322 
A THIRD MEMOIR ON SKEW SURFACES, OTHERWISE SCROLLS. [410 
equation contains the constant factor AF + BG + GH, so that throwing this out, the 
reduced equation will be only of the third degree in the coefficients. 
74. The transformation is a very troublesome one, but I will indicate the steps 
by which I succeeded in accomplishing it. Each of the functions (p, q, r) is a quadric 
function of (X, Y, Z, W), say, 
we have to form the value of 
(■H, F, C, B, A-F, -G$p, q, r) 2 , 
viz. representing this for shortness by 
d, / g, h, l, m, n 
the coefficient of X 4 is 
(II, F, G, B, A-F, -G\2af, 2af', 2a"/", af" + a"f, a'f+af", af' + af), 
and so on, the successive terms a 2 , a 2 , &c., 2a/, 2a/', &c. being derived by an obvious 
law from the first terms a 2 , 2af, &c.; and these first terms are merely the coefficients 
of the terms X 4 , X 3 , Y, &c. in the development of 
f, = {(a, 6, c, d, / g, h, l, m, n\X, Y, Z, W) 2 } 2 ; 
viz. this is 
a 2 2af 2ag 2al 2ab 2af 2am 2ac 2an 2ad 2bh 2bg 2bl 2ch 
+ h 2 + 2 gh + 2 hi +g 2 + 2 gl +l 2 + 2fh + 2 hm + 2fg 
XYZW, XYW\ XX, XZ-W, XZW 2 , XF 3 , F 4 , Y 3 Z, Y 3 W, F 2 X, Y-ZW, F 2 IF 2 , YZ 3 , 
2If 2dh 2eg 2cl 2dg 2dl, b 2 , 2bf, 2bm, 26c, 26n, 2bd, 2cf 
+ 2 mg + 2 Im + 2 gn + 2 In +/ 2 + 2fm + m 2 
+ 2 nh 
YZ 2 W, YZW 2 , YW 3 , Z\ Z 3 W, Z 2 W 2 , ZW 3 , F 4 
2cm + 2df 2dm, c 2 , 2cn, 
+ 2fn + 2mn 
2 cd, 2 dn, d 2 
+ n 2