1. Denoting by A, B, C, F, G, H the co-factors of a, b, e, f, g, h, in the determinant

the problem in question is to eliminate x, y, z from the three equations

and it lias been discussed by Sylvester, Cayley, Muir, Tait, and Lord M'Laren.

Sylvester deduces from (1) this new system

and hence finds the dialytic eliminant

the expansion of which (an obvious error being corrected) he states to be

where

so that “rejecting the special (N.B., not irrelevant) factor abc, we obtain”