73 



Introducing in (176) the expressions for k and m, we find for 

 P an expression, corresponding to the first term of (17(/). As to the 

 terms of lower order the theory of Einstein agrees therefore with 

 that of Newton. 



§. 3. Second example of a surface of discontinuity. 



Now we shall consider another kind of surface of discontinuity 

 viz. one in which 



'•» 

 Urn \T\dr = Q (19) 



but where T[ changes discontinuouslj. Sucli a surface of discon- 

 tinuity we have e. g. when an electric charge is spread over the surface. 

 Formula (8) shows that in the case in question ii changes conti- 

 nuously at the surface : 



«, = «1 (20) 



Above we showed already by formula (10) that w changes conti- 

 nuously. 



This time too we must multiply formula (Jl) by iü, integrate a 

 layer and pass to the limit of an infinitesimal thickness. As in the 

 last part of the left-iiand side all quantities remain finite at the 

 limit, this part gives the limiting value zero. As further u and }ii 

 change continuously, we obtain 



R 



P— ^uw(Tr,— 7,,), 



or, introducing the components of the volume-tensor 'X 



p = |(.^:,-x:.;). ....... (21) 



The meaning of this equation is trivial. It expresses the equilibrium 

 between the surface-tension F at the spherical surface and the 

 normal force perpendicular to that surface, the magnitude of which is 



1'r^ — 5:J,, per unit of surface. The gravitation has evidently no 

 infliuence. 



When on the surface we have an electric charge e and inside the 

 surface no matter, we find (II, note p. 1240) 



Now we shall assume that neither outside the surface there is 

 any matter except the electric field, and "we shall calculate the mass 



