258 
PROFESSOR CAYLEY ON CUBIC SURFACES. 
50. And the coordinates of the 21 distinct lines are 
0) 
m 
(/) 
is) 
(70 
whence equations may be taken to be 
l 
0 
0 
0 
-1 
1 
(1) 
X=0, Y+ 7Z==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 
i- 1 
0 
0 
0 
-1 
1 
(2) 
X=0, Y+ l- ] z = 0 
0 
0 
1 
0 
-1 
(4) 
Y = 0, Z+m“ 1 X=0 
0 
0 
n~ l 
-1 
1 
0 
(6) 
Z=0, X+ n~ l Y=0 
1 
n 
m 
0 
m 
Py 
n 
Py 
(45) 
X+ wY+»nZ=0, X+j3yW=0 
n 
1 
l 
l 
ytx 
0 
n 
ya 
(16) 
Y+ lZ+nK=0, Y + y«W=0 
m 
l 
1 
i 
•* 
m 
~^P 
0 
(23) 
Z +mX+ ZY=0, Z -(- a|3 W = 0 
1 
l 
n 
m 
0 
m 
aS 
1 
no. 8 
(46) 
X+ w" 1 Y+mZ=0, X-«W=0 
n 
1 
i 
l 
1 
p 
0 
n 
(26) 
Y + 7- I Z+wX=0, Y — /3£ W = 0 
l 
m 
l 
1 
l 
y8 
1 
my 8 
0 
(24) 
Z +m- 1 X+ IY=0, Z -y&W=0 
1 
n 
l 
m 
0 
1 
mo. 8 
n 
a8 
(35) 
X+wY+m- I Z=0, X-«W=0 
1 
n 
1 
l 
l 
/38 
0 
1 
n \ 38 
(15) 
Y+ZZ+r‘X=0, Y — (3^W=0 
m 
l 
l 
1 
1 
Zy8 
m 
y8 
0 
(13) 
Z A-mX+7- 1 Y = 0, Z -y&W=0 
1 
l 
n 
1 
m 
0 
1 
m/3<y 
1 
n Py 
(36) 
X+ w-'Y+m-'Z =0, X+/3yW=0 
1 
n 
1 
1 
l 
1 
Zya 
0 
1 
ny'A 
(25) 
Y+ 7- 1 Z + w- 1 X=0, Y -f-yaW = 0 
1 
m 
1 
l 
1 
1 
Za/3 
1 
mycn 
0 
(14) 
Z+m- ! X+ 7 _1 Y =0, Z+«j3W=0 
1 
0 
0 
0 
0 
0 
(12) 
0 
II 
£ 
o' 
II 
X 
0 
1 
0 
0 
0 
0 
(34) 
Y = 0, W=0 
0 
0 
1 
0 
0 
0 
(56) 
Z =0, W=0 
