378 
A MEMOIR ON CUBIC SURFACES. 
[412 
p — a Y Z 
— 0 —X -\ h 
2 n m 
— Imn 
1 - - — ) (p - a) - 
m 2 n 2 ' 
X p — a 
n 
Y+ 
Z 
Imn 
i _i _ i 
n 2 ¿ 2 
Z 7_ p-g 
m l 2 
iv — kn ( — f 1 — — 0 
n \ I- m- 
W 
mn) p + /3 
2 \ W 
nl J p + /3 
2 \ W 
-«)“ 
ImJ p + /3 
= 0, [25' = p 2 ] 
= 0, [15.23.46= qj 
= 0, [53' = rj 
- ? X+nY+mZ-j^-(l( 1 - m 2 - n 2 ) (p - a) - 2wm) —-= =0, [61' = Pl ] 
° Imn K £ p — p 
nX- p -^Y+lZ-^-(m{l-n 2 -l^(p-a)-2nl ) =0, [36'= qj 
2 imn p — p 
Imn 
mX - IY- P ~ Z- 7 — (n (1 - P - m 2 ) (p - a) - 2Zm) = 0, [13.26.45 = r,] 
2 Imn p — p 
43. The coordinates of the 27 lines are then found to be as follows: