386 
A MEMOIR ON CUBIC SURFACES. 
[412 
50. And the coordinates of the 21 distinct lines are 
(a) 
(b) 
<*) ! 
(/) 
(9) 
(h) 
whence equations may be taken to be 
l 
0 
0 
0 
- 1 
1 
(1) 
X=0, Y+ IZ = 0 
0 
m 
0 
1 
0 
- 1 
(3) 
Y= 0, Z + mX = 0 
0 
0 
n 
- 1 
1 
0 
(5) 
Z = 0, X+ nY= 0 
r 1 
0 
0 
0 
-1 
1 
(2) 
o 
II 
N 
T 
+ 
N 
o 
II 
N 
0 
m _1 
0 
1 
0 
-1 
(4) 
7 = 0, Z + m~ 1 X= 0 
0 
0 
-1 
1 
0 
(6) 
Z = 0, X+ n~ l Y= 0 
1 
n 
m 
0 
m 
Jy 
n 
~Wy 
(45) 
X+ nY + mZ= 0, X + /3y\V=Q 
n 
1 
l 
l 
ya 
0 
n 
ya 
(16) 
Y+ lZ + nX = 0, Y + ya ]V = 0 
m 
l 
1 
l 
a/3 
m 
ay3 
0 
(23) 
Z + mX+ IY= 0, Z + a/3W=0 
1 
1 
n 
m 
0 
VI 
a8 
1 
wa8 
(46) 
X+ n~ 1 Y + mZ = 0, X-a8IY=0 
n 
1 
1 
l 
1 
l{38 
0 
n 
"y8S 
(26) 
Y+ l~ 1 Z + nX= 0, r-yS31F=0 
1 
m 
l 
1 
l 
y8 
1 
my8 
0 
(24) 
Z +m" 1 A+ ¿7=0, y8JY=0 
1 
n 
1 
m 
0 
1 
maS 
n 
a8 
(35) 
X+ nY + m~ 1 Z= 0, X-a8W=0 
1 
n 
1 
l 
l 
/38 
0 
1 
n/38 
(15) 
o 
II 
OO 
CQ- 
1 
KS 
o' 
II 
H 
1 
§ 
+ 
N 
+ 
m 
1 
7 
1 
1 
ly8 
m 
7 8 
0 
(13) 
Z + mX + T 1 7=0, Z- y 8W=0 
1 
1 
n 
1 
m 
0 
1 
m/3y 
1 
n(3y 
(36) 
X+ n~ l Y + vi~ l Z = 0, X + (3yW= 0 
1 
n 
1 
1 
7 
1 
lya 
0 
1 
nya 
(25) 
7 + l~ 1 Z+n~ 1 X= 0, 7+yaJF=0 
1 
m 
1 
7 
1 
1 
la(3 
1 
mya 
0 
(14) 
^ + w“ 1 X+ r i F=0, Z + a/3W=0 
1 
0 
0 
0 
0 
0 
(12) 
h 
it 
o 
il 
o 
0 
1 
0 
0 
0 
0 
(34) 
7 = 0, T7 = 0 
0 
0 
1 
0 
0 
0 
(56) 
N 
ll 
© 
ll 
o