1066 
where differs very little from ds? = da,? — dxv,? — dv,? — dz,’ and 
becomes equal to this expression at infinity, the 4,,’s might simply 
with a high degree of approximation be calculated by means of the 
formulae (13) of Einstein). Inside the body and in its neighbourhood 
this solution will be the same as in the absence of the stationary 
field of gravitation, and just as before there will be no direct 
influence of the own field of gravitation on the motion of the body. 
Further it is easily seen, that the values of the A,,’s at large 
distance from the body to a high degree of approximation will 
depend only on the total mass of the body, because at such large 
distances the influence of the body can be considered as that of a 
singular point (or as a singular line in the space-time-extension) 
characterised by the integrals of the quantities 7, over the volume 
of the body. But, always neglecting small quantities of the order 
vy? and higher orders, the integrals involving the 17%/s may be 
neglected, while those of the 7%,’s disappear, because the centre of 
gravitation is at rest; so that we only have to do with the integral 
of 7, extended over the volume, that is with the total mass M of 
the body. Thus we find that the body will exert small forces 
proportional to M/ on the bodies, which give rise to the stationary 
field of gravitation. The motion of these bodies will therefore undergo 
a small perturbation, and as a consequence of this the g,,’s of the 
stationary field of gravitation itself will again undergo a modification. 
Instead of (24) we must therefore write 
Os — Jp + Ais + Sis 2 . ° . ° « (25) 
where the A's represent the modifications just mentioned. The 
A's are terms, which will be small compared with the 4,,’s, and 
which will be proportional to J/; in contrast to the terms 4,, they 
will, however, in general have an influence on the motion of a 
body, which clearly will be proportional to MM. 
In order to discuss this influence we will confine ourselves, for 
simplicity, to the case that the 4',,’s are independent of the time. 
In this case the quantities aan will in general not be equal to zero 
B 
in the point P, so that there must be found a point P’ in the 
neighbourhood of P, where the centre of gravity of the body may 
remain at rest. Further in order to determine the components of 
the rotation-vector we will have to introduce in the formulae (5) 
instead of the quantities g,, the values of the quantities g,, + A', 
and of their derivatives in the point P’. In this way a small modi- 
fication proportional to M will be found in the values of the rotation- 
