118 
PROFESSOR CAYLEY ON SKEW SURFACES, OTHERWISE SCROLLS. 
70. Writing for shortness 
( H, -G, A£X, Y,Z, W)=a, 
(-H, F,BX „ )=/3, 
( G, -F, . , CX „ )=y, 
(—A, — B, — C, . X „ )=&, 
and therefore 
aX+j3Y+yZ + 5W=0: 
the two equations are 
? 2 Xy+£(-yY-/3X)-SW=0, 
g> 3 X- ? Y+^Z-W =0. 
Writing the first equation in the form 
y( f 2 X- f Y+Z)— /3( ? X— Y)+«X=0, 
mutiplying by — g, and reducing by the other equation, 
j3(g 2 X-fY) - gaX — yW=0, 
or, as this may be written, 
j3(g 2 X — gY-f-Z) — a(gX — Y) — aY — j3Z — yW=0. 
From this and the preceding equation we deduce the values of f 2 X— gY+Z and gX— Y 
viz. writing for shortness 
/&— P y—c3, ay— /3 2 =p, q, r, 
we find 
f *X- f Y + Z : fX-Y : l = -rZ+qW : rY-pW : -r, 
or, what is the same thing, 
fX-gY+Z= Z-^W, 
fX-Y =-Y+2W; 
whence also 
g 3 X-g 2 Y + ? Z-W= 0, 
8 ’X- g Y =->, 
§x = £w, 
and thence 
s (z-iw)= w, 
g (Y-Evv)=3w, 
* X =|W, 
