8' ART. 15 H, NAGAOK.V: NOTE ON THB POTENTIAL 



In practical calculation, the part requiring the most painstaking 

 is the evaluation of «, for which the expressions given in Prof. 

 Schwarz's "Formeln und Lehrsätze zum Gebrauche der elliptischen 

 Functionen" p. 71. will be found very useful. For convenience 

 in calculation, the following values of f («)— ^^^ have been tabulated 



A 'lax 4 ax . | 



«.(«)-.,= ±- (^=(i=É:(e,-e,) (15) 



A '2 ax 4 ax 



A 2 ax 4 ax 

 Thus e2<:^(a)<e, 



A \ 2 / 



1 (g + xf + ^- _ (g + xf + Z' ,^ . 

 A %ax 4: ax 



e,-e,= A_ (a-xf + z^^(a + xf + z\^^^_^^^ 

 A 'lax 4 ax 



Putting 



— . . — 77^, , ~ - 77= — r,r7 —=lt where l=— j== 



and So=l + ('— )'V+(-!A,)V+f-lM_yV-4- •• •■ 



\ 2 / \ 2.4 / \ 2.4.6 / 



«•■■= {\M^MW^'"- 



^- (iry"-(ilrr^''^- 



