20 Choice in the Distribution of Ohservations 
(3) The determinant of the order jp. 
1 
1^ 
2q+l 
1 
2^+1 
1 
2?T3 
2^ + 2^9-3 
1 
2q + 2p-l 
2q+2p-3 2q + 2p-l 2(? + 4j9 - 5 
which includes the two types of the denominators in (23), shall first be evaluated. 
g I q 2^ 
We find , A = ~ and gA = -t^ =—,7^ ttitf^ , 
' 2q-l ' (2g - 1) (2g + 1)- (2? + 3) ' 
and it shall be j^roved that if 
„A = {f f-i . 2f-2 (p_2)^p-] )P . 2» 'f-i' . 
.(24) 
up to the order p, ^11 being the product of the elements of pA, the rule holds 
for determinants of any order. 
It is clear that 
Q (Z+S q q q 3 + 1 
j)+iAi,i = })A, p+iAjj+i, = j,A, p+i^i,p{— l)**"*"^ = 35 A 
q q+2 
^^^^ D+lAj,+l, 3,+l,l,l = J)-lA. 
If we therefore in the general relation for an orthosymmetrical determinant 
q 
put s = 1 and s' = + 1 and A = A, we find 
q 3+2 3+1 
1 A A — A^ 
114. i ^ — 
and, using (24), 
3+2 
q ^ (jj _ 2)2 (jO - 1)}^ 
P+l -{l2;-2 _2f-3 (^- 3)2(p- 2)}2 
9(p-l)(j)+2) » 
q 3+2 3+1 
n . „n - 
3+2 
3 
.n 
3+2 
Now, according to the definition of IT, 
= {2q - 1) {2q + 1)^ [2q + 3)^ {2q + ip - 3)^ (2q + ip 1) 
X {2q + 2p~ 1)2, 
3 3 
^+1^ j^+ill 
3+1^ 
= {2q - 1)2 (27 + 1)2 (2q + 3)2 {2q + ip - 3)2 (2g + 4jo - 1)^ 
,,+in2 
and 
3+2 
(2(? -1) (2</ + 1)2 {2q + 3)2 {2q + ip - 3)2 (2(? + ip - 1). 
