PEOPESSOB CAYLEY ON CUBIC SEEPAGES. 
279 
and we thus have 
or, what is the same thing, 
4M 2 + 3LN=0, 
LM + w 2 N=0, 
L 2 -12w 2 M=0, 
L, 
12M, 
— 9N II 
w 2 , 
L, 
M 
for the equation of the cuspidal curve. Attending to the second and third equations, 
these are quartics having in common w 2 =0, L=0, that is, the line y=0, w=0 four times ; 
or the cuspidal curve is a partial intersection 4x4 — 4: d =12. 
Section VI=12— B 3 — C 2 . 
Equation WXZ+Y 2 Z b , c , Y) 3 =0. Article Nos. 95 to 102. 
95. The diagram of the lines and planes is 
Lines. 
4— CO tO 
to to CO 
VI=12- 
B 3 — 0 2 . 
CO 4^ 4^ 
^ CO to 
^ M » 
- 
o 
>-*| os 
^ X 
bO| 
X 
1! 
05 
CO 
X 
CO 
II 
CO 
x 
CO 
II 
I 05 
X 
1! 
Ci 
0 
1X6= 6 
* 
• • 
Biplane touching along axis, and 
containing transversal ray. 
00 
1X6= 6 
• . . 
Other biplane. 
22' 
* 
• 
• 
33' 
3x6 = 18 
• 
• 
Planes each through the axis and 
containing a ray of the binode 
and a ray of the cnicnode. 
Planes. 
4^ CO tO ^ 
* 
• 
3x3= 9 
• 
• 
" 
Biradial planes of the binode, 
each containing ray of axial 
biplane and a ray of other bi- 
plane. 
2'3' 
2'4' 
3x2= 6 
: 
^ * 
Biradial planes of the cnicnode. 
3'4' 
IT 45 
• 
o 
d> 
S’ 
Cnicnodal rajs. 
Biplanar rays of other 
biplane. 
Biplanar ray of axial 
biplane, being a 
transversal ray. 
Axis, joining the two 
nodes. 
