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the first place this is easily seen to hold for the quantities goor, 
because goo by the transformation (1) is only multiplied by a constant 
factor; but neither the quantities go, can all of them at the same time 
be reduced to zero, because this would mean, that the components of 
the rotation-vector would be equal to zero, and this is in general 
not the case. On the other hand it is obviously always possible to 
perform such a special transformation, that the system of coordina- 
tes in the three-dimensional extension with the line-element do? = 
= Gi der da, becomes geodetic in the point P. In this way we get 
ise = 0 and consequently also gui, = 9, since gz; = — Gy 5 seek 
Oxy N Joo 
and since the quantities gz. are equal to zero in the point P. 
Let us now imagine, that by means of (1) the line-element has 
been given such a form, that in a given point P the following 
relations are valid 
d) Juv = Ens 
B)  gki,v= 0 (9) 
ec) gok,1 + 9ol,k= 0 | 
As regards the third of these conditions it will be observed, that 
it is always possible by a suitable transformation of the time to 
effect, that the symmetrical quantities Az; == Gort + Goi,p become equal 
to zero in P. In fact, it is easily shown that, if the conditions (a) 
and (6) are already fulfilled, but not yet (c), the transformation 
aw’, =a, + 4 (An)P (ar — (re) p) (wi — (2) Pp) leads us to the desired 
purpose. Thereby we have denoted the value of a quantity in the 
point P by adding the index P on the right below. Let us now 
perform a transformation of coordinates, which corresponds to a 
uniform rotation, around an axis through P, of the z,, 2,, 2,-space 
(considered as a Euclidean space with the line-element do? = dv,’ + 
de,” + dx,?), the angular velocity of which considered as a vector 
has the components #', k?, and R*. After the performance of this 
“rotation transformation’, which does not belong to the group 
of transformations (1), the relations (a) and (6) are still valid, 
but also all the quantities go, have become equal to zero. This 
may be proved by a direct calculation, and the proof becomes 
especially simple, if we assume, that in P the quantities /* and 2? 
are equal to zero, so that we have to do with a uniform rotation 
round the axis of the coordinate #, with an angular velocity 
k?=w. Since in the point P the quantities A, reduce to 
4 (Gom, Jolm), we have in consequence of relation (c), that of all 
* 
