or 



THIRD ELLIPTIC INTEGRAL AND THE ELLIPSOTOMIC PROBLEM. 253 



S = 4.9 ( 8 + *f _ [(1 + y) S + X yJ = ( 5 ). 



ihen, with 



m?a (1 2m) a m 2 a ? 



l v ' ?/ == ~ , s = , (6) 



(a - m)- a - m (a - m )~ 



a m I ( L - 2m) (a m) 



and Z breaks up into two quadratic factors, Z, and Z.,, 



Z = 2 2 _ m ( X ~ 2m + 2m2 ) _i_ _ m? ( l m Y_ 



' (I 2m) (a m) '* h ( L ~2w) 4 "(a ' ~m)- 



and by means of a homogeneity factor 



7/1 



replacing z by ^ . , we may replace Z; and Z., by 



Z t = [z - -HI (I - m)j-' - (1 - 2m)- 2 



26. The resolution of T in the spherical catenary for p, = 4w + 2 is not the same 

 as for p. = ~2 a + 1 ; we must put 



rp rp r- / ^ | >\y i y2\2 |^ o/ / 1 /2\ / 1 \ 



and then in 20 

 so that 



" '" ' "' ""' :^^n = (3>, 



