KiRSTiNB Smith 
5 
In particular is found from 
"» 
2 
G 
0 
0 
0 
... 1 . 
.. 0 
0 
mo 
.. . 
.. w„ 
0 
m. 
0 
mg 
W3 
OT4 . 
• Winn. '2 
1 
.. .. 
0 
TO„_^2 • 
• ^D+n •• 
• W2tt 
= 0 
•(8), 
(4) Let us call a determinant, identical Avith that of (6) except that it has 0 
iV 
instead of the element 6' . , , A, let A,. ^ be its minor not containing the rth row 
and 5th column, again let A^,,, j,, a be the minor of this not containing the ^)th 
row and the gth column of A. We then find from (8) 
CT^ A 
* l)+2. l)+2, 1. 1 
^ ' A,,, 
With this notation we obtain from (6) 
.(10). 
In the following we shall drop the index r and indicate by „ay the standard 
deviation of a ^/ adjusted by means of a function of the nth degree. 
If we were dealing with a function of {n — l)st degree and retained the observa- 
tions distributed as before we should find 
.2 / A 
and therefore 
J _ ■> A^ ^ ^ ■ ^n+t,n+2 A ■ An _)_2, n+2, 1 , 1 
«ct;, „_iO-; — • A A " ' 
^1, 1 • ^«+2. n+2, 1, 1 
but A is orthosymmetrical and therefore the numerator of this fraction equals 
A^+2,i,and 
^' Ai,i. A„+,, 
n+-i. 1, 1 
It was shown before that 
0-2 A 
^2 ^ n+2, 1, 1 
Ai,i 
hence A^^^ and A„+2,n+2,i, i bave the same sign, and „ct^, — „_icr;, is therefore a square 
of a function of x. In the same way we can express n-\^\ — n-a"'^ ^^^^ thus further 
0-2 1 
down all the differences till ^ ^-^ ■ by which means „ct'; is developed in a sum 
of squares and takes the shape 
