MR. R. C. ROWE ON ABEL’S THEOREM. 
721; 
Next, the two values of y under the sign % being 
y=± 
(i+: 1 + 
, or say ±- 
n 
the first two terms in the expression of vXjXdx compound into 
a /n na — b , 
ST 
jn_ 
\/n 
l 
k 
n 
Yc 
n 
u/ n na — b , 
= — nr lo s 
(n — g) 2 — (k +_p y/n t) 2 
(n—q) 2 — (k — p v 7 ni Y 
which is easily rationalised, and gives 
. na — b , 
n—;— tan 1 
2pkx/ 7 , 
(n — qY +pPn — k~ 
which, substituting for Jr its value (1 -\-n)(c 2 -\-n) 
Ip 
,-iia — l . q “— c 
\ 1 -A- 
— tan' 
]+« 1 
P*-(g- fl) 8 l 
? 2 -c 2 J 
Now, if £c ls x z , aq be the roots of the equation E=0, we get at once the relations 
2 p 
Xl x,x 3 = - —-* 
q~ —c 
■p + x.p -f a.p —- 2 — g 2 Xi 2 x 2 2 x 3 2 = 2 
q--c 2 
r p~-(q+l) 2 
(i-xY){i-xY)(i-x 3 2 = \—~n 
2 
