AND LINES IN THE INTERSECTIONS OF A SYSTEM OF SURFACES. 225 
^ xxy - 
'U'xxy 
w 
v v xxy 
y 
v xxy 
w 
V 
U 
y 
u 
w 
+ two similar terms 
' 
U xx 
w 
y v XX 
y« 
Uxx 
by,. 
V* 
1 
+ < 
w. 
v y 
u. 
+ 
w 
V 
u 
> 
- 
y 
U 
w 
v. 
u. 
iv y 
- 
'U'xy 
W 
yv xy 
Y 
v xy 
'U'xy 
W , y 
Y 
¥ *y 
- 
+ 2 < 
by. 
v x 
u. 
+ 
w 
V 
u 
> 
y 
U 
tv 
V. 
u. 
w x 
- 
-4- two similar terms 
> + two similar terms 
u y Wj y y 
u x by x y 2 
Mi’ by , y a; 
+ 2 
W, v* U, 
+ 2 
Wy Vy XJ y 
+ 2 
by, v x u. 
y , U x W, 
y, bT, tV x 
~V y bJ y Wy 
(151). 
u 
&xyz — 
xys 
w 
y 
w 
xyz 
V 
u 
v 
* xyz 
u 
w 
+ two similar terms 
+ 
+ 
+ 
+ 
Uy 
Uy 
W, 
yy 
U z 
by, 
y 2 
by. 
v x 
u. 
+ 
bv 2 
u. 
+ 
by. 
u. 
y 2 
U 2 
tv. 
V, 
u. 
w. 
Uy 
Wy 
by. 
V, 
i \i x 
by. 
y. 
by. 
V, 
Uy 
+ 
bly 
+ 
by. 
u 2 
y. 
u. 
w x 
y. 
u. 
w 2 
yy 
Uy 
Wy 
U X y 
by 
YV X y 
Y 
v xy 
'V'xy 
by, y 
Y 
v xy 
u z 
by. 
y. 
W 2 
v z 
u. 
+ 
by 
V 
u 
+ 
W ay 
V xy 
Uay 
y 
U 
w 
y 2 
U 2 
w z 
y 
u 
W 
u 
bV 
y 
u z 
w z 
y 2 
u 
bV 
y 
if 
■S 
V xy 
u„. 
+ 
by 
V 
u 
+ 
W; 
U, 
v. 
u. 
tv, 
Y 
* ay 
U*y 
Way 
Y 
v xy 
Uay 
tV x y 
4 - six determinants, w ? hich can be obtained from the last six by interchanging 
x and z 
+ six determinants, which can be obtained from the same six determinants 
by interchanging y and 2 ............. (152). 
mdcccxcii.—a. 2 a 
