78 

 we find for u 



n = ~ (40) 



1 



a' 



That u is negative for .s'<^'/, does not canse any tronhle, as the 

 fundamental tensor depends on u'^ only. 



Now we mnsl introdnce in eqnation (6) the expressions (37) and 

 (40) for }' and u. introducing to begin with the expressions on the 

 left hand-side only we obtain 



-v-Uv''')-^"'' ■ ■ ■ ■ '«"> 



Introdnt'ing the expressions on the right-haiul side loo we tind 

 for 7' ' as a function of s 



4 



7 s^ 



G 



4 3 a* 



^^^^^—7T. ^, (41) 



"A3«' V 



Tiie formulae derived here hold evidently only inside the material 

 system of which the outer boundary may be indicated by s ^ S. 

 In order that the space occupied by the system may cross itself at 

 any point we must have because of (37). 



5>K3a. 



In the limiting surface .? = <S we have according to (40) u<^l. 

 In order that in that surface u may pass continuously into the 

 value it has in the field on the outside, u must also in the outer 

 field be smaller than 1 for s = S. This follows also from formula 

 (li) II, when the system has only a sufficient great electric charge. 

 Further it does not matter tliat u would change discontinuously at 

 the boundary, if only this is a material plane as considered in § 2. 



Formula (41) shows that in the interval V^a^is^^ST^ is 

 negative, which though somewhat startling is not at all absurd. 

 Further formula (41) indicates that 7^4 becomes infinite for 5 = ^^3 a. 

 Within a finite extension there is however onlj^ a finite mass of 

 matter, which follows from the fact that r'^T^, is everywhere finite 

 according to (41). 



The equations (40) and (41) for u and T^ involve together with 

 (37) that the fundamental equation (6) is satisfied. Now we raust 

 still determine lo, T\. and T^p as functions of s, so that also the 

 equations (5) and (7) are satisfied. As (5), (6) and (7) form the 

 complete set of field equations for a stationai-y gravitation field, we 



