1065 
Until now we have neglected the influence on the field of gravi- 
tation due to the body itself, but in the applications to special cases 
such a neglect might not be justifiable. When e.g. in the next 
§ we will discuss the praecession of the axis of the earth, we have 
to-do with a body, the “own” field of gravitation of which is much 
stronger, e.g. at its surface, than the field of gravitation arising 
from the sun (which appears as is well known in the forces, which 
cause the tides). We might imagine that in such a case other forces 
might influence the motion round the centre of gravity, which are 
much stronger than the forces just considered, or which disturb 
these forces essentially. A closer consideration shows, however, that 
if the mass of the body is so small, that at large distances it can 
only cause small changes in the original stationary field of gravitation, 
the own field of gravitation will only cause a small change in the 
motion of the body, which may be considered superposed on the 
influences of the stationary field of gravitation considered above, 
and which will be proportional to the mass of the body. 
In order to show this let us first imagine the body placed in a 
space, in which no other matter is present, and the line-element of 
which approaches to ds? = der, — dx,? — da,’ — da,’ at infinite 
distance from the origin. Then it is easily seen, that in first 
approximation the own field of gravitation will have no influence 
at all on the Pornsot-motion of the body, because the “forces” 
determined by the g,,’s, which the different parts of the rigid body 
exert on each other in first approximation will fulfill the principle 
of action and reaction, just as is the case in Newton's theory of 
gravitation. This may easily be proved by applying Einstein's 
approximative solution of the field equations, described on page 1058, 
on the impulse energy equations (19), but for the sake of brevity 
we will not enter into this proof. 
Let us again imagine the body placed in a stationary field 
of gravitation with its centre of gravity at the point P. Let us 
suppose, that the original values of the g,,’s only undergo small 
changes A,, on account of the presence of the body, and let the 
new values of the g,,’s be denoted by g',,, so that 
Puss = Jp» + An . . . . . = . . (24) 
Then we obtain, by applying the field-equations (10), for the 4,,’s 
a set of 10 partial linear inhomogeneous differential-equations of the 
second order, of which we will assume that there exists a regular 
solution. (If necessary boundary conditions must be given. If the 
stationary field of gravitation is such that the line-element every- 
