248 
PROFESSOR CAYLEY ON CUBIC SURFACES. 
where 
#= P , az=lmn+^-, (3= to— — , 
— 2{p — «)’ /wm’ r «n» 
then the equations of the planes are : — 
w=o, 
[12'=w] 
ZX+mY+ M Z+w[l +i(j-4) (m-h) 
(-!)]=», 
[23' =4] 
t+I+!+ w [ 1 -K z_ ^) ( w_ «) 
x=o, 
Y = 0, 
Z = 0, 
;)]-»• 
[3V=fl 
[12 . 34 . 56=#] 
[42' =y] 
[14' = 2 ] 
X+i(»-s)(-5) W =°* 
[2i'=g 
y+IH)H) w=0 ’ 
[32'=*,] 
z+i(z-i)( m -i)w=o, 
[13'=?] 
®+I+!+w=o, 
[41'=f] 
7+*»Y+§+W=0, 
[34'=g] 
f+^+z+w=o. 
[13 . 24 . 56 =h] 
y-H^Y-f nZ-fW=0, 
[24'=f] 
ZX+ I +mZ +W=0, 
[14.25.36=g] 
K+mY+;+W=0, 
[43'=h] 
x+ l{p ~ P Tr n W =°’ 
[12. 35. 46 =x] 
Y+^^W=0, 
[52'=y] 
r, , »(?-«) + 2?n *W_ f) 
Z + ^ W U ’ 
[15'=z] 
1 2 
~j(p — a) H 
x+' "”w=o, 
P + l 3 
[12.36. 45 =x] 
1 2 
— (p — «) 3 — i 
Y+“ „ W-0, 
P + P 
[62'=y] 
