22 Clioice in the Dist7^ihution of Observations 
a 3+1 
A = (■— A 
8 3+1 
A —I— T^P+i A 
so that all the determinants on the right side in (27) can be evaluated by (25). 
They all have the factor 
{lP-2 _ {p- 3)2 {p - 2)}2 . 2"^-!' 'p-^' 
in common, when that is divided out there remains 
q ^ ^ 3+2 '/ 3+1 
3 ~ 3+1 3+1 3+1 3+1 ^ 
2)4-1 "^1,3) + ! /^J)-l,S--2 • ^j)-l,s-l (3)^3-1,1 • !p^j>,s p^p,l • D^s-I.s) 
Now indicating by the product of the elements of the rth column or rth 
g Q 
row in and by e,., the element of the j,+iA common for the rth row and sth 
column we find 3^ 3+2 (72 
^ "eii-e^i' 
3 
3+2 
3 
3 
n„ 
? 3) n 
3 
3+1 
? 3) n 9. 
'3)+l> 3)+l • ^JJ+l, S 
^1, J)+l ■ ^s, 1 • ^S, 3)+l 
Hence the factor of the numerator in (28) is reduced to 
yii ^s,l^Jls, 3)+l f X 
For the IT's of the denominator we find 
5+1 (7, (7 
rr —17 ri 
3)+l^^l, 3)+l ^ 3)^'s-l,l • 
^sl • ^S, 3)+l • ^1, 1 
TT = TT ^3)+l • '^ f 
111. 3)+l 35' 1 J), 5 • 
"s, 3)+l • ^3)+l, 3)+! • 5 
3 
3)+! rii, — s)!!,,^^ 
1, 3)-t-l • ^11 •^2)+l, 3)+l 
3 3+1 r*-' 
TT — TT ' 
2)+l '^1. J)+l ~ 3)'^.<-l. «• 
TT- '^^ ' ^+i"'' I'J • g+i _ p \ 
3)+l -"^1. 3)+l /-)2 I'^ls • *^3)+l. S "^l, 3)+! • "^ss/- 
^SS • ^61 • ^S, 3)+l 
the factor containing Il's of the denominator of (28) is therefore equal to 
Introducing these two expressions in (28) and substituting for the one factor 
3 
Jt+^l^ the value ^^^^^ . ^ we hence find 
n ^1, 3)+i 
3)+l 3)+l 1 1 
9 _ 3 
3)+! _ / o ^r. 3)+i • ^3)+]. 3)+i 3)+i riss 
~ ( 1)''^2)-1. s-2^3)-l.s-l 
^SS- ^1,31+1 ^l,S-^3)+],S 
g \ rp-l. s-2r2)-l.s-l -I 1 ■ 3 
A n 
31+1 '-^l. 3)+l « ^ „ „ 3)+l ^^1, S)+l 
