412] 
A MEMOIR ON CUBIC SURFACES. 
447 
Section XIX = 12 — j3 6 — (7 2 . 
Article Nos. 190 to 193. Equation WXZ + Y~Z + X 3 = 0. 
190. The diagram of the lines and planes is 
where the equations of the lines and planes are shown in the margins. 
191. The axis is a facultative line counting three times (as will appear from the 
reciprocal surface); p' = b' = S, t'= 1. 
192. The Hessian surface is 
Z(WXZ+ Y-Z — SX 3 ) = 0, 
viz. this is the oscular biplane Z = 0 and a cubic surface. 
The complete intersection with the cubic surface is made up of X = 0, Z = 0 
(the edge) six times, and X = 0, Y = 0 (the axis) six times. There is no spinode curve, 
a-' = 0; whence also /3' = 0. 
Reciprocal Surface. 
193. The equation is at once found to be 
Q±zw 3 + (y 2 + 4 xw) 3 — 0.