Mur/innjcA'rrox of elliptic fctnctions. 193 



Part Second. 



§ 18. 



To avoid oonfiision, we sliall ndopf once for 'ill the following 

 notntioM : 



X — finir, ç=\/Ji fin)/, ^ = sn-//.. 



Following Jncoln in his lectnre><, we write* 



ß (,,)^i +22l-"lV' g'' cos '^, Uu)= ^2 ^^ ' ^ cos ^^^^ ^1^'^" , 



Put fo=— loo; (^= ^ , then 



l)nt 



hence 



(JH _ -- d-h u (IK (W 

 (/(o /i- r//r K dio du ' 



,,,-r(f) 



■ ^ c//^^ r/A- dit dk 



0])serve tliat tlio 8:nne ditferentinJ e(|u;ition is s;iti8He(l hy ^^, ^aiind fly 



* .Tacohi's ^rosainmelte Werke, Bd. T, pp. 501, 511, and 512. 

 ** Ditto p. -^59. 



t Pitto p. 260, 



