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vector at the point, where the body is situated, and in consequence 
of this a corresponding modification in the perturbing influence, 
which the field of gravitation exerts on the motion of the body. It 
will also be clear that the influence which according to equation 
(23) is exerted on the motion of the body, will undergo a modi- 
fication proportional to M. 
The results of this § may be briefly stated as follows. If a rigid 
body is situated in a stationary field of gravitation with its centre 
of gravity at rest, the Pornsor-motion, which the body in the absence 
of the field of gravitation would perform in the way well known 
from classical mechanics, will be disturbed by a superposed uniform 
rotation, which is independent of the properties of the body, and 
at the same time by the influence of a conservative field of accel- 
eration, an influence, which is closely connected with the properties 
of the body (c.q. with the ellipsoid of inertia). The “own” field of 
gravitation of the body will — in first approximation — have the 
effect that all quantities, which characterise the position and the just 
mentioned perturbations in the motion of the body, will undergo 
small modifications proportional to the mass M/ of the body. 
In practical applications all these influences may of course be of 
quite different orders of magnitude, and it may happen that some 
of them practically may be neglected, while others are so large, 
that the approximation perhaps has to be carried on further than 
indicated in this §. 
- § 4. Influence of the field of gravitation of the sun on the 
rotation of the earth. 
The line element of the field of gravitation, to which the sun, 
which is supposed to be at rest, gives rise, can be written in the 
following: form, which for the first time was given by SCHWARZSCHILD: 
a (1 oe “) dR= gee rin idee) 
SUN r 1s a 
x 
where 7’ represents the time, the unit of time being chosen such that 
the velocity of light at large distance from the sun approaches to 
unity. 7, 7, p are polar coordinates, which determine the position 
of a point in space, and «a is a constant, which is connected with 
the mass Mz of the sun by the formulae 
