320 
A THIRD MEMOIR ON SKEW SURFACES, OTHERWISE SCROLLS. 
[410 
From this and the preceding equation we deduce the values of p*X — pY 4- Z and 
pX — Y; viz. writing for shortness 
we find 
/38-7 2 , /3ry-a8, ay — /3- = p, q, r, 
p^X-pY + Z : pX-Y : l=-rZ+qW : rF-pF : -r, 
or, what is the same thing, 
Avhence also 
and thence 
= Z 
F, 
p n -X- P Y+Z 
L 
P X - Y =- F+P F; 
r 
p s X — p-Y + pZ — F= 0, 
P 2 X — pY 
= - - F, 
r 
pX 
p(z-^w 
w) 
a X 
= E TV, 
r 
= w, 
r 
= - F, 
F 
= ) Z-^ W = -l Y— - W) = -X, 
p 
and we have therefore 
or omitting the first equation, we have (independent of p) a system which it is clear 
must be equivalent to a single equation. 
71. I take any one of these equations, for instance the equation 
or, what is the same thing, 
qrZ — r 2 F + (pr — q 2 ) F = 0, 
and I proceed to reduce it so as to obtain the result in a symmetrical form. For 
this purpose I observe that from the values of a, ¡3, y, 8. if only AF + BG + CH not = 0, 
we have 
F = ( 
• } 
-G, 
B, 
-F^a, 
ß, % S) 
:( 
c, 
• ) 
-A, 
-GK 
„ ) 
:(- 
B, 
A, 
• } 
-hi 
„ ) 
: ( 
F, 
G, 
H, 
-I 
„ )