A. Ritchie-Scott 
107 
being determined so that the probable error of the mean r so found shall be a 
minimum. 
Let 
r = 
.(62). 
C\i + C'i2 + • . . 
Then (6'i, + 6',2 + ...) dr = C'lA^ + C^Jti,^ + (63). 
Squaring, summing for all possible values and dividing by the number of 
samples, 
where 
Let 
s = s (C',,a,,)2 + 2E (C',,r;,,c7,,cT,,i?,,,.,), 
c = S iC,,). 
Then for a minimum 
3*S' 9*,S ,,, _ 
dS = rfC'i, + r/C'i2 + ... = 0, 
dC = r?6'n 
ds 
dC\, 
+ ... = 0. 
= ... = 0. 
GuCFll' + '^'l20-nO'lii-Sll,12 + C'lgCTiiCTisi?!!,!;, + ... A. 
CllO"llO'l2^n,12 + t'*120"l2''^ + t'i:jCTi.,CTj:3i?,2, J3 + ... = A 
.(64), 
•(65). 
Let 
Then 
A = 
1 
1 
1 
1 
0^13 
1 
1 
^11. 1? 
-^11, 13 
1 
0'12 
-^11, 12 
1 
■^12,13 
1 
0-13 
-^11, 13 
^12, 13 
] 
'^'^0011 
^0000 
_ •^^0012 
^0000 
may put S 
(a,) 1, 
A (A, 
A. 
0000 
1 
A (A - A, 
cr,, CT,, 
■0000; 
A, 
0000 
.-. A = - 
A- An 
.(66). 
.(67). 
.(68), 
.(69). 
