PROFESSOR CAYLEY ON CUBIC SURFACES. 
261 
(Jew) 4 = 2dbc xyz(l2t$> - Sf )+ W( - 30+12f) 
+U 2 (-20+4f)+2UY(-4£)+Y 2 
- 3 <6abc xyzV — 1 8UW + 7 2abc xyztU 
— 16U 3 
-108 aWatyV , 
(Jcw) z = 2afo^3O 2 -12f0)+W(12£0-8f) 
+ U 2 4tf O + 2UY( -20 + 4f ) + Y 2 ( - 4 1) 
- 18YW + 72 ahc xyztV + 36£UW- 36afo tfyzOU 
— 48U 2 V 
-108«fo^W, 
„ ( Jewf= 2abcxyz(-6t® 2 )+W(3&-12f<!>) 
+ U 2 0 2 +2UY(4^O)+Y 2 (-2O+4f) 
+ 36#YW- 36«5c xyz®Y- 180UW 
-48UY 2 
— 27W 2 , 
„ (£w)' = 2afo^(-0 3 )+W(-6£0) 2 
+ 2UY0 2 +Y 2 (4£O) 
-180YW 
— 16Y 3 , 
„ (*w)°= W(-0 3 ) 
+ V 2 0 2 ; 
but I have not carried the ultimate reduction further than in Schlafli, viz. I give only 
the terms in (lew) 7 , (Jew) 6 , (Jew) 5 , and (Jew) 0 . 
55. I present the result as follows ; the coefficients deducible from those which pre- 
cede, by mere cyclical permutations of the letters a, Jj, c and f, g, Ji, are indicated by („). 
)=(Jew) 7 .2abc xyz 
fz 2 
Z 2 X 2 
x 2 yz 
xy~z xyz 2 
-y(Jew) 6 . j a i bc+1 
” 
33 
abef — 1 4 
gebh + 4 
fz 2 
y 2 z 6 z 
; 3 ar z 2 x 3 
xhj 1 x~y 3 
xhyz xifz xyz 3 
a?bcg—6 
a 2 bch — 6 
ab : c‘ 3 — 6 
erbef —32 
33 
„ 
a'cfk + 2 
a?bfg+2 
abef 2 +42 
abrjfgh + 64 
b-cg 2 + 2 
abfg z -24 
bc-h 2 + 2 
acflr —24 
bcfgh —24 
af-gh + 8 
+ (to)».-K[(A, B, C, F, G, H I*, y, z )»]%»-2/y 2 +Jz»)(®*-2^+tf)(5 ;e >-2%+a/). 
