24 
Choice in the Distribution of Oh sen-nations 
V+\^S, 2)+l J)ns_^, J, . 
a+2 G^,c, 
and v+i^ii = j)n.9_i, s-i • ^ * J 
q q p-i 
n - rr 
31+1. P+1 • '^h 3)+l 
5+1 
rr _ n "^s^^j)+i 
J)+l^^ll — J>lll,s-1- p p 
Substituting; the Il's found from these relations into (30) and eliminating the 
Q 
jj+llls, 35+1 
one factor »'±iHfi^i bv 
Q 
we get ^ 
3)+lIIll 
( 
■^I ^S, ?)+l 
^J)+l ^1,1 
1 
1 
^1, s 
•^1, J) + l ^1. 1 • 
^S. J) + l 
1 1 
^S, J) + l ^.9S • + P + l 
"^11 : : p+i^^i, 1 
3J+l^ll 
or introducing the values of the e's 
q 
Q 
31+1^1, 1 
{2q + 2s-3){2q + 2p~l)-{2q-l)(2q + 2p + 2s-3) 
q 
Pp-i.s-2 ' {2q + 2p + 2s-3)^-i2q + ^s~5)i2q + ^p-l) f. 
7 
^s. 3)+] 
1 
1 
Now 
Q r/ + 2 <? 
Ai, 1 = , A = {1^-1 . 2^-2 {p-2)' {p - 1)}2 . 2^ <^-i> n^, 1 , 
and hence 
p+iLp+i = (- 1)'+^+^ ,-i{l^-^ . S''-^ {p-2)^ ip - 2^<''-i' ,+in.,,+i 
in agreement with (25). 
(7) It now remains to prove that (25) holds for p+iAg^^ when both s and r 
are different from 1 and p+1, and r different from s. 
For this shall be used the relation 
between an orthosymmetrical determinant and its minors. 
Putting A = p+iA, s = p + I, s' = r and s" = s and solving the equation with 
regard to p+iA,. we have 
3)+1^7)-l 1, ?i 1-1 
where p+i^p+i, 39+1, r, s ~ s- 
