422 
A MEMOIR ON CUBIC SURFACES. 
[412 
125. The cuspidal curve is given by the equations 
| 3 (a -f-1), 
— %ay — ¡3, ay*- + у : 
II - 2ay - /3, 
ay 2 + y, -S 
or say by the equations 
3 (a +1) (ay* + y) - (2ay + (3)*- = 0, 
that is 
a (a — 3) y*- + 4,a/3y — 3 (a +• 1 ) у = 0, 
and 
— 3 (a + 1) В + (2ay + /3) (ay* + y) = 0, 
consequently o' = 6. It is to be added that the cuspidal curve is a complete inter 
section, 2x3. 
Section IX = 12 — 2B 3 . 
Article Nos. 126 to 136. Equation WXZ + (a, h, c, d\X, F) 3 = 0. 
126. The diagram of the lines and planes is 
Lines. 
05 СЛ W ЬЭ 
P* 
14 
25 
36 
!-2 B s . 
<i! as 
X 
oo 
II 
toi h-i 
00 
1x9= 9 
1x6= 6 
. . . 
Common biplane, os 
cular along the axis. 
2x6 = 12 
. . . 
Other biplanes of the 
two binodes respect 
ively. 
3x9 = 27 
6 45 
• 
’ 
Planes each through 
the axis and contain 
ing rays of the two 
binodes respectively. 
Rays, 1, 2, 3 in the non- 
axial biplane 7 of the one 
binode, and 4, 5, 6 in the 
non-axial biplane 8 of the 
other binode. 
Axis joining the two bi 
nodes.