PROEESSOR CAYLEY OjST CUBIC SUREACES. 
313 
Section XVI=12-4C 2 . 
Equation W(XY+XZ+YZ)+XYZ=0. Article No. 177 to 180. 
177. The diagram of the lines and planes is 
XXX 
X 
X ' 
X x 
+ + + 
II 
II 
II II 
|| 
|| 
^ N Kj 
O 
o 
o o 
o 
o 
© o © 
II 
CS3 
11 
3 N 
II II 
II 
ii 
k| K csa 
+ + + 
N 3 3 
II II II 
o o o 
o 
o 
o o 
o 
o 
6 
CO bo 
CO 
CO 4*- 
CO £ 
5 
5 
01 CO 
GJ 
XVI = 
12— 4C 2 . 
X 
X 
IT 
r 
Planes are 
Z +W=0 
12 
• 
Y +W=0 
13 
• 
Y +Z =0 
14 
6x2=12 
. . 
Planes each touching along 
an axis, and containing 
X + w=o 
23 
• 
• • 
a transversal. 
X +Z =0 
24 
• 
X +Y =0 
34 
• 
X =0 
1 
; 
• 
Y =0 
2 
4x8=32 
. 
* 
Planes each through three 
Z =0 
3 
l 
axes. 
W=0 
4 
• 
* 
* 
X+Y+Z+W=0 
1234 
1X1= 1 
. . . 
Plane through the three 
TT 45 
: : : 
transversals. 
o p 
a m 
o § 
g jLo 
§ g 
§- 
g g © 
ij? 
* *3 g* 
§ 
^ 89 
( p- 
° 
rt- 
g* g 
o . 
where the equations of the lines and planes are shown in the margins. 
178. The transversals are each facultative : q'=b'=o ; t r =l. 
179. Hessian surface. The equation is 
4XYZW -(X+Y+Z+ W)(WXY + WXZ + WYZ + XYZ) =0, 
MDCCCLXIX. 2 U 
