MULTIPLICATION OP ELLIPTIC FUNCTIONS. j (j^ 



XoAV 



log ß(ni/) = log V + n- loo- fliif) - {),^--})\oa ß{()) . 

 Siihstitntiiig ill (i'l), we g'et 



f//r \ ail / ( r/?^ a/,- ) du 



r//,- '( (hl- (Ik ) 



Au-:nn. ^-^ = Z(i/) , 6 (0) = J- ; 



au 'y - 



ainoreiitiMtino-, ;nifl oi)servini>- -yy- = — ^r^^ — 7 ^^'^ ohf-nn 



(Ik kk 



(05) ^-lo^%) ^,^.^..jIog^^_^.^„.^^ 



Siihstitntinf)- tliis in (i)4), 



r/?r \ dii / ( r/?/ dk ) dir 



dk 



or 



+ 2nn-k'^'^+ }i\)r- - 1 )/.-2sn^// V= 0. 



Iiitrofliiciiio' ^-^-^/k^^^)f :is tlio new indepeiiflent vnriable, and 

 o]).ser\inu- (9!2), 



* .Tacolii's «^esauiuiplte Werko, Btl. T, pp. 1!>8 and 235. 



