1898 - 99 .] Mr E. J. Nanson on a Set of Quadrics . 
355 
the eliminant may also be expressed as 4 8 a6'c" times the determi- 
nant 
a A +/F K' B' + g\ g r - af"), g"C" + h"(g'h - of) 
hA +f(h"f - Vg ") 5'B' + g f G' /"C" + h"(h’f - Vg) 
gA+f(fg'-c"h') fB' + g\fg"-c"h) cT + OT 
(4) 
6. If with Sylvester and Muir we reject the special factor 
4 z ab'c" the eliminant of (1) is the third order determinant (3), or 
what is the same thing, the third order determinant (4). 
From (3) it is obvious that when 
a = b' = c" = 0 
the eliminant reduces to FG'H" A and from (4) it is obvious that 
when 
f=g' = h" = 0 
the eliminant reduces to AB'C" A 
7. Beturning now to the other method of elimination we find, 
on eliminating x 3 , x 2 y, etc., dialytically from the Jacobian J and 
the nine equations obtained from (1) by multiplying each equation 
by x, y , z, for the eliminant of (1), the determinant 
a 
. 
. 
9 
h 
/ 
V 
. 
h' 
g 
r$ 
. C 
r 
g" 
. 
V 
/ 
. 
. 
a 
h 
g 
f 
g 
a 
h 
V 
r 
9 ' 
. 
ii 
. 
\ . 
g 
hr 
V 
f 
c" 
g" 
ti" 
f" 
f" 
n 
C 
h" 
g" 
- aF 
- 5'G' - c" H" 
(4) 
(5) 
(6) 
(?) 
(8) 
(9) 
(10) 
where 
(4) = h'ipj'h + E !) , (6) = c"(2 af + F") , (8) = a(2l/g" + G) 
(5) = d\Wg + G") , (7) = a(2c"h' + H) , (9) = b'(2 af" + F) 
(10)= A +4a5V # . 
Taking out the factors a, b', c" from columns 1, 2, 3, and then 
reducing to zero all the elements common to rows 1, 2, 3 and 
columns 4, 5, 6, 7, 8, 9, 10 by subtracting from the last 
