1071 
vity, and these perturbations will be small quantities proportional 
to the mass M4 of the earth. From elassieal mechanies we know 
already in first approximation the influence on the orbit: the sun is 
not at rest, but deseribes round the centre of gravity O of sun and 
earth an orbit similar to that of the earth, in sneh a way that its 
distance to O is always equal to the distance of the earth to O 
V4 
multiphed by a Assuming that the orbit of the earth is again a 
. 
fr 
2) 
circle, we shall still have, that the product of the square of the 
angular velocity w and the cube of the distance earth-sun will have 
a 
a constant value, but this value will no longer be equal to q? butto 
z (1 +> If we again introduce a system of coor- 
2 Mz : 
dinates rotating with angular velocity @, with respect to whieh the 
centre of gravity of the earth is at rest, the field of gravitation will 
again be stationary in these rotating coordinates, (if we look apart 
from the motion of the sun and of the earth round their respective 
centres of gravity ')) but the distance from the earth to QO corre- 
sponding to this angular velocity is no longer the same as when 
the mass of the earth was neglected, but smaller in the proportion 
2M 4 é : . 
(1— ) Thus we have to do with a displacement of the point, 
3Mz 
where the centre of gravity of the earth may remain at rest, which 
is a consequence of the own field of gravitation of the earth, and 
which is proportional to the mass of the earth. According to the 
considerations on p. 1066 such a displacement was to be expected. 
We must further consider the possibility that the absolute value 
of the rotation-vector at the centre of the earth is no longer exactly 
; 4 Maz 
equal to w, but may, e.g. be written in the form @ (1 +h 5 } 
Mz 
where & is a numerical factor of the same order of magnitude as 
unity. Here it must be remembered, that when speaking of the 
rotation-vector at the centre of the earth, we mean the quantity, 
which according to the scheme indicated in the former $ (p. 1066) 
1 From some interesting considerations by EINSTEIN, Berliner Berichte 
1916 p. 695, it follows, that the field of gravitation in question may only be 
regarded as stationary to a certain degree of approximation, because we must 
expect that, analogous to what according to the classical theory of electrons 
would take place in a system of moving electrified particles, a system as that 
considered here will radiate energy in space in the form of socalled 
gravitational waves. 
