f 
324 
A THIRD MEMOIR UPON QUANTICS. 
The second derived functions (omitting the factor 6) are 
(a, 
h, 
3 
y> 
z), 
(k, 
b, 
f! x > 
y> 
z), 
(ff> 
i> 
c §x, 
y, 
z), 
(l, 
f> 
i Jx, 
y> 
z), 
(j> 
l, 
ffl x > 
y> 
Z), 
(h, 
k, 
l fx, 
y> 
z). 
No. 59. 
The operators which 
reduce a 
co variant to zero 
are 
( j> 
3/, 
c, 
2 i, 
g> 
2l'$dj l , db, 
dì, 
3/, 
di, 
dk) — 
ydz, 
( a, 
k, 
3g, 
21, 
2h 
m, d f , 
d c , 
di, 
dg, 
di) — 
zd z , 
(3 h, 
b, 
i, 
f 
21, 
2k'§d a , d k , 
dg, 
di, 
dj, 
d h )~ 
xd y , 
( h, 
b, 
3 i, 
2/, 
21, 
kjdj, d f , 
d c , 
di, 
3g, 
di )- 
zdy, 
(3j, 
/> 
c, 
i, 
2g, 
21 $d a, d k , 
dg, 
di, 
dj, 
d h )~ 
xd z , 
( a, 
3k, 
g> 
2l, 
j ’ 
21i$d h , d b , 
di, 
3/, 
di, 
d k )~ 
ydx• 
No. 60. 
The evector is 
(3 
a, 3j 
, do df, 
3g, 
3/i j dì, dj 
dk, 
«?. 
V, ?)*• 
No. 61. 
Hessian is HU 
= 
- 
(a, h, 
jjf> 
y> 
z), 
(h, 
k, 1 \x, y, 
z), 
(j> 
l, 
gl x 
y> 
(h, k, 
IJx, 
y> 
z)> 
(k, 
b, fjx, y, 
z), 
(l> 
f> 
ijcc 
y> 
(j, h 
gfa> 
y> 
z), 
(l, 
f y> 
z), 
(g> 
i, 
c\x 
y> 
which is equal to 
z) 
*) 
z) 
f 
agk — 1 
òhi - 1 
cij - 1 
beh — 1 
acf - 1 
abg — 1 
bcj - 1 
ach — 1 
obi — 1 
abc — 1 
aP + 1 
bP +1 
cP +1 
bgl + 2 
ai 2 +1 
afl + 2 
bf +1 
afg -1 
«/ 2 + 1 
afi + 1 
gip + 1 
f 2 h + 1 
fg 2 +i 
bij -1 
chi + 2 
aik — 1 
cfh - 1 
ail + 2 
bgh-ì 
bgj + 1 
hjl -2 
fkl - 2 
fkl -2 
ck 2 + 1 
cjk — 1 
bf +1 
ckl +2 
eh? +1 
bjl +2 
chk + 1 
j 2 k + 1 
ih? +1 
Pj + 1 
f 2 j + 1 
fgj +i 
fhj -2 
Ai +1 
ff +1 
fjk -2 
fgk - 3 
i 
fgk -2 
g 2 k + 1 
ghk + 1 
gik - 2 
gjk + 1 
glP + 1 
fjl +2 
{ 
/hi +1 
g hi — 2 
m +i 
hi 2 +1 
hij — 2 
hki + 1 
gkl + 2 
fp -1 
gP -1 
hP -i 
iP -1 
jP -1 
kP -1 
hil + 2 
ijk — 3 
P - 2 
■ J 
±3 ±3 ±5 
±5 ±5 
±5 
±5 ±5 ±9