THIRD ELLIPTIC INTEGRAL AND THE KLLIPSOTOMIC PUOHLEM. 271 



(21), 



(22), 



' 



-2^ + (5 4 I 1 + 13 + U+1+ (2,r 4 4n + 3) /A 

 - 23 



_ .< _ 4 _ <) _ i (; _ -20 1 4 5 (a :! 4 :>, + 4 4 3) V /A 



2( 41)' 



_ ,,o _ 5 15 :!4 58 ?:? 0:1 31 (i 4 



, +( _,,'-._4-y- 14- .14-8- 1) V /A 



2 (a +!)>* + + 1) 



f 1 -5-11 64 I44:!l 4 2!) 4 I74C4 1 

 i +(- i --4-5 -<;-<; --4-- I), 'A 



4a+(a+ l) a ( i + a+ 1) 



+ (1 + 2+1- -2-- l) x A 



4V (a 4 1 )(.- 4 '* + i) 



Expressed in terms of ct, tlie parameters employed !>y KIKI-KKT (' Math. Ann..' :'>2. 

 p. 1 28) are ^iven liy 



l = ,r4^-2,-14 v /A (2g)i 



fc-i -" ('< 4- I ) 



T IS l>eiiit>' (liKRSTKit's T ('Math. Ann.,' 14. p. 540), 



T ^ =4 " ll= 2a(a+ I) 



.. f.v' <r 4 2( 4 1 4 

 ?:! " 4a (u 4 1 ) 



a+_8o + q-- 1 - v (32) 



2 ( a -' - 3,, - 1 ) 



