PROFESSOR CAYLEY ON CUBIC SURFACES. 
291 
118. Take m x , m 2 as the roots of the equation (to — 1 ) 2 = 4am, so that m x -\-m 2 =2-\-ia, 
m{ra 2 — 1, then the planes are 
x=o, 
[ 7] 
Y = 0, 
[ 8] 
Z =0, 
[ 9] 
Y+Z+X=0, 
i[ 12] 
Y+X+W=0, 
[ 34] 
Y+Z+W=0, 
C 56] 
rH 
1 
g 
¥ 
[ 13] 
Y=(m 2 — 1)X, 
[ 24] 
tsf 
i — 1 
l 
¥ 
[ 16] 
Y=(m 1 -l)Z, 
[25] 
Y=(m 1 -l)W, 
[46] 
Y=K-1)W, 
C 35] 
o' 
II 
[789] 
Y+X.+Z+W=0, 
[789] 
119. And the lines are 
a 
h 
C 
/ 
9 
h 
equations may he written 
0 
0 
0 
0 
0 
1 
(7) 
X =0, Y=0 
0 
0 
0 
1 
0 
0 
(8) 
Z =0, Y=0 
0 
1 
0 
0 
0 
0 
(9) 
W=0, Y=0 
1 
1 
1 
0 
0 
0 
(7) 
Y+Z+X=0, W=0 
0 
0 
1 
—1 
1 
0 
(8) 
Y+X+W=0, Z =0 
1 
0 
0 
0 
-1 
1 
(9) 
Y+Z +W=0, X =0 
0 
0 
0 
1 
m x — 1 
1 
1 
J « 2 — 1 
(1) 
Y=(w 1 -l)X =(m 2 -l)Z 
0 
0 
0 
1 
m 2 — 1 
1 
1 
m i — i 
(2) 
Y=(m a ~l)X=(m 1 -l)Z 
-1 
1 
m 2 — 1 
0 
0 
0 
l 
m 2 — 1 
(3) 
Y=(m 2 -l)W=(m 1 -l)X 
-1 
1 
m 2 — 1 
0 
0 
0 
1 
TTij — 1 
(4) 
Y =(m x — 1) W = (m 2 — 1)X 
0 
1 
m x — 1 
1 
1 
m 2 — ] 
0 
0 
(5) 
Y=(m 1 -l)Z =(m 2 -l)W 
0 
1 
1 
m 2 — 1 
1 
772 1 — 
0 
0 
(6) 
Y=(m 2 -l)Z =(m 1 -l)W 
2 r 2 
