402 
Proceedings of the Royal Society of Edinburgh. [Sess. 
Cayley, A. (1856, December). 
[Memoir on the resultant of a system of two equations. Philos. Trans. R. 
Soc. (London), cxlvii. pp. 703-715 ; or Collected Math. Papers, ii. 
pp. 440-453.] 
As the resultant, R 3 2 say, of the pair of equations 
ax 3 + hx 2 y + cxy 2 + dy s = 0 , px 2 + qxy + ry 2 = 0 , 
is homogeneous and of the 3 rd degree in the coefficients of the second 
equation, and at the same time homogeneous and of the 2 nd degree in the 
coefficients of the first equation, Cayley seeks a convenient form of 
representation in which this double homogeneity will be prominent. What 
he obtains is * 
where the first square represents a 2 r 3 , the second — abqr 2 , the third 
— 2 acpr 2 + b 2 pr + acq 2 r, and so on. The result is reached in two ways, the 
second being by developing the dialytic eliminant 
* Three misprints being corrected. 
