92 
ON CERTAIN OCTIC SURFACES. 
[654 
Reverting to the original equations 
{fO 2 + g) (k6y — x) 2 + h(k — 1 ) 2 0 2 z 2 = 0, 
(ibk 2 6 2 — a) ( 6y — x) 2 + h (k — l) 2 (fiw 2 = 0, 
say these are 
(a, b , c, d, e \6, l) 4 = 0, 
(a', b', c', d', ¿\d, 1) 4 = 0, 
then the coefficients in the two equations have the values 
fk 2 y 2 , bk 2 y 2 , 
— 2 kfxy, — 2bk 2 xy, 
fx 2 + gky 2 + h(k — l) 2 z 2 , bk 2 af — ay 2 + h(k — l) 2 w 2 , 
— 2gkxy, 2 axy, 
gx 2 , — ax 2 , 
where observe that only c contains z 2 , and only c' contains w 2 . The result of the 
elimination is 
a, 
b, 
c, 
d, e 
a, 
b, 
c, 
d, 
e, 
a, 
b, 
c, 
d, 
e, 
a, b, 
c, 
d, 
e, 
a', 
b', 
c', 
d', e' 
a\ 
v, 
c', 
d', 
e', 
a', 
v, 
c\ 
d', 
e', 
a', V, 
c', 
d', 
e', 
viz. here the only terms which contain 
z 8 and 
w 8 are 
c 2 a' 2 e' 2 + c' 2 a 2 e 2 , 
and hence the terms in z 8 and w 8 are 
A 4 (k — l) 8 z 8 . a 2 b 2 k^y i + A 4 (k — l) 8 w 8 .f 2 g 2 k i x A y i , 
viz. these are 
= h 2 k A (k — l) 8 ctfy* (a 2 b 2 h 2 z 8 + f 2 g 2 h 2 w 8 ), 
or assuming that the determinant contains as a factor the function b 2 c 2 f 2 a?+... + 2£lx 2 y 2 z 2 w 2 , 
with a properly determined value of il, we see that the other factor is =h 2 k 4 (k — l) 8 # 4 y 4 , 
which agrees with a preceding result.