THIRD ELLIPTIC INTEGRAL AND THE ELLIPSOTOMIC PROBLEM. 303 



Put b = ac, 



C * + 3 (a + l + ") C * 

 1 1 1 



a," a 



1 



a? c 2 



(9). 



Put - + a = t, 



ct 



(I + z 3 ) (1 + 22 - 62 2 - 2e 3 + z 4 ) + 

 as in (2), 42, for ^ = 20. 



_ (js + ^ _ 2t _ 3) C 2 _ t * _ t + j = Q 

 Put c 2 = x \, 



x* + 3to 2 - t (t* + < + 4) x + 3 = (11). 



Put x = yt, 



-( + + 4)y + s =0 (12). 



Put 



(14), 



~ 52 - z 3 + t 3 + 4,/Z 



3 



.. 2 == VZ (v/Z + 1) 



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(20)> 



