62 Generalised Probable Error in Multifile Normal Correlation 
Table of Generalised Probable Error's. 
Number of 
Variables 
Probable Error 
1 
0-674,4898 
2 
1 -177,4062 
3 
1-538,1667 
1-832,1239 
5 
2-086,0146 
6 
2-312,5982 
7 
2-519,0869 
8 
2-710,0022 
9 
2-888,3962 
10 
3-056,4366 
11 
3-215,7402 
The method of calculation was as follows 
equations on p. 61 : 
If n be even we have from the 
1 
V2 
•1994711. 
= •25, 
If n be odd : 
since I^jN = ^. 
The problem therefore resolves itself into an interpolation in the tables. Let 
y be the required argument of the table and x the corresponding value of ; 
let ajo, a?!, be the two values in the table immediately below x, and x^, x^ 
immediately above x ; then the formula 
I 'l{x-x^{x-x.^{x-x^ 
y = y2 + io - 
{x. 
— x{) (Xq 
^2) ("^0 
{x 
- «o) 
- 002) {x - 
{Xi 
^o) (^1 
X2) {Xj 
-X3) 
(x 
— Xi) (x - 
- X2) 1 
was used to find y, i.e. a cubical parabola was passed through the four points. The 
accuracy of a variety of other interpolation formulae was found to be less. 
Having found the values of the first eleven probable errors, an empirical 
formula was then sought which would closely express them, and which accordingly 
might be used for extrapolation. The form of curve finally adopted was that 
found by adding the ordinates of a line to that of a logarithmic curve. Its 
equation, after the adjustment of its constants by the method of least squares, was : 
p.E. = - -067,769 + •07l,986?i + 2^308,272 logio (-994,484 + n), 
giving the probable error in terms of the number of correlated variables n. 
Of course we must not expect such an arbitrary formula to be true to more 
than some four figures. As a matter of fact in fitting it only the values fi-om 3 to 
11 were taken. The following give the calculated and actual values: 
