79 



raaj choose foi- one of (he quantities to, T'" and 7'J! an arbitrary 

 single-valued function of .s. When also the expi-essions for r, u and 

 1\ are introduced, the equations (5) and (7) determine now the two 

 quantities. All these possible inalerial systems give — if only the 

 distribution of 1\ is the same — a three-dimensional space of the 

 same curvature, because the formulae (25)/ peifectly determine (he 

 space-components of the fuudamental tensor (when /> =i h. The 

 curvature of the four-dimensional space-time continuum on (he 

 contrary depends also on the distribution of T\. which cpiaulity 

 according to (5) influences jü. The following simj)le assumptions 

 might e. g. be made to obtain a detinite system : //; = constaut, 7''' = 

 or T\ =. T'l, (normal pressure in all directions). Perfoiming the 

 integration of (15) and (7), we might choose the integration constanis 

 in such a way, that at the boundary .s' = *S u) takes the value that 

 holds there for the outer field, for, as was pro\ed in ^ I, v/; changes 

 continuously into a surface of discontinuity. 



The purpose of our investigation being reached no further calcu- 

 lations will be added. We have shown that Einstein's theory of 

 gravitation really admits such a distribution of the stress-energy-tensor 

 T, that (he (three-dimensional) space crosses itself at a cei'tain point. 

 We can also prove without difficulty, that systems can exist in 

 which the space filled with the matter runs out into a narrow neck. 



It is still of some importance to investigate the action of the 

 electric forces within the space which is just dilated and afterwards 

 again contracted. We might e. g. investigate the state, when, with 

 constant 1\, T\, T'^, for the non electro-magnetic matter, a point 

 charge was placed at the centre of symmetry. The gravitation field 

 will evidently change. We have not only to calculate this field, but 

 also the laws of the equilibrium and the motion of other electric 

 (point)-changes in the new electric field. Here we must treat the 

 matter as perfectly permeable. These indications may however suffice, 

 which show already that Einstein's theory opens wide possibilities 

 to explain the state in the inside of an atom. 



