438 Tetraclwric Functions for Fourfold Correlation Tables 
Now let 
then the equation becomes 
N'' 
_ Hvn^ y and 
h + d c + d 
N 
+ S(t,,t,/j-). 
It is clear from the above, that t,/ is the same function of ^--^ as t„ is of 
N 
and that one table of these functions will serve for both, if we enter the 
h + d 
table with 
N 
c + d 
It 
argument for the latter, and with for the former. 
should be noted that these quantities ^ are identical with ^ (1 — a), 
where ^ (1 + a) and a are used as arguments by Sheppard* in his published tables 
and to avoid ambiguity have been tabulated under that heading. 
In the present tables the values of the first six t functions, henceforth to be 
termed tetraclwric functions, have been computed for values of |- (1 — a) from 
•001 to '500 by successive increments of "001 ; the last column contains the values 
of /if (or k) corresponding to the value of ^ (1 — a) given in the first column, 
and required for computing the functions of liigher order than the sixth as 
well as for the probable error of r. 
In the auxiliary table are given the values of p„ and qn required to compute the 
functions of the seventh to twelfth orders by means of the difference formula 
T(» = hpnTn-\ — <ln'^n-l- 
Illustrations of the Use of the Tables, 
(a) With interpolation. 
Consider the hypothetical table given below : 
1668 
131 
1799 
137 
64 
201 
1805 
195 
2000 
Here 
= •09750, "-4;^ = •] 0050, ~ = •032000. 
JSf N N 
* W. P. Shoppard, " New Tables of the Probability Integral," Diomelnlia, Vol. ii. p. 174. 
t -r of Shepijard's Tables. 
