1070 
From formulae (28) the ratio of the two time units in question is 
« ; : 
found to be equal to the value of Aa — —— rw’ sin? & at the point 
r 
€ 
; ' Xm 
where the earth is situated. Since at this point r= A, oe a: the 
oUt 
° AA 
It is therefore seen, that a system of coordinates in which the 
law of inertia holds, at the point where the earth is situated will 
sa 3 : 
rotate with an angular velocity ia. Gee a v? w (where v is the velo- 
city of the earth in its circular orbit) with respect to the fixed stars 
in the same sense as that, in which the earth rotates round the sun. 
From this result, and from the results in the former §, we may 
therefore conclude that according to the gravitation theory of EiNsTerN 
there will be a contribution to the precession of the axis of the 
earth in progressive sense, which is independent of the constitution 
of the body of the earth, and which amounts to an angle equal to 
one and a half times the ratio of the velocity of the earth to the 
velocity of light, i.e. to 0,019 are seconds anually. The existence of 
a non-Newtonian precession of this kind has for the first time 
been suggested in a paper by Professor Scnouren.') In this paper 
attention was drawn to the circumstance, that the field of gravita- 
tion of the sun is such, that a small body, which was made to 
move geodetically along a circle round the sun with radius A, would 
no longer have the same position as before at its return to the same 
ratio in question is equal to 1 — 
za 
point, but tbat it would be turned by a small angle equal to 7 
in the same sense as that, in which the body had moved along the 
circle, and it was pointed out, that this result suggested a possible 
precession of the axis of the earth with respect to the fixed stars. 
Now it remains to investigate the influence, which what we have 
called the “own” field of gravitation of the earth, may exert on its 
motion. According to what has been said in the former $ (p. 1067), 
we may expect, that this influence will cause perturbations as well 
in the orbit of the earth as in its motion round the centre of gra- 
precession of the kind described. I am indebted to Dr. FOKKER for the remark, 
that in doing so I had overlooked the difference in the time unit, in which 
the two angular velocities in question were expressed. Compare A. D. Fokker, 
These Proc. Vol. XXIII. N°. 5, p. 729 (1920). 
1, These Proc. Vol. XXI, p. 533 (1918). 
