1
-è -Ê
iiaa
-e i i
-Uiii
14
In the cofactors-tensor of the corrections as in the one in III,
B the following properties are found:
1) Symmetry about the main diagonal.
2) Symmetry about the second diagonal.
3) If the tensor is divided into four equal parts, following the
lines \n, \n 1, in every part separately symmetry exists about
both its diagonals.
4) The cofactors of two directions in a quadrilateral are equal
to those of two corresponding directions in another quadrilateral.
E.g. e®, el en, e® e16, e14 etc.
5) The cofactor of a direction in a quadrilateral, in combination
with a direction that is not directly connected with that quadri
lateral is zero.
By these properties the tensor of a chain of an arbitrary number
of quadrilaterals can be written in a closed figure. The tensor of
the corrected directions becomes as
I? It 1 if a 8, and l* lf= O if a i=- 8.
a 3 r' a 3 1
(Valid for both odd and even numbers of quadrilaterals.)
II
T 7 7
1 1- Itl IT»
in KN (M O 171 0
9 10 11 12 13 14 15 16
cccccacc
1
16
0
0
n-15
n
2
15
0 0
j 0 0
n-14
n-1
3
'14
000!
1 0 0 0
n-13
n-2
4
13
0000!
0 0 0 0
n-12
n-3
5
12
00000'
0 0 0 0 0
n-11
n-4
in-10
6
11
00000 jy
0
0
0
0
0
n-10
n-5
ln+11
■fin- 9
7
10
-2 +4 +2 +2 -2 0
CN«2 +2 -2 -2 -4+14
n-9
n-6
gn+10
fin- a
8
9
+14 -6 -4 -2 -2 +2<.2 0
0 +r^2 +2 +2 +4 -6 -2
n-8
n-7
hzt+ 9
9
8
34 +6 +4 +2+r-2+2 0
0 -2 +2^*2 -2 -4 +6 +2
n-7
n-8
fint 6
fin— 6
10
7
34 +4>z +2 -2+2 0
0-2+2 -2^2-4 +2
n-6
n-9
7
In- 5
11
6
+4 +4 -4+4 01
0-4+4-4 -4m
n-5
n-10
fit»- 6
fin- 4
12
5
+35 +5 -5 -1 +6
-6+13 -7 +7 +1
n-4
n-11
in* 5
fin- 3
15
4
+35+13 -7 -6
+6 -5 -1 +1
n-3
n-12
firn- 4
In- 2
14
3
+35 +7 +6
-6 +5 +1
n-2
n-13
fin+ 3
In- 1
15
2
+35 +6
-6+1
n-1
n-14
|n+ 2
fin
16
1
+36
+12
n
n-15
fn+ 1
8 7 6 5 4 3 2 1
r N <t KI «O t-
0
b
a
occcacaa
a
b
0
KN r
r (M m in
b
I
To write out the rows the rules are:
1) All factors between the dotted vertical lines are zero.
2) 9 9
Combine the numbering Ha with the left part of la until <p ip-
Then use Ila itself until 9 17 9 (the line PQ in the scheme
fig. 5). Afterwards combine with Ilia, IVa, and of la the right part.
