Physics. — “On geodesic precession.” By Prof. J. A. ScHouren. 
(Communicated by Prof. H. A. Lorentz). 
(Communicated at the meeting of February 26, 1921). 
In a preceeding communication [*) have demonstrated geometrically, 
that a system of axes, moved geodesically along a closed curve in 
a non-euclidean V,, will show a deviation when returned to its 
starting point. For the special case that the linear element of the 
V, is the spacial part of the linear element of ScHWARZsCHILD and 
that the curve is a circle round the sun with a radius equal to the 
mean radius of the orbit of the earth, this deviation is 0.013" after 
one revolution. 
Now if firstly the fourdimensional problem of the motion of a 
material point in a static gravitational tield, neglecting as usual 
3 
a 
quantities of order RY could be reduced to a problem of classical 
mechanics (mechanics with the fundamental theorem: force = mass 
XxX geodesic acceleration) in a threedimensional non-euclidean space, 
and if secondly we could demonstrate that a geodesically moving 
system of axes may be regarded in first approximation as an inertial- 
system, than we might conclude for the earth to a deviation of the 
ordinary precession to the amount of 0.013". 
In the mean time Fokker’), starting with the complete linear 
element of ScuwarzscnHiLD, has demonstrated with a fourdimensional 
calculation, that, apart from other relativity-corrections on the ordinary 
precession, a geodesic precession exists, that is exactly 1'/, & 0.013". 
Now we can show that this difference is caused by the fact, that 
the fourdimensional problem can be reduced then and only then 
to a threedimensional one, when the square of the velocity is of 
2 
a 
order Re the square of the real occuring velocity in general being 
a 
f order —. 
of order — 
The world-line of a material point is given by the equation: 
|e Oe) a 
1) Proc Kon. Akad., XXI 1918, p. 533—539. 
2) Proc. Kon. Akad. XXIII, 1921, p. 729. 
