156 
Tables for Testing Curve Fitting 
and that P will then be calculated from : 
if 11 be even, and from : 
re + 2 ^2.4^2.4.6^""^2.4.6...(n'-3V 
if n be odd. 
Now although p^- can be found quite easily without any special mathematical 
knowledge, the calculation of P from the above formula? is very troublesome. 
But it is quite clear that some test of the above kind is absolutely needful in all 
biometric enquiries in which we wish to test theory against observation. In the 
paper referred to a small table for P in terms of n and was given, but this table 
beside being far from extensive enough for actual practice, was based in some 
entries on values of the probability integral which had not been calculated by the 
use of higher differences. The present Table I. is an attempt to provide a more 
extensive and accurate system of values for P. It gives the values of P for w' = 3 
to 30 and from %^ = 1 to 30 by units and from = 30 to 70 by tens. 
Method of Calculating Tables. 
In order to simplify the work of calculating P for values lying outside the 
range of this table, or in cases where interpolation would not give sufficiently 
accurate results a series of additional tables are given which were used in the 
calculation of Table I. Thus Table II. gives the values of log \/''~ 
log (e~^^') to eight figures. Table V. gives log and ^(>g jy — to ten figures*. 
Table III. gives the cologarithms of n (?i — 2) (n — 4) ... 1 (or 2) needed for the 
coefficients of the powers of to eight figures. Table IV. gives the values of 
/\J^ j %" = 1 ^0 to eight figures, i.e. as long as it is practically 
sensible. Further values of this integral may be deduced from the tables for 
2 f 
-7= I e~^^ dt, which are given for i = 0 to 4"80 to eleven places of decimals for the 
Vtt 0 
higher values in Czuber's Theorie der Beuhachtungsf elder, Leipzig, 1891. 
In calculating the tables Erskine Scott's 10-Figure Logarithms and Filipowski's 
7-Figure Antilogarithms were used. The method of calculation was, briefly, as 
follows. Tables were first made of log {^/^ — e~^'x-^ and log e~^x" by continuous 
* Thus incidentally the ordinates of the normal probability curve, «/ = J are given 
for the squares of the abscissae. 
