4 jt (f 





( 362 ) 



+1 



(1 — a^) du 



— 1 

 —1 



(1 — ?/^) du 



3f r 



i/{x-^aui3y + {\-ir){if-\-z^) 



+1 



(32) 



As the two integrals equal each other, we get the following 

 rigorous expression: 



+1 



3g r 



2 J )/ia; 



(1 — u'^j du 



\/{x-^rau^Y-^r{l-^'){y'+z^) 



(33) 



We dispense with the evaluation of' the integral, which is likewise 

 possible in an elementary way as in the case ?; <^ c, and we put 

 a = 0. Then 



26 



47np = — — (34) 



^/.^•V^-(l_^^)(^/^+^^) 



The equipotential surfaces are now hyperboloids of revolution about 

 the direction of motion with two shells. Yet only one of these two 

 shells concerns us as lying in region III. 



Region III is bordered by the cone K.^; in its points ^ve have 

 according to (22) 



{X + a^y = iii^ - 1) if' + c=). 



If Ave substitute in (34) and write x^ — |^"j on account of the 

 negative sign of .v in region III, we get by neglecting a": 



2f 

 4.T^ = ^ (35) 



This value is large of a higher order than those in the interior of III, 



because it contains [/a in the denominator, but it is nevertheless 



tinite. Yet you can doubt its legitimacy, as we already omitted 



members of the range a in passing from (33) to (34). However 3^ou 



confirm the value (35), if you calculate the integral (33) rigorously, 



which does not give much trouble for the points of the cone /Vg. For 



at3 

 it you exi)and it in powers of - — r and restrict yourself to the lowest 



\x\ 



power, the rigorous value becomes : 



8 f 



4:JT<p Z= — (36) 



5 \/a^\x\ ^ ^ 



