353 
939] ON A CASE OF THE INVOLUTION AF + BG+ CH=0. 
values which satisfy 
F + N = 0, 
K+L =0, 
B + M -f- Q = 0. 
The quartic function is thus seen to be 
= (y 2 — zx) (By 2 -f Fyz — Qzx + Kxy) = 0, 
viz. we have By 2 + Fyz — Qzx + Kxy = 0 for the equation of the conic (7 = 0. 
Moreover, substituting for p, q, r, s, &c., their values, we have finally for the 
required involution 
[/3/3'x 2 + (aa' + /3 + /3') y 2 + z 2 — (a + a) yz — (a/3' + a'/3) ®y] 
x [/3'73'V + (a"a'" + /3" +/3"') y 2 + z 2 - (a" + a'") yz - (a"/3'" + *'"/3") xy] 
- [/3/3'V + (aa" + ¡3 + A') y 2 +z 2 -(a + a") yz - (a/3" + a"/9) xy] 
x [At3 m x 2 + (a a" + /3' + A") y 2 + z>- (a' + a"') yz - (a! A" + «"'/3') ay], 
- (y 2 -zx)x f [(a/3"' - a"'/3) (a' - a") + (a'/3" - a"/3') (« - a'") - (/3 - /3"') (/3' - /3")]\ 
+ yz [(a - a"') OS' - /3") + (a' - a") (/3 - /8"')] 
^-^[(/3-/3"')(/3'-/3")] 
l-xy IW" - a "'/3) (/3' - /3") + (a /3" - a"/3') (/3 - /3"')] 
It will be recollected that this is the solution for the case A = 1234, ^=5678; 
B= 1256, (7 = 3478: being that to which the present paper has reference. 
C. XIII. 
45