1178 



tlie equations between the cliai-acteristic luunbers become the well- 

 known relations between the geodetic differentiation and the ordinary 

 partial derivations with respect to the fundamental variables .r. For 



8,., 



this case tiie characteristic numbers of A become the Christoff"el- 

 symbols 



1' 



We shall apply the pi'oved theorem to a static problem of the 

 theory of relativity. 



Space and lime in static prob/ems. 



In the theory of relativity in general we cannot speak of "the" 

 space. Only in thus-called static pioblems in which the line-element 

 has the form : 



,/,s' = <7„, rf.'-"' + '^ 9,y da;' dx^ = ./^^, d.r- — <//'. . . (14) 



where (/«„ and (/,„. depend on .€'>. r and .i"' 0)i/i/, we can asci-ibe a 

 definite meaning to the words space and time, at least when (Lr^^ 

 is considered as a diff'ereiitial of the time, (//. and (// as a line- 

 element of the space and when ahnays the problem is tieated 

 statically. 



The motion of a material point in a static (fravitation fieUL 



The equations of motion of a material point (which is supposed 

 not to alter the field) are: 



d'' 



0. (15) 



This ec^uation can be transformed into: 



1' / 



diy 



When now ƒ/„„ has the form (1 — g)c'', where f is very small and 



fdl\ ' , . 



when I — 1 is ot the order of magnitude ot fc*', we have, neglecting 



quantities of the order t ^ : 



U U 



ƒ.,=,ƒ l(i ^ -;)--. (;g';./<= - .f ||e' i j(g' | * = h^d 



