680]
ON THE HESSIAN OF A QUARTIC SURFACE.
275
and we thence have
]/•4 Tr.2/o#.2 Ti2^».2
bo -f* = ^ - - ftT (2Q + %») - ~(2« + 42/=) + 4Q a + 8 Q (y + z%
g h-af=lyz(^-2Q},
whence, forming the analogous quantities ca — g 2 , Sac., it is easy to obtain
abc — af 2 — bg 2 — ch 2 + 2yp/i
kfw 6
ct 2 b 2 c 2
c 2 « 2 a 2 b 2 ))
+ Av)l2< ? (I + 6 t + t)-8<2Pj
- 24 Q 3 ,
which is to be multiplied by d, = k 2 P. And
— [l 2 (be — / 2 ) + ra 2 (ca — g 2 ) + n 2 (ab — h 2 )
-i- 2 mn (gh - af) + 2 nl (hf- bg) + 2 Im (fg - ch)]
4 &®w/ 6 P
~ a 2 b 2 c 2
which is
— 4& 6 w 4
^ la. 4 u> 2 c 2 / 6 4 Vc 2 a 2 ) c 4 W 6 s
4y 2 V /1 1 \ 2 4ete* /1 IV 4Vy 2 /1 _ 1V
+ a 2 V6 2 c 8 / + T 2 Vc 2 a 2 ) + c 2 U 2 b 2 )
+ 4&%> 2
+ SQ\yv( 1 si - 1 f + ^{l l
I_IV)
a 2 b 2
4 k 8 w 6 P
d¥d f
+ W | 8 {w + cW + tfW PQ ~ SW ® + 16 ibv + cW + 5%=) p
+ ^ ! |_48(| + |I + i)<2 i + 32P a e}.
35—2
