Del 
and (5) gives £=0O. But the conviction that this is the true 
value, and has any preference over any other values, is based on 
the belief in an absolute space, and must be abandoned if the latter 
is abandoned. We must do one of two things. Either we must believe 
in an absolute’) space, to which we may impart some substantiality 
by ealling it “Ether”. Then /;=0 is the true value, and that this 
is sO is a property of space or of the ether. Or we can believe that 
there is no absolute space. Then we must regard the differential 
equations as the fundamental ones, and be prepared to have different 
constants of integration in different systems of reference. 
The difference between the two points of view is shown very 
clearly by the values of g,, for r ==. In the absolute space we 
have g,,=0 at infinity. In Ernsrem’s theory the value of g,, at 
infinity is different in different systems of coordinates. However, no 
observation has ever taught us anything about infinity and no obser- 
vation ever will. The condition that the gravitational field shall be 
zero at infinity forms part of the conception of an absolute space, 
and in a theory of relativity it has no foundation. ’) 
1) It should be noted that. owing to the indeterminateness of EINsTEIN’s field- 
equations, this “absolute” space is mot completely determined by the condition 
that the fixed stars shall have no rotation in it, or that at an infinite distance 
from any material body the gravitational field shall be zero. There are an infinity 
of systems satisfying these conditions. We can limit the choice eg. by putting 
g=—1, as Etnstern generally does, but even this does not fix the system of 
reference, and it is also entirely arbitrary. 
2) We could imagine that there was a system of degenerated values towards 
which the g;; could converge in infinity, and which were invariant for all trans- 
formations, or at least for a group of transformations of so wide extent that the 
restriction of the allowable transformations to this group would not be equivalent 
to giving up the principle of relativity. Prof. ErNsreiN has actually found such 
a set of values. They are . 
EE een. 
and we must limit ourselves to such transformations in which at infinity a’, is a 
function of 2, alone. Consequently the hypothesis that the gij actually have these 
values at infinity, and that at finite, though very large, distances from all known 
masses there are other unknown masses which cause them to have these values, 
is not contrary to the formal principle of relativity. But also denying the 
hypothesis is not contrary to this principle. The hypothesis has arisen from the 
wish to explain not only a small portion of the gij (i.e. of inertia) by the influence 
of material bodies, but to ascribe the whole of the gij jor rather the whole of 
the difference of the actual gi; from the standard values (z)] to this influence. 
Theoretically it is certainly important that thus the possibility has been shown 
od 
