276 
ON THE HESSIAN OF A QUARTIC SURFACE. 
Hence, uniting the two parts, we have 
B - 
+ kPw 4 
^ (& 2 c 2 c 2 a 2 + a 2 6 2 ) 
y _ 
24 
a 2 b 2 c 2 
+ 12 
& ■ y 2 ■ - 
6 2 c 2 c 2 a 2 <x 2 P 
+ ^( 12(I + 1 +l)r<2> 
r*)« s 
. „ / ¿T y 1 Z* 
_48 (&v + 3w + a*P 
\+24P*£ ] 
+ & 2 { — 24PQ 3 }. 
Writing herein Q 2 = k 2 w 2 P— U, and transposing all the terms which contain U, 
have 
B + w{- (I +1 +i)r- 4MW g + £ + £)- 24P «] 
= k 6 w*P 
27k 2 
a 2 b 2 c 2 
wr 
+ 161 
( 1 1 
1 ' 
\b 2 c 2 c 2 a 2 
a 2 b 2 , 
+ 12| 
/ 1 1 
1 
( P + P + 
c 2 , 
+ 12| 
(* + £ + 
^6 2 c 2 c 2 a 2 
¿r 2 ' 
orb 2 , 
— 48 | 
( x 2 v 2 
+ * + 
z 2 ' 
cP 
Q 
where, in the term in { }, the last four lines are 
= 18 (pp + &a? + tip) ® 
( x 2 y 2 Z 2 \ 
- 36 (â* + l + c*)- 
Hence, writing for shortness 
2¥ 
© = - 
ct 2 6 2 c s 
+ kv +p+?) p _ (S + 1 + ?) ~ 2PQ<