AND LINES IN THE INTERSECTIONS OF A SYSTEM OF SURFACES. 257 
The fourth and sixth determinants are 
Uy 
w 
vv .y 
y 
v y 
u x 
w. 
v. 
w. 
v x 
u, 1 + 
W 
u 
U, 
Y 
u 
w 
V 
u 
w 
UV 
WY, + VW, - llXJy 
UW, 
UV, 
YW, 
u,w + UW, - 
” YgV YU, 
V 
— u 
u 
- w 
u 
— Y 
u 
+ UV 
WV, + VW, - ttU, 
UW, 
UY, 
YVY, 
U,W + UW, - 
-V,u VU, 
V 
— u 
it 
-w 
XL 
- V 
u 
U u 
WV, + YW, UW y + WU, UV, + vu, 
VW, U,W + UW, - Y.V YU, 
u W V 
+ 
XJu 
WY, + VW, UW, + WU, 
UV, + YU, 
YW„ 
u 
U,W + UW, - Y y v YU, 
W V 
Hence the coefficient of U, is 
JL 
U a 
0 
w 
V 
wv,+vw, u\v.+" 
vw* 
u,w+uw,- 
Y,« YU, 
4- 
i 
Uw 
0 
W 
u 
w 
V 
XX 
w 
1 
w 
Y 
1 
UW, UV, | 
~ ^ 
UW, - V*t> 
0 
+ TT 
W V 
V 
Y 
I 
f (VvV. - VUW, + UVW, - UWV,) = 0. 
L 
MDCCCXCII. — A. 
9 
