349] 
ON A CASE OF THE INVOLUTION OF CUBIC CURVES. 
335 
49. We have now to find the coefficients of F 2 and Z*. 
coeff. + ¿X 
2fj,v 
= X-5 + 4X -2X ^ + 
(0 2 + A) 2 (0 2 + /a) ($2 + z>) 
^o.-^+^+éx ,+ 0, a, + i+ 0 S 
(02 + A)“ 
and observing that the terms 
2 h ^ 
(d 2 + /i) (0 2 + v) 
2/iv 
(0 2 + A) 2 (0 2 + ya) (0 2 + v) 
only differ from those of coeff. X 2 by having 0 2 in the place of 6 r and are therefore 
= 0, we have 
a n ,fyv_2fxv 
01-6* ^ 1 2 0i 02 
coeff. F 2 = X 
( 0 2 + A) - 
-2X 
(0 2 + /A) (0 S + V) 
I 1 
= (8,-8,) 1 S.„ .'.-22 
1 - 
2 fxv } 
0i02 
V (0 2 + A) 2 (0 2 + (0 2 + v) ^ 
Here 
-1 
+ 
(0 2 + A) 2 ((02 + A) (0 2 + X) (02 + A) (0 2 + v) 0. 2 (0 2 + A) 
= 0- X |— (0 2 + V) — (0 2 + fl) + 0- (0 2 + (0 2 + l>) j , 
1 V ( _L 
= ®, 2 r +!,+ x 
^{ 2( x + , + ,,) + 2 ^ + V}, 
and 
2X 
_ Zjiv 
0A 2 s 
(0 2 + yaf (0 2 + v) ©2 
= - @T ^ I 02 + X 
( 1_ |a) ( ^ +x) ’ 
2/u.y 2A/ai> 
( 
2 
@2 
30 2 + A + /a + v 
0i 0AJ* 
2 (/iv + v\ 4- A¡x) 6A/jlv 
0i 
0A j ’