38 Choice in the Distribution of Observations 
Treating it as j,h was treated under (2) of this section, except that now two 
rows or columns are left unaltered, it takes the form 
1 
0 
0 
0 
1 
•2q-\ 
2 
2 
2 
(23-1) (2? + !) 
(2(? + l)(2g + 3) 
■" {2q + 2p 
-5) (23 + 2P-3) 
2 
2.4 
2.4 
2.4 
(2q-\)C2q + \) 
(23-l)(23 + l)(2g + 3) 
{2q + l)(2q + 3)(2q + 5) - 
{2q + 2p- 
5) ... (2q + 2p-l) 
2 
2.4 
2.4 
2.4 
(23 + 1) (2,? + 3) 
{■2q + \)(2q + Z)(2q + 5) 
{2q + S){2q + 5){2q + 7) 
■■ (2q + 2p- 
3) ... (2q + 2p + l) 
2 
2 . 4 
2.4 
2.4 
,2(? + 2;)-5)(2? + 2p-3) 
(2q + 2p-5) ... {2q + 2p-l) 
(23 + 2p-3) ... (2^ + 2^ + 1) 
{2q + 4:p - 
9) ... (2j + 4p-5) 
Hence we find from (38), 
Now from (43) and (45) we get 
2^%D ^ (p +I)j2q + 2p - 1) 
and therefore 
2i)(^,}= +a) I 2 j 
•(47), 
iV^ ^ ^|l + a(p+ 1)(250+ 1)^ H-a^9(2^+ 1) 
or 
s (1 + «) (2f + 1) {rr„ ,/riM2„ + 1) + 1 + ^2^+1) 1 ••■(«'■ 
In the same way we get from (39), 
1 2 
,,_,a-; = (1 + a) /-^^'^ + . 
^ ,8 .8 ^ 
'7 
which by the relation between ^Z) and p+^S just found is reduced to 
2^.-1^^;, - ]vr ^ "^1 + a^o (2^9 - 1) ^ 1 + a?) (2?) +1) 
Both (48) and (49) are covered by the formula 
.a, = ^ (1+ a) (., + 1) l^^:^^:^^^^^^ + 2 + a(., + l)(^ 2)} 
(7) The evaluation of „ct';; for special values of n can be made easier by a trans- 
formation of the determinant 
(1 + ^ ^^^^K. + ^^-^i-^ . . \ (49) 
