mm
12
144]
A THIRD MEMOIR UPON QUANTICS.
No. 49 A.
319
ag +
1
ah +
6
ai +
15
aj
+ 20
Qjfa/ -f-
15
al
+
6
am
+
1
V-
6
bg -
30
bh -
54
bi
- 30
bj +
30
bk
54
bl
+
30
ce +
15
<f +
54
eg +
24
ch
- 150
ci —
270
cj
—
150
ck
+
24
d 2 -
10
de —
30
df +
150
dg
+ 430
dh +
270
di
—
270
dj
—
430
e 2 -
135
e f
-270
eg +
495
eh
+
1080
ei
+
495
P~
540
fg
—
720
/A
+
720
9 2
—
840
±16
±60
±189
±450
±810 ±1140
±1270
bin + 6
cl + 54
dk - 150
ej — 270
fi +1080
gh - 720
cm + 15
dl + 30
ek -270
fj. +270
gi + 495
Id — 540
dm + 20
el - 30
fk -150
aj + 430
hi -270
em + 15
fl - 54
gk + 24
hj +150
i 2 - 135
fm + 6
gl -30
hk +54
ÿ - 30
gm + 1
'hi - 6
ik +15
/ -10
±1140
±810
±450
±189
±60
±16
5*’ vT-
No. 50.
agm
+
1
cfl
_
54
did
+
270
ahl
—
6
cgk
+
24
eVc
—
135
aik
+
15
chj
+
150
fj
+
270
af
—
10
ci 2
-
135
egi
+
495
bfm
—
6
d 2 m
—
10
eld
—
540
bgl
+
30
del
+
30
Pi
—
540
bhlc
-
54
dfk
+
150
fgh
+
720
bij
+
30
dyj
-
430
f
-
280
cem
+
15
± 2200
Resuming now the general subject,-
54. The simplest covariant of a system of quantics of the form
(*$>, y, ...) m
(where the number of quantics is equal to the number of the facients of each
quantic) is the functional determinant or Jacobian, viz. the determinant formed with
the differential coefficients or derived functions of the quantics with respect to the
several facients.
55. In the particular case in which the quantics are the differential coefficients or
derived functions of a single quantic, we have a corresponding covariant of the single
quantic, which covariant is termed the Hessian ; in other words, the Hessian is the
determinant formed with the second differential coefficients or derived functions of the
quantic with respect to the several facients.
56. The expression, an adjoint linear form, is used to denote a linear function
£x + yy + ..., or in the notation of quantics (f, 77,...}£#, y,...), hav'ng the same facients as
