THIRD ELLIPTIC INTEGRAL AND THE ELLIPSOTOMIC PROBLEM. 297 



26 2 



= dny [V (6* + 1) /(6 3 - 26 - 1) - (6 + 1) 



) J __ LV v i .*/ v \" I V" ~r -; v/ v" /K\ 



,-2 A 7_ '-t \ / 



o 4 o 



I (w) = l cos - ! o + if V + ' y ^ X ls 



^_u -- a; ; 



= isin- lK " i* Jf" '^VjX, (6), 



^ ar; 



/ 4- r- /'7^ 



X -|- X ^^, 



RO = D 2 (8), 



_ 4 _ 4 _ 2 



K i - ' ' o /l4 (9), 



R, = - 



26* 



' 2b + ] + v/6 



P (7-) _ zii/K' 4 (6 + 1 ) x/ (^' - 1 ) (b- - 21 - 1 ) - (//- + -2b + 3) (Ir - -2b - 1 ) (ll} 

 M o 166- 



Q(")_(&+l)v/(6*- l)(/r-26- 1) 

 M 3 26 2 



Bisection formulas for /A = 8 in the region /.' = K'i will lead to the same results, 

 with ffl s = , 



v / ^2 + 26 _j + x / /,? - 26 

 < 



6 2 + 26 - 1 - v/ 6 3 ~- 26 - 1 



6^ 1+a (15), 



ct" 



having the substitution 



Hence the following table of section-values for /A = 16, holding in the region 



00 > b > v/2 + 1 ; tested numerically by 6 = ( - v ^- ) , o = %, K = %, as on p. 278, 



\ Z / 



region C : 



VOL. com. A. 2 Q 



