282 
PAUL BIEFELD 
It is important that the two-fold meaning of the g’s be fixed in 
mind, namely, that they on the one hand express the metrical 
properties of space and on the other the potential of a field of 
force. In the absence of such a field of force the field is called 
Galilean — in which the law of inertia holds and the g’s are rep- 
resented by the array : 
—10 0 0 
0—1 0 0 
0 0—1 0 
0 0 0+1 
It is hardly to be attempted here to go into details in deriving 
Einstein's law of gravitation, as that would involve the develop- 
ment of tensor analysis ; but a few interesting facts in connection 
with the same should be mentioned here. 
The complete mathematical analysis had been developed before 
Einstein attacked the problem. The theory of tensors by Rie- 
mann and Christoffel in 1867 and 1896 respectively and by Ricci 
and Levi Civita in 1901 in connection with the theory of sur- 
faces, non-Euclidean geometry and absolute differential calculus 
including tensor analysis lay ready at hand. 
As an example of tensors may be mentioned the fundamental 
covarient tensor g/xv of the second order, used in connection with 
the transformation to rotating axes above. A tensor of the first 
order is identical with a vector of common vector analysis, and a 
tensor of zero order is identical with a scalar. Like vectors, ten- 
sors are represented by their components. Tensor analysis rep- 
resents a very powerful tool for the development of the general 
theory of relativity, symbolizing the laws of nature in connec- 
tion with a space-time frame of reference that are consistent with 
the laws of relativity. 
Mathematical and Experimental Tests of the General Theory 
of Relativity 
Before going into this matter it is well to keep in mind that 
we are not concerned with the +roof' of the theory. Einstein 
himself has said, that no amount of experimental demonstration 
could prove him correct; and that a single experiment could at 
any time prove him incorrect. 
We are concerned only with a theoretical, experimental or ob- 
servational test of phenomena predicted on the basis of the 
