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quantities gox,, only the two quantities Joie and goo, are different 
from zero in such a way that W = 902.1 = — Yos. The rotation- 
transformation can now be written in the form 
#, —(«,)p=2', cosw ax, —a2', sin wc, 
©, — (e)P= et! sinw x, + 2', cosw a, 
If now by means of this formula the line-element (2) is trans- 
formed, and if we make use of the above mentioned relations (a), 
(6) and (c) it is easy to verify: 
That for the transformed quantities Ju» in the point P the rela- 
tions (a) and (6) are still valid. 
That, although the g,,’s will contain the time #,, their first derivatives 
with respect to the time will be equal to zero in P, and that equally 
all derivatives of Jor Joz and go3 have become equal to zero. 
We thus see in the first place that, after the rotation-transforma- 
tion, the equations for the world-line of a mass point, the velocity 
of which is small compared with that of light, assume in the point 
P the simple form 
so that the term corresponding to a Coriolis-force appears no more, 
which was naturally to be expected from the above considerations. 
Let us further consider the special case, that in the point P the 
mass point can remain in equilibrium; that is, that in this point the 
quantities goo, in the original system of coordinates are equal to 
zero. In this case we find, that in the new system of coordinates, 
to which the rotation-transformation has given rise, all quantities 
Yu», Without exception disappear in the point P, so that this system 
of coordinates is geodetic in that point. 
§ 2. On the field of gravitation, which is produced by 
stationarily moving masses. 
Let us consider a space-time-extension, for which the line-element 
at large distances from the zero-point of the coordinates approaches 
to ds? = dx,*—dz,?—dx,’—dz,? ') and in which there exist masses, 
which perform stationary motions; that is, the components 7, of 
the energy-tensor of matter do not depend on the time. The field 
of gravitation, to which these masses give rise will then be stationary 
') Here and in the following we shall always assume that the centimeter 
has been chosen as unit of length. The unit of time is then determined by 
the condition that the velocity of light is equal to 1. 
