376 Distribution of Correlation Coefficient in Small Samples 
and Degen gives the logarithms of the factorials up to 1200 ! to eighteen mantissa 
figures, there is no difficulty in getting the logarithms of the g'„'s to 18 figures. 
77 77 
All we need is the value of either log - or - to an adequate number of places*. 
But for modern methods of machine calculation the logarithm is of small service 
and we need in this case to find also the antilogarithm. Let us illustrate the 
process in the determination of q^^^ : 
log = 104 log 2 \= 31-307119,549054,044280 
+ 2 log (52 !) I + 135-813296,784409,541764 
- log 104 - 2-017033,339298,780355 
-log (104!) J - 166-012795,764264,301069 
= 1-090587,229,900,504,620. 
Thus far the work is very straightforward. But to obtain the antilogarithm 
to twelve figures is another matter. Tables like the original Vega (to 10 figures) 
or Mendizabel (to 8 figures) are not of service. We are thus compelled to use 
Briggs's 14 figure Table of Logarithms, but the fundamental defect of that magnifi- 
cent piece of work is the largeness of the differences. The nearest logarithm to 
the above is log (-12319) = 1-090575,455222,21 with the remainder 
r = -000011,774678,29, 
and the difference -000035,252606,20. Mere hnear interpolation gives 
•1231,9334,0087,32, 
which is wrong in the tenth figure. 
We have therefore used the method of inverse interpolation given in the 
Tables for Statisticians •\ as (vii)'^'® on p. xiv. Unfortunately there are two 
misprints in the value given there (corrected in the Errata) ; it should run 
6^ J (— — Ml + + u^) + d I (5tti — 3^0 — — Mj) + Uq — (d) = 0 
(xciv). 
But from Briggs's tables, 
= -0905,4019,9754,24, 
Uo = -0905,7545,5222,21, 
M+i = -0906,1070,7828,41, 
= -0906,4595,7573,32, 
whence 
•0001,4101,614786 d = -0000,4709,8713,16 + 6^ x -0000,00005723,06, 
•4709,8713,16 -00 00,5723,06 
~ r4Tor,6147,86 + " 1-4101,6147,86 " 
* ^= 1-570796,326794,8966; log | = •196119,877030,1527. 
f Cambridge University Press, 1914. 
