537 



plane tlie circle-sector describes the «[Kice-sectioii described. By 

 this method i( does not at once become obvious that now the 

 obtained euclidian space nia}' indeed replace the originally existent 

 non-euciidian tangent -space along (5). The motion of the compass- 

 body can now be easily traced. In the euclidian space xyn the 

 compassbody always moves parallel to itself. If a constant dii-ection 

 in A in this body has the dii'ection of the radius, then that direction 

 in B forms with the radius an angle 2.t (1 — cos /) situated in a 



(I 

 plane// at the j;!/-plane. Now — is very small, hence: 



R 



''««X=l - £^ . • (12) 



so that the total deviation 6 in one revolution amounts to: 



^=^^ (13) 



A compassbody moving around the sun, as its central point, i»i 

 a circle with a radius equal to the average distance from the earth 

 to the sun will show according to this formula aftei' one revolution 

 a deviation of 0.013". If the radius is equal to the average 

 distance from Mercury to the sun, the deviation amounts to 

 0.0328". If the radius is equal to the radius of the sun, the 

 deviation amounts to 2.73". If, from another cause, the compass- 

 body already has a revolution around an axis, which is oblique 

 relatively to the plane of the orbit, there will set in, merely oii 

 account of the deviation described, a precession-motion, which in 

 the first of the above-mentioned cases would result in a complete 

 revolution of the equinoxes after ± iOO.OOO.OOO years. It is note- 

 worthy that the effect described is of the same order as the deviation 

 of a ray, passing the sun at a distance R from the central point. 

 According to Einstein this deviation indeed amounts approximately 



2a 

 to — . 

 R 



Whether the deviation computed of the precession motion for the 



earth will indeed set in, depends on the question to what extent 



and to what approximation a mass of the quantity and the coui- 



position of the earth has the proporties of a compassbody. In order 



to answer this question it is necessary to make definite suppositions 



as regards the physical qualities of the earth, in particular the 



mutual attraction of her parts, and starting from tliese suppositions, 



to integrate the four-dimensional dynamical equations of motion. 



