1221 
A B 
dij ee dij 
pony (9 pens 
I = 1 Dre. 
= roi 
All g,, outside the diagonal are zero. If 5 is very small the ga 
for moderate values of rand / have very approximately the values (1). 
At infinity they degenerate to the values (2 4) and (2 B), which 
have already been given above. 
In order to find the relation between o and ò we must substitute *) 
the values (5) in the equations (4). We must, in doing this, allow 
for the possibility that it may be found necessary to introduce a 
‘““world-matter”. We neglect all ordinary matter, and we will suppose 
the world-matter to be unitormly distributed *) over the whole of space, 
and at rest, so that 7’,,=4,,9, and all other 7,,=0. The field- 
equations then become 
Jij= 
ty — (à + bx) gy = 0, 
Gi Ar (A =e 3%0) Vg =) Gag ee 
For the quantities G,, we find in the two systems 
A B 
Gij =86 gij | Gius = E20 g 
Cia; Ju 1 | 
From which 
tA | Se 
85 DE DE IE ie en (6) 
OE | 
The result for A is the same as found by Einstein. For B we 
have 9 =O: the hypothetical world-matter does not exist. 
Which of the three systems is to be preferred: A with world- 
matter, 4 without it, both with the field-equations (4) and at infinity 
the g,, (2A) or (24); or the original system without world-matter, 
with the field-equations (3) and the g,, (1), which retain the same 
values at infinity ? 
From the purely physical point of view, for the description of 
1) We can, of course, as well take the values in any other system of reference. 
2) The meaning is a distribution in which @ is constant, @ being the density 
in natural measure. The density in coordinate-measure then, of course, is not 
constant, but (in the system «x, y, 2, ct) becomes zero at infinity. 
78* 
