378 Distribution of Correlation Coefficient in Small Samples 
Something corresponding to the above process must be used for values of 
with n > 105, if we require the function correct to ten or twelve figures. The 
usual approximate formulae for the factorial, or for the F-function, do not converge 
rapidly enough and generally give the logarithm, so that they really involve the 
use of the logarithm tables to 14 places and the antilogarithm process. 
For values of 100 and upwards the following formida will be found good : 
For n even we deduce by Stirhng's Theorem from Eqn. (xcii) 
1-2533,1413,7315/, -25 -03125 -039,0625 -0102,5390,625N 
/, -25 -03125 -039,0625 -0102,5390,625\ 
1 + — + 2 
xcv 
in - /- 
V n 
For example, n = 100 
gi„o= 1-2533,1413,7315 x -1002,5031,64165, 
= -1256,4512,9017,89, 
which is correct to twelve places. 
For n odd we deduce by StirUng's Theorem from Eqn. (xcii) by somewhat 
more lengthy algebra precisely the same value. 
[Owing to the growth of this memoir far beyond its original limits, it has 
been found impossible to include in this first portion the experimental work 
which accompanied the algebraical investigations, nor to give illustrations of the 
various uses which the tables serve. These matters are therefore reserved for a 
continuation of this memoir, which will appear later.] 
