294 
PBOFESSOE CAYLEY ON CUBIC SUBFACES. 
or say by the equations 
3(a-t-l)(a/+ y )-(2^+/3) 2 =0, 
that is 
a[a — 3)t/ 2 + 4«/3y — 3(a + 1 )y = 0 5 
and 
— 3(«+l)^+(2a?/+/3)(aj/ 2 +y)=0, 
consequently d — 6. It is to be added that the cuspidal curve is a complete intersec- 
tion, 2x3. 
Section IX=12-2B 3 . 
Equation WXZ +(a, b, c, dJX, Y) 3 =0. Article Nos. 126 to 136. 
126. The diagram of the lines and planes is 
Lines. 
a cn ^ CO tt> H- o 
IX = 
= 12— 2B 3 . 
05 
X 
03 
II 
*®[ £ 
X 
CO 
CO 
0 
1x6= 6 
. . . 
Common biplane, os- 
cular along the axis. 
7 
A 8 
2x6 = 12 
: : : 
Other biplanes of the 
two binodes respect- 
ively. 
S 14 
• : 
• 
25 
36 
3x9 = 27 
: : 
• 
Planes each through 
the axis and contain- 
ing rays of the two 
binodes respectively. 
6 45 
• • 
. 
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. 
127. Writing (a, b , c , dJX-, Y) 3 = — <2(/iX— Y)(/ 2 X— Y)(/ 3 X— Y), the planes are 
x=o, 
[0] 
Z =0, 
[ 7] 
w=o. 
[ 8] 
*! 
II 
_o 
[14] 
/;x-y=o, 
[25] 
f,X- Y=0, 
[36]; 
