Physics. — “The geodesic precession: a consequence of EINSTEIN’s 
theory of gravitation.” By Dr. A. D. Fokker. (Communicated 
by Prof. H. A. Lorentz). 
(Communicated at the meeting of October 30, 1920). 
It is well known at present what parallel displacement or geodesic 
translation means in non-euclidean space’). And we know also that 
a compass rigid, moving parallel to itself and completing a closed 
circuit, in consequence of the curvature of space, will not regain 
the same orientation which it had before: a certain rotation of 
curvature will become apparent. Now it occurred to ScrourenN that 
the earth’s axis of rotation — provided the earth were a sphere — 
should remain parallel to itself in the general geodesic sense during 
the motion of the earth round the sun. Thus, after a year, we must 
expect the earth’s axis to point to a slightly different point of the 
heavens according to the curvature of space produced by the sun’s 
gravitation. This affords an additional precession which superposes 
itself on the precessions due to other causes known in astronomy ’). 
The problem however is not so simple as it is put here. Though 
it can be proved that the axis of rotation will remain parallel to 
itself in the geodesic sense, yet in reality we have to consider the 
dragging of the earth’s axis along her four-dimensional helicoidal 
track through time-space and not a circuital displacement in the 
ecliptic at some definite instant. The problem should be put as one 
of four-dimensional geometry; it is a problem of mechanics, and 
not a problem of three-dimensional geometry. If this be done properly, 
then the result is that we are to expect a precession one and a 
half times the precession foreseen by ScHoureN, viz. 0.019 of a 
second of are per annum’). This will be shown in the present paper. 
The idea at the bottom of the argument is the following. Imagine 
that in order to describe motions taking place in the neighbourhood 
of the earth’s centre we choose axes such that the time is always 
1) Levi Crvrra, Rendic. Cere. Mat. Palermo, 42, p. 1, 1917; Scuouren, Direkte 
Analysis zur n. Relativitätstheorie, Verhandelingen Kon. Akad. v. Wetensch. Amster- 
dam, XII, no. 6, 1919; Wevr, Raum, Zeit, Materie, Berlin 1920, 3rd ed.; Cf. 
also an article of the present author in Proceedings Kon. Akad. v. Wetensch. 
Amsterdam, 21, p. 505, 1918. 
2) Scuouten, Proceedings Kon. Akad: v. Wetensch. Amsterdam, 21, p. 533, 1918; 
with appendix by De Sitter. 
3) Cf. also a paper by Kramers, Proc. Amsterdam, September 1920. 
