1883.] of Elliptic Functions. 



and we have to verify that, if 



x = en u, y = en | (1 + i sjo) u, 



X X 



"■"-"'JBjB- 



x %c a 



where a = en | (K — iK') ; also 



i-/=a+;<o(i-*)(i-|y-A 



*" ( 1 + I)( 1+ f/' 



where /3 = en § (K—iK 1 ), 



and therefore a/3 = zc. 



Since x = 1 when y = 1, therefore 



^i=v<-^), v /(^) J 



determining a or en ^ (.ST— liT'). 



Again x = ft = — ., 



where ?/ 2 = 1 ; 



therefore 1 = — «j . =- . ( -= ) , 



a + 1 V* + «v 



which should be satisfied by the preceding value of a. 

 Differentiating y logarithmically 



I ? 



1 dy _ ic a 



if (XCC ^ Ob -. Jb 



J 1+^ 1--, 



c a 



2 1/2 1\ s 

 a jc Vac ixc J 



