412] 
A MEMOIR ON CUBIC SURFACES. 
443 
Section XVII = 12 - 2B 3 - C 2 . 
Article Nos. 181 to 185. Equation WXZ+ XY 2 + Y 3 = 0. 
181. The diagram of the lines and planes is 
XVII = 12 - - C 2 . 
Planes are 
^ N) ^ ^ k 
II II II II II t- 
© © OC P 5 
X * 3S ” 
+ + H II ii | 
^ O o o 
II II 
o o 
03 OS I-* © 
Oil to 
X 
05 
II 
Ml 
05 
to 
X 
05 
II 
h-* 
to 
I— 4 
X 
o 
II 
o 
A'=0 0 
Z=0 13 
JP=0 24 
Y=0 012 
X + Y = 0 034 
lx 6= 6 
• • • 
Common biplane, through 
the axis joining the two 
binodes. 
2 x 6 = 12 
• 
• 
Remaining biplanes, one 
for each binode. 
lx 18 = 18 
• 
• 
Plane through the three 
axes. 
lx 9= 9 
5 45 
• 
Plane through the axis 
joining the two binodes. 
Biplanar rays, one 
for each binode. 
Axes each through 
the cnicnode and 
a binode. 
Axis joining the two 
binodes. 
where the equations of the lines and planes are shown in the margins. 
182. There is no facultative line ; b' = p = 0, t' = 0. 
183. The Hessian surface is 
X (WXZ+ SYZW + IP) = 0, 
viz. this breaks up into X = 0 (the common biplane), and into a cubic surface. 
56—2