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invariance of the g,, at infinity has no real physical meaning. It is 
purely mathematical. 
The system A, with at infinity the values (2 A) of the y,, satisfies 
this postulate, if it is applied only to the three-dimensional world, 
and if we do not require invariance for all transformations, but 
only for those which at infinity have ¢’—¢"'). If the postulate is 
applied to the four-dimensional world, and to all transformations, 
then the system B is the only one that satisfies. We thus find that 
in the system A the time has a separate position. That this must 
be so, is evident a priori. For speaking of the three-dimensional 
world, if not equivalent to introducing an absolute time, at least 
implies the hypothesis that at each point of the four-dimensional 
space there is one definite coordinate x, which is preferable to 
all others to be used as “time”, and that at all points and always 
this one coordinate is actually chosen as time. Such a fundamental 
difference between the time and the space-coordinates seems to be 
somewhat contradictory to the complete symmetry of the field- 
equations and the equations of motion (equations of the geodetic 
line) with respect to the four variables. 
Some features of the systems A and £ may still be pointed out. 
In A the velocity of light is variable *), at infinity it becomes in- 
finite. In B it is always and everywhere the same. From the facts 
that we can identify lines in the spectra of the most distant objects 
known to us such as the Nubeculae, and that the parallaxes of 
these objects are not negative, we can conclude that at these distances 
we have still approximately gij= — dij, g,,—=1 and consequently 
that for Aor’, and for Boh’ must be very small. In the case A 
we can derive in this way an upper limit for o. In B on the 
other hand we have, in consequence of the constancy of the velocity 
of light, 4? —=0 for all purely optical observations (if we neglect 
the influence of matter). 
As to the effect of o on planetary motions: in both cases the 
1) Thus e.g. an ordinary Lorentz-transformation : 
vu—qet ; ct — qu 
ET 9 Lg) 
is not allowed in the system A, but must be replaced by 
hee 
ta 
eget 1 +or* 
— ‚ Ol 
¢ q q 
i ( net a i“ ¢ i Tee, 
?) In the system x, y, 2, ct; in the system 7, Uv, 9, ct it is constant, 
a 
