76 



We eliminate — between tliis equation and (31). In this way 

 w 



we find 



2 dp n rdr 



+ - :— - = .... (34) 



(() + 3p)(Q -\-ji) 3 ^Q 



1 1 



3 



The integration gives 



log loq I / 1 r* r= const. 



Tiie integration constant lias to be determined with the aid of the 

 condition that for r = R p = 0. We therefore find 



(35) 



Thus the pressure-scalar p is determined as a function of /■. 

 Eliminating p between this ecjuation and (32) we obtain for //; as 

 a function of r the expression : 



in this way we have perfectly determined the gravitation (ield 

 and the pressure distribution inside our sphere. The formulae we 

 obtained become identical with those of Schwarzschild when for r 

 we substitute 



r :=: \X — sin /. 



§ 5. On the gravitation field as it may be imagined to eJtist 

 in the inside of an atom. 



In the theory of atomic structure of Rutherford-Bohk we meet 

 with difficulties arising from tlie assumption that in an atomic nucleus 

 of very small dimensions there exist units of charge which — at 

 least when they are liberated in the form of electrons — have a 

 greater diameter than the atomic nucleus. As now Einstein's gravi- 

 tation theory states that the space in a gravitation field when 

 expressed in natural units is non-euclidic, the question arises whether 

 this theory leaves the possibility of the assumption that the atomic 

 nucleus fills a greater space with a narrow neck or perhaps a 

 space which crosses itself at a certain point. This question will be 

 investigated here. 



