340 
ON A CASE OF THE INVOLUTION OF CUBIC CURVES. 
[349 
and 
0. 2 2 ©x — 62%.2 = 6.?6x — 6^6.? + — 0^8») {/XV + V\+ \/x) + (d£ — 8i) \/XV, 
= l 3 {8^8^ — 8282 {/iv + v\ + A,/jl) — (82 + 8. 2 ) \/xv], 
— l 3 {8 1 1 8.f + 828« {8280 + 8382 + 8 2 ) — ^ (81 + 8 2 ) 828383), 
= I38282 {^8382 + ^ 83 {82 + 0 2 )}> 
“iWAlW.-^i + W 
= - l 828.213 s ; 
so that we have 
K _ì_ = _IL_ 
K • l *82 828Ì ' 2 ~ 2 
82 ’ 
that is 
K=-ikkV, 
and the equation of the nodal cubic is 
- * №4* v + yg%) + e,n + g^) - A- (£+ f ) V+*)■= 0. 
54. To complete the reduction we have 
coeff. p = I -1=^ (flfe, - №) ; 
coeff. F 2 J£ = 
1 _8i_28l 
(82 + A) ((9., + /x) (0 3 + v) 0 2 2 0o0 :; ’ 
®! ^ 8, + A 
82 s 
®2 8 3 + X 
8Ì83 
® a 8 s + 28-2 
82 s 
<8)2 82 
8?83 
_ 4 ®i W 
83 em 
=~rn®m em ’ 
so that substituting for 0 2 2 ®] — 6f% 2 its value = — \ 8,8.,1 s , the terms in F 3 and Y 2 Z 
—* w *k( p -***)> 
and in like manner the terms in YZ 1 and Z s are 
= + *№¿(1 T» + P), 
are