324 
A THIRD MEMOIR ON SKEW SURFACES, OTHERWISE SCROLLS. 
[410 
+ XY 3 
-2 FGH 
+ XY 2 Z 
AFH - BGH - 3F 2 H + 2FG 2 
+ XY 2 W 
2ABH - 2AFG - BFH + 2GGH + ( SF 2 G 
+ XYZ 2 - 
-AFG- 2BFH + BG 2 - GGH 
+ XYZW 
A 2 F- 3AF 2 -SABG + AGH- 2B 2 H + BFG + 5GFH- 2GG 2 
+ XYW 2 
2A 2 B - SABF+ 2AGG + B 2 G + BGH - 6GFG 
+ XZ 3 
AF 2 - 2CFH + GG 2 — F 3 
+ XZ 2 W 
2 ABF -2 AGG- 2 BGH - 3 BF 2 + GFG 
+ XZW 2 
A 2 G + AB 2 + 3ACF — 3B 2 F + BGG - 2G 2 H 
+ XW 3 
SABG-B 3 + SG 2 G 
+ F 4 
F 2 H 
+ Y S Z 
BFH - F 2 G 
+ F 3 If 
AF 2 + B 2 H - 2GFH - F 3 
+ Y 2 Z 2 - 
-BFG+GFH + F 3 
+ Y 2 ZW 
ABF—B?G + BGH + 2GFG 
+ Y 2 W 2 
AB 2 -2AGF - R-F + G 2 H + 3GF 2 
+ YZ 3 
BF 2 — GFG 
+ YZ 2 W 
ACF+ 2B 2 F- BGG - 3GF 
+ YZW 2 
ABC + B 3 — 2BGF — G 2 G 
+ YW 3 
AC 2 + RC — SC 2 F 
+ Z i 
GF 2 
+ Z 3 W 
2 BCF 
+ Z 2 W 2 
B 2 C+2G 2 F 
+ ZW 3 
2 BG 2 
+ If 4 
c\ 
where, in regard to the symmetry of this equation, it is to be observed that we may 
interchange X and W, and Y and Z, leaving A, F unaltered but interchanging B 
and — G, and also G and H; thus the coefficient of X 3 Z being AH 2 — 3FH 2 + G 2 H, 
that of YW 3 is AG 2 — SFC 2 + B 2 G, = AC 2 + B 2 C — SG 2 F. Or, again, the coefficient of Y 3 Z 
being BFH - F 2 G, that of YZ 3 is -GFG + F 2 B, = BF 2 - CFG. 
77. But the equation may be written in the much more simple form 
X (- a 2 8 + 3a/3 7 - 2/3 3 ) (Rec. III.) 
+ F (—• a/38 + 2a 7 2 — /3 2 7 ) 
4- Z ( a 7 8 — 2/3 2 8 -f /3 7 2 ) 
+ W ( a8 2 — 3/3 7 8 + 2 7 3 ) = 0,