44 
ME. W. SPOTTISWOODE ON THE CONTACT OF CUEVES. 
whence 
also 
h: a\ h : G 
^2 
2yz 
2zx 
2xy 
2Byz 
2Bzx 
2'Dxy 
(19-) 
DV 
2B^yz 
2Jy^zx 
2Jy‘xy ; 
Tyyz= 
^ dy dz 
+3,D^-^D 
dz ’ 
T>zx = X Wzx —■ xT> 
J)xy = -x^ J)‘^xy=-x'D^- 
Moreover the minors formed from the first two rows of the matrix, and from the 
columns below written, have the following values : — 
whence, finally. 
, 2yz=x^ 
BU] 
y2 
, 2zx=x^ 
1 
1 
. BU] 
J.2 
, 2xy=x\^ 
f BU 
[ 
1 
1 
(N 
1 
1 
2zx, 2xy = 2(f^^^ 
2xy, 2yz=2xy^'~, 
2yz^ 2zx=2xz^'^^; 
h : a \ h : G 
2xyz 
H 
dx dy dz ' (ra— 1)^ 
1) 
{n — 1)® 
where H is the Hessian of U. 
( 20 .) 
