THIRD ELLIPTIC INTEGRAL AND THE ELLIPSOTOMIC PROBLEM. 289 



I () = \ 



*/ X 



, 



D - x 2 X /X,X 2 ' 



= icos- 1 ft-J* + ^ + Bad*? y^x, , 



_ 



X t> X. = 1 C.c - x 2 (7), 



_,_ 1( , . v 



'- 2(o 



/ ., \ 



(!!l = (12), 



M 3 v 



X 



(13), 



while Kj and R c can be calculated and the whole result verified by differentiating (6) 

 and equating coefficients of powers of x. 



A change of b into b will change v into !)v. 



The c employed for p 10 is --,, so that, putting 



l+o />' + 1 

 we find 



so that, with 



u^f"-^-, A = 46* (16), 



a = a (?*), a' = a (u ^w) 



(KlEPERT, ' Math. Ann.,' 32, p. 107), and then, with a = a 20 , 

 VOL, CCIII. A. 2 P 



