640 
MR. A, CAYLEY’S THIRD MEMOIR UPON QUANTICS. 
No. 58. 
The first derived functions (omitting the factor 3) are — 
(a, Jc, g, /, j, hXx, y, zf 
(h, b, i, /, I, hXx, y, zf 
U, / c, i, g, I Xx, y, zf. 
The second derived functions (omitting the factor 6) are — 
(a, 
h, 
ih 
b, 
/I 
h 
cjx, 
y^ 
2) 
a 
/ 
iXoo, 
y^ 
Z) 
1, 
y^ 
{h, 
IJx, 
y^ 
No. 59. 
The operators which reduce a covariant to zero are — 
( 3^ 
3/, 
C, 
2i, 
g’ 
2/IB„ 
B/, 
B^, 
Ba)- 
■yB^ 
( 
k, 
3^, 
21, 
2i, 
hX'^j, 
Be, 
B., 
B„ 
B.)- 
■zd^ 
(3A, 
b, 
h 
/ 
21, 
2k X^ a, 
B., 
B,, 
Ba)- 
-x'd^j 
( b, 
b, 
3i, 
2/ 
21, 
kx^j, 
Be, 
B„ 
B„ 
B.)- 
-z^. 
f. 
c, 
i, 
2^, 
21X'^., 
B„ 
B., 
B,, 
Ba)- 
-x'b. 
( a, 
3k, 
g^ 
21, 
2hXA, 
B„ 
B„ 
B„ 
Ba)- 
-i/B.. 
No, 60. 
The evector i 
is 
b, 
!> 
Bft, 
B/’II, Jj, 
No. 61. 
The Hessian is HU= 
(a, 
h, 
y^ 
z), 
{h, 
k, 
iXx, 
y^ 
0 '^ 
/, 
3/, 
(h. 
k, 
IX^, 
3 /, 
z), 
(k, 
b, 
y^ 
2), 
(/, 
/ 
iXx, 
y. 
1, 
gl^, 
y^ 
z), 
{1, 
/, 
iXx, 
y^ 
(^r, 
y^ 
