412] 
A MEMOIR ON CUBIC SURFACES. 
389 
(Jew)* = 2abc xyz (12£4) — 8t 3 ) + W (— 3$ + 12£ 2 ) 
+ U 2 (- 24> + 4i 2 ) + 2 UV (— 4£) + V s 
— 36abc xyz F — 18 UW + 72abc xyztU 
— 16 U 3 
— 108a 2 6 2 c 2 x 2 y 2 z 2 , 
(Jew) 3 = 2abc xyz (34> 2 — 12i 2 4>) + W (12i4> — 8£ 3 ) 
+ lMt<& + 2 UV(- 24> + 4i 2 ) + F 2 (- 4i) 
— 18FTF + 72abcxyztV + 36£f7TF — 3 Gabc xyz<t>U 
-48 U 2 V 
— lOSa&CirysTF, 
„ (Jew) 2 = ‘¿abc xyz (— 6£4> 2 ) + W (34> 2 — 12¿ 2 4)) 
4- Z7 2 4) 2 + 2 £7F (4i4>) + V 2 (- 24) + 4£ 2 ) 
+ 36iFTF — 3 6abc xyz&V —184) UW 
-48 UV 2 
-27 W 2 , 
„ (Jew) 1 = 2a6c xyz (— 4> 3 ) + IF (— 6i4)) 2 
+ 2t7F4> 2 + F 2 (4i4)) 
-18 4>FF 
— 16 F 3 , 
„ (&w)° = TF (— 4> 3 ) 
4_ F 2 4) 2 ; 
but I have not carried the ultimate reduction further than in Schlafli, viz. I give 
only the terms in (Jew) 7 , (Jew) 6 , {Jew) 5 , and (Jew)°. 
55. I present the result as follows ; the coefficients deducible from those which 
precede, by mere cyclical permutations of the letters a, b, c and f, g, h, are indicated 
b y (»)• 
0 = (Jew) 7 .2abc xyz 
+ (Jew) 6 
y 2 z 2 
Z 2 0X 
X 2 y 2 
x 2 yz 
xy 2 z 
xyz 2 
a 2 bc + 1 
55 
55 
abcf — 14 
gebh + 4 
55 
55 
y 3 z 2 y 2 z 3 z 3 x 2 z 2 a? a?y 2 x 2 y 3 x 3 yz xy 3 z xyz 1 xy 2 z 2 xhyz 2 x?y 2 z 
+ (Jew) 5 
a 2 bcg — 6 
a 2 cfh+ 2 
a 2 bch — 6 
a?bfg + 2 
ab 2 c 2 - 6 
abcf 2 + 42 
b 2 cg 2 + 2 
bc 2 h 2 + 2 
bcfgh — 24 
a 2 bcf - 32 
abcfgh +64 
abfg 2 — 24 
acfh 2 — 24 
a/ 2 gh + 8 
+ (Jew) 0 . — K [(^4, B, C, F, G, H][x, y, zf\ 2 (cy 2 — 2fyz + bz 2 ) (az 2 - 2gzx + bx 2 ) (bx 2 —2Jixy + ay 2 ).