TABLES OF THE F-FUNCTION. 
The following tables have been prepared by Mr J. H. Duffel 1, Associate of the 
Institute of Actuaries, from the standard tables in Legend re's Traite des Foiictions 
Mliptiques, Paris, 1825 — 8. Those tables give the values of the log F-functions to 
12 places of decimals. The present tables provide the values of logr(p) from 
j)=l'000 to 2-000 proceeding by differences of "001, and recording seven figures. 
The tabled first differences are the differences of the recorded values, and not the 
nearest value to 7 figures of the differences of Legendre's tabled values*. It is 
very usual for biometricians to work with tables of 7 figure logarithms, and the 
need of a table of logr(p) to 7 figures has been long experienced. The original 
Legendre's table is in a scarce and expensive work and goes to more figures than 
are required in biometric practice. A number of six-figure V (p) function tables 
have been issued, notably the clear table of Mr W. Palin Elderton (Frequency 
Curves and Correlation, C. and E. Layton, 1906). But in view of the forthcoming 
issue by Biometrika of " Tables for Statisticians, and Biometricians," it seemed 
desirable to have stereotyped plates of the log F-function to 7 figures, as this 
number is the working standard adopted in this Journal's numerical tables. 
For every value of p greater than 5, and for almost all practical purposes for any 
value of p greater than 2, we can readily calculate log F (p) from the formulaf : 
which has the advantage of giving T (x + l)j{ocFe'^), the quantity usually required 
in biometric work. 
For values between 2 and 5 of p, or for values of p less than unity, the formula 
of reduction V {p-\- \)—p F {p) and the present table must still be used. 
* W. Palin Elderton has kindly tested this point theoretically, and finds that the differences of the 
recorded values are the best to use in such cases. Ed. 
t Pearson, Biometrika, Vol vi. p. 119. In the example line 19 for " log a;^e-^= -818,4081 " read 
"log A-»^= 3-526,3058." 
log 
F(^ + l) 
= 0-399,0899 + i log a; + -080,929 sin 
25°-623 
X 
6—2 
