THIRD ELLIPTIC INTEGRAL AND THE ELLIPSOTOMIC PROBLEM. 235 



^-1 + 5 + 3-21-21 + 56 + 4(5 - 114 - 39 + 158-3-135 



+ 52 + 91 - 37 - 22 + 35 + 14-5 + 2 + 4 + c~\ 



^ = 1 + 3 4 15 + 14 + 35 41 37 + 65 



+ 12 - 61 + 8 + 31 -- 16 - 14 + 5 + 1 - 3 - ^ (9), 



,,n 



A- = I + 7 + 1 2 22 74 + 38 + 223 - 7G - 448 + 205 + 014 - 403 - 551 

 + 555 -1- 305 - 442 68 + 353 + 47 - 99 + 57 + 70+7 1 + 10 



?n 



B 5 = 1 + 5 + 1 28 - 16 + 91 + 35 - 205 - 2 + 301 - 97 - 290 



+ 169 + 120 - 176 - 79 + 90 + - 54 7 + 7 5 - 5 - <: 5S (to). 



By means of an appropriate homogeneity factor M, we can express 



52 P (re) p n ,p 12^/v , /, , 



M % '' x/ ' M- 



in such a manner that the substitutions 



'c, -, | correspond to ('', 3r, !)/) 



and 



(v/C, - v /0) to (r, 5r) 



(L.M.S., 25, p. 255 ; 27, p. 416), and 



M = (M,M.,M.,M,M,M (; )' or (M.M,)' (12). 



13. /i=15 : r = 2 -**, (L.M.8., 25, p. 258; ' Msitli. Ann.,' 52, p. 485), 



y, 5 = is reducible to a bicursal C v 



Changing c in L.M.S., 25, p. 259, into 1> I, and normalising by a homogeneity 

 factor 



- | 





T,, T 2 = 2< :i Q 2 + 2R S (3) 



2 H 2 



