^Xt Mffi^^ liF. Sylvester on a remarkable Discovery in the 



that is to say, this last resultant remains absolutely unaltered in 

 value when for x, y we write respectively 



h:-\-my 

 nx-^-pyy 

 provided that lp^mn=\* 



Hence by definition this resultant is an invariant /(a:, y), and 

 X being arbitrary, all the separate coefficients of the powers of \ 

 in this resultant must also be invariants. I proceed to express 

 this resultant in terms of \ and the coefficients of [Xj y). Let 



Ki)'-' i ■ -(i)"' i/«(-"-- - 



E. 



;^-(i)-(l)''-(i)-"-(i)V^M-„-.^=S 



2 



(4)* • Hi)'-f--^' =^'# 



Let now 



-lOT'^b brtP/i4 •'TtrMf* ar/ot -k, "^ -.r-h 



