412] 
A MEMOIR ON CUBIC SURFACES. 
391 
Section 111 = 12— B 3 . 
Article Nos. 60 to 72. Equation 2W(X + Y + Z)(IX + mF + nZ) + 2kXYZ= 0. 
60. The system of lines and planes is at once deduced from that belonging to 
11 = 12 — 02, by supposing the tangent cone to reduce itself to the pair of biplanes; 
3 of the planes (a) of II = 12 — C 2 thus coming to coincide with the one biplane, and 
three of them with the other biplane. 
61. The diagram is 
24 
25 
26 
34 
35 
36 
Lines. 
|—L |—i 
os Cr< ^ 
05 Oj CO to h-* 
111 = 12 
1—*| to 
w X 
I-* 
II 
6x3=18 
123 
456 
2x6 = 12 
• • • 
Biplanes. 
14 
• 
15 
m 
• 
16 
# 
• 
24 
<D 
-5 25 
Ph 
26 
9x3 = 27 
• 
• 
Biradial planes each con 
taining a ray 1, 2, or 3 
of the one biplane, and 
a ray 4, 5, or 6 of the 
other biplane. 
34 
• 
• • 
35 
: ' 
• 
36 
• 
• 
14.25.36 
14.26.35 
15.26.34 
15.24.36 
16.24.35 
6x1 = 6 
• 
• 
Planes each containing 
three mere lines. 
16.25.34 
17 45 
• 
• 
Mere lines, in each 
biradial plane, 
one. 
Rays 1, 2, 3 and 
4, 5, 6, in the 
two biplanes 
respectively.