iVIE. A. CAYLEY ON THE EESULTANT OF A SYSTEM OF TWO EQUATIONS. 707 
where it is to be observed that the figures in the squares of the third column are 
obtained from those in the corresponding squares of the first and second columns by the 
ordinary rule for the multiplication of determmants, — taking care to multiply the dexter 
lines (^. e. fines in the direction \) of the fii'st square by the sinister fines (i. e. fines 
in the direction / ) of the second square in order to obtain the sinister fines of the third 
square. Thus, for instance, the figures in the square 
are obtained as follows, viz. the first sinister fine ( + 3, —1) by 
(-1, +1X-2, +1)= 2 + l=+3 
(-1, +1X + 1, 0)=-H-0=-l, 
and the second sinister fine ( — 1, 0) by 
(0, -lX-2, +1)=0-1 = -1 
(0, -ix + 1, 0) = 0 + 0= 0. 
I have calculated the determinants required for the calculation, by the preceding process, 
of the Resultant of two quartic equations, and have indeed used them for the verification 
of the expression as found by the method of symmetric functions ; as the determinants 
in question are useful for other purposes, I think the values are worth preserving. 
