3(3 Choice in the Distribution of Ohseroations 
(3) It shall be proved by induction that 
{ 1" ■ 2/^-1 ...{p-'^f-V ■ '2"l"-2) (p + 1) 
'(•2<l~l) (2q + ly^ [2q + . . . {^q + 'Ip - o)""! (2(/ + 2^ 3)"(2j + 2p - ly (2q + -Ap + 1)"(2(/ + -Ip + 5)'-^ .. . {^q + -kp - '6f{2q + ip - 1) 
(13). 
It contains the 2p+ I different factors of the elements with indices increasing 
from 1 at the extreme to p in the middle so that the three factors of which the one 
diagonal line of the determinant consists occur with the index p. 
For p = 1 the formula gives 
{■2q-l){2q+l){2q+3) 
as it ought to. 
As the determinant is orthosymmetrical the relation 
A 
holds. 
Applied on p+iD for s = 1 and s' = p + 1 it may be written 
3 (Z+2 g+1 
.(44). 
Looking first at the numerator of (43) we see that it has the same value for the 
two terms of the numerator of (44), and divided by the corresponding factor of 
3+2 
j,-iD it becomes 
l"'.2^^''~" .{p--2)Hp-l)^ p^] ip+l)^ ,,_3, ■ 
If-i . 2^-2 (p-2)^p-l) i p 
= {l"-^' .2" {p- 2)* {p - ir p' {p + 2»'-^ 
q 
To evaluate the factor in p+iD arising from the denominator of (43) we shall 
give a table of the indices with which the different factors occur in the D's and 
their ratios. 
+ u 
7+1 
p-iD 
q-12g+l 2q+-S . 
'2q+?p- 
1 2(?+2yj+l 2g+2p+3 2-2+2p+5 
23+233+7 . 
.. 2g+4p- 
1 2q+ip+l 2g+4p+3 
1 2 
3 .. 
. p-1 
P 
V 
p 
p-^ 
p-2 
p-3 . 
1 
1 . 
. p - 3 
p-2 
p - 1 
P 
V 
P 
p-1 . 
3 
2 1 
] . 
p-2 
P- 1 
P- 1 
p-\ 
p-2 
p-3 . 
1 
4 . 
■ 2 ip - 2) 
2 0.-1) 
•^P 
■2p 
2p 
2{p- 1) 
2{p-2) . 
4 
2 — 
1 2 
3 .. 
. i;- 1 
P 
P 
p+l 
P 
P 
p-1 . 
3 
2 1 
— 2 
3 .. 
. p-l 
P 
p+l 
p+\ 
p+l 
P 
P-1- ■ 
3 
2 — 
