272 
MR. A. CAYLEY’S ANALYTICAL RESEARCHES CONNECTED WITH 
The coefficient of y is 
i_,r/ 
(_P_g=+h’+5^)(®+(-f+g+h)’-2J(-f+g+h)) 
-f‘-g‘-h‘+2gV+2h”P+2Pg’-i^y!^|, 
2 
or, after all reductions, 
and similarly the coefficient of z is 
_ f g-^_ h^+2g-V+2hT=*+2Pg^- j, 
or, after all reductions, 
2j(f2_g2 + h2) 
2fh 
and the coefficient of w is 
(l +j)f(~^”4-g+h)2>/K\X l~jV^ ~P- 
Whence, forndng the equation of the resultor in question, and by means of it those 
of the other resultors, the equations of the resultors are 
— 2fgh 
-f+g + 
— 2fgh 
I-JV '-J 
(j(Sf^-f+g+h+2J-^ 
I / 2fgh , - 
2 % 
^ ( 
) 
/“j; 
') 
J v'3S \ 
-« 
"i 
J 
. jJ 
-pw=i 
0 4( 
) ^-( 
') f 
-j) 
J V€\ 
X 
+ 2v/K\/l-j\/ l-f\/ 1-jx/- 
pw=0 
