2-20 PROFESSOR A. U. GREENHILL ON THE 



Thus 

 .,() = -*, tV( r) = .r (10), 



,s(2r) = 0, V(2r) = .ry (ll), 



V (3r) = ,/ - ;K - ?/ - (12), 



x (y x) / / , \ "' (y *' v 2 ) (y x ) 2 /-, r,\ 



.s'(4?') = --' 2 ' y, w(<iv) = x y s ' (13), 



.xv (?/ x if] / / c \ '/ 2 (a?V a;~ ?/ 3 ) x (y x y~)~ 



s(ov)= ' ^ ^ J ' x, iti'(5v) = x-'~ 7^ v< (14), 



(y - *)'- (y - x ) 



,y ( 6t.) = y ( ^ ~ x}:{x(! > ~ x ~ } ~. } ~ ( ' ry ~ x '~ f] (15), 



y,r 

 s (nr) = x* ZiiL^- 1 _ lT) ? V (>jr) = a;^ (16). 



y" 7" 



.3. For the determination of P (ra;) we h.ave the formula (HALPHEN, ' F.E ,' 1 , p. 1 02) 



^3 = *-() = (F'fp l y. (i); 



whence, by logarithmic differentiation, 



,,p (,,)_. p (,,,')= i(nt>- C'//r) 

 _ W 2 _ i $".,. i r / y// 

 '' 



- ~ (i 4. w \ 4. " 4. 



Sn ^ J} n 7 ,\SxcM Sydw 



Now for every homogeneity factor, and as elliptic functions of degree zero, 



2J- xy (1 + t/) _ x ( 1 + y) 

 xy x 



5-8(1+*) (4), 



/ 



