448 
A MEMOIR ON CUBIC SURFACES. 
[412 
The section by the plane w = 0 (reciprocal of B tì ) is w = 0, y = 0 (reciprocal of 
edge) four times. The section by the plane z = 0 (reciprocal of C. 2 ) is z = 0, y 2 + 4xw — 0 
(reciprocal of nodal cone) twice. 
Nodal curve. 
The equation gives 
1 „ i*Jz , p 
showing that the line w = 0, y = 0 (reciprocal of edge) is an oscnodal line counting as 
three lines ; 6' = 3. 
There is no cuspidal curve; c' — 0. 
Section XX = 12 — JJ a . 
Article Nos. 194 to 197. Equation X-W + XZ 2 + F 3 = 0. 
194. The diagram of the lines and planes is 
XX=12- u 8 . 
Plane is 
X=0 0 
1x45 = 45 
1 45 
Uniplane. 
H 
*3’ 
where the equations of the line and plane are shown in the margins. 
195. There is no facultative line; b'= p = 0, t' — 0. 
196. The Hessian surface is X 3 Y = 0, viz. this is the uniplane X = 0, three times, 
and the plane Y — 0 through the ray. The complete intersection with the cubic 
surface is made up of X = 0, Y = 0 (the ray) ten times, and of a residual conic, which 
is the spinode curve; a — 2. 
The equations of the spinode conic are Y = 0, XW + Z‘ z = 0, viz. the plane of the 
conic passes through the ray. Since there is no facultative line, /3' = 0.