[345 
346] 
289 
5 points 
ex case, 
f these 
al; the 
ay have 
alue of 
of the 
flexions, 
Ve may 
he two 
ay have 
l point. 
pullata, 
NOTE ON AN EXPRESSION FOR THE RESULTANT OF TWO 
BINARY CUBICS. 
[From the Quarterly Journal of Pure and Ayyplied Mathematics, vol. vi. (1864), 
pp. 380—382.] 
Mr Warren, in his paper “Illustrations of the Theory of Critical Functions,” 
Quarterly Mathematical Journal, t. vi. pp. 231—237, (1864), has given for the Resultant 
of two binary cubic functions, an expression which is in effect as follows; viz. considering 
the cubic 
i points 
ex case, 
f these 
al; the 
ay have 
alue of 
of the 
flexions, 
Ve may 
he two 
ay have 
l point. 
pullata, 
its Hessian 
(a, b, c, d\x, y) 3 , 
(a, b, c\x, y) 2 , = (ac — b 2 , ad — be, bd — c 2 \x, y) 2 , 
and the cubicovariant 
{A, B, C, DQx, y) 3 , = ( a 2 d — Sabe + 2b 3 , 
3 abd — 6ac 2 + 3 b 2 c, 
[ — ad 2 + 3 bed —2c 3 , 
and in like manner the cubic 
its Hessian 
(a', b', c', d'\x, y) 3 , 
(a', b', c'\x, yf, 
and the cubicovariant 
and writing 
21 = ad’ — 3be' — We — a'd , 
23 = ac' + a'c — 2bb' , 
6 = AD' - 3BC + SBC - A'D, 
c. V. 
37