1188 
The possibility of snch an experimental decision disappears imme- 
diately when also in a stationary laboratory, in which there is a 
field of force, the rays of light are admitted to have a corresponding 
curvature. 
The “hypothesis of equivalence” on which Einstein bases his 
attempt at a theory of gravitation *), really requires such a curvature 
of the rays of light in a field of attraction. 
The hypothesis of equivalence, namely, demands that a laboratory 
L', which rests in a field of attraction, is equivalent with respect to 
all physical phenomena with a laboratory L without gravitation, but 
accelerated. 
It is therefore required that the observers which are in £, cannot 
ascertain in any way by experiments, whether then laboratory has 
an accelerated motion, or whether it is at rest (in a corresponding 
field of attraction). So we are here concerned in the first place with 
an attempt to extend the theory of relativity of the case of wi form 
motion of a laboratory to that of non-wzform motion. 
The physical significance of EinsreiN’s hypothesis of equivalence 
would, however, chiefly lie in this that it requires acertain functional 
relation between the field of attraction and other physical quantities 
(e.g. the velocity of light). 
When working out the hypothesis somewhat more closely, EINSTEIN 
is confronted by certain difficulties. These led him to pronounce the 
supposition *) that the theory of equivalence would possibly only be 
valid for infinitely small regions of space and time, and not for 
finite ones. 
Einstein confined himself here to a mere supposition, as the said 
difficulties only presented themselves in the consideration of the 
dynamic phenomena in the laboratory LZ’, and he had to do there 
with derivations from so great a number of suppositions, that it 
becomes difficult to see, where the difficulties arise from: the hypo- 
thesis of equivalence, or one of the other more special suppositions 
(as e.g. concerning the dynamic actions of rigid kinematic connections). 
The following considerations try to throw light on this question. 
They show that similar difficulties already occur in those phenomena 
which are the most elementary in Enysrery’s theory : in the propa- 
gation of rays of light in a statical field of attraction. 
The principal result is: All the statical fields of attraction with 
the exception of a very particular class, are in contradiction with 
Linstein’s hypothesis of equivalence. Already the statical field of 
1) Ann. d. Phys. Bd. 35 (1211) p. 898; Bd. 38 (1912) p. 355 and 445. 
*) Ann. d. Phys. Bd. 38 (1912) p. 452 — 456. 
