Differentiation formulas:
By the differentiations, the relation is therefore not dissolved, and within that relation will therefore appear in the fields as well. But if is an arbitrary function in this relation, it follows
which was to be proven. ”