17 



T,,=i^ (82) 



a quantity which depends on r and which we shall assume to be 

 zero outside a certain sphere, we find from the field equations 



II r I 



rQch 







I 1 r r 



We thus obtain 



r r 



(83) 



r3«=0, t^^=:_i,.^^ (84) 



§ 50. If first we leave aside the first term of t^'^, which would 

 also exist if no attracting matter were present, it is remarkable 

 that the gravitation constant x does not occur in the stress t^\ nor 

 in the energy f^^; the same would have been found if we had 

 used other coordinates. This constitutes an important difference 

 between Einstein's theory and other theories in which attracting or 

 repulsing forces are reduced to "field actions". The pulsating spheres 

 of Bjérknes e.g. are subjected to forces which, for a given motion, 

 are proportional to the density of the fiuid in which they are imbedded; 

 and the changes of pressure and the energy in that fluid are likewise 

 proportional to this density. In this case we shall therefore ascribe 

 to the stress-energy-complex values proportional to the intensity of 

 the actions which we want to explain. In Einstein's theory such a 

 proportionality does not exist. The value of (4* is of the same order 

 of magnitude as 2/ in the matter. To our degree of approximation 

 we find namely from (82) 1/ = r^g. 



§ 51. If we had not worked with polar coordinates but with 

 rectangular coordinates we should have had to put for the field 

 without gravitational! ^ g^^ = 9»^ = — ^^ 9^4 = '^> ffni> = for « =1= b. 

 Then we should have found zero for all the components of the complex. 

 In the system of coordinates used above we found for the field 



without gravitation r/ = — ; this is due to the complex t being no 



tensor. If it were, the quantities ta' would be zero in every system 

 of coordinates if they had that value in one system. 



2 

 Proceedings Royal Acad. Amsterdam. Vol. XX. 



