THIRD ELLIPTIC INTEGRAL AND THE ELLIPSOTOMIC PROBLEM. 295 



R, 2 = D 2 , R,,,_, -= - [2nP (v) + P (2ww)] R^, R 2 ,_, = (- 1) (11), 



9 w = ( " 2 ) sn / K ' CI1 / K ' dn / K ' < 12 >- 



In this case II. put 



(a - m) (a m + 1) = 2 a 4 (13), 

 then 



= 



e+ 



e = 



fe' 1+6 



and the relation (13) becomes 



a pa. b 



F 5 a -a 4 ) 



~ 



6 s 



4a 2 et 2 a- ct 



-a 4 ] _. i^* 4 2_ 



(a m) 4 ' 

 S = s (?;) s (w s ) = (positive) (15). 



Ot ^^ 771 



Now, with 



1 2m = p, (1 2m) a = m(l m)^3 = m(l m) (16), 



Z 



,_,, t+ +'- = (20), 



1 - n* , 1 -P' 2 ^(1 + ?') /->n 



4. m - m * = -r = (i+2&f^ (21)> 



- (22)> 



