1082 



for the components of the fundamental tensor we then have the 

 following expressions 



g,^.^ = -'^{u^-p^) for fi =!=»'• 



. (25) 



•2/ 



where ft, v = 1, 2, 3. 



For the components of the conti-avariant fundamental tensor we 

 have : 



«V ^ _ ___ for fi == r, 



' . . (26) 



As we consider also the field inside the matter, the material 

 stress-energy-tensor 1/ occurs now too in our formulae. Because of 

 the spherical symmetry we can write for its components: 



■l.^ ^'^{X/-l/) for ii=\=v, j 

 r ' I 



' . . (27) 



fi, r = 1, 2, 3. 



That here ï^'=2:/=:0 rests on our assumption that the energy 

 of the system remains constant. No radial energy -current can 

 exist then. 



Now we shall deduce formulae for the gravitation field from the 

 variation principle of the form {la). We chose this form of the 

 variation principle with a view to a better correspondence with the 

 article of J. Droste. 



By a right choice of the limits of integration the equation (la) 

 becomes : 



4 jtö i dt j ( - |/^ G + X ^1)2) r» dr — 



h '-1 

 or by division by 4 .t (^j — t^) 



d |V^ G r' dr = z Ö f^^i r* dr . . . . . (28) 



