EctOn S, Pearson 
79 
breaks were caused by some chance external factor, or were due to a conscious 
change in estimate made by the observer on deciding, whether rightly or wrongly, 
that his second count was too short or too long*. 
It will be noticed that the standard deviations of differences between these 
special pairs of judgments are in all cases greater than the corresponding standard 
deviations from the total 1000 judgments; this is to be expected, for the judg- 
ments yt from which all the differences are taken are not a random selection of 61 
(or 33) judgments, but include many of the most erratic and therefore those 
furthest from the mean. 
{h) The Combination of the Series. 
In combining the twenty series, Bk,Sk and were calculated from the thirteen 
correlation tables of the judgments, and the values of these constants are given in 
Table XIV below. A glance at any one of the correlation tables showed that the 
1000 judgments in any group did not follow a normal distribution, and in order 
to get a measure of this, the coefficient of skewness for the 1000 judgments in 
the combined Groups 1 (i.e. for the judgments y-^, y.^.-.y-M of the twenty series) 
was calculated from the expression 
Q, V;8;(/3,+ 3) 
^^'"'''''' = H5K^^y 
where and are the fundamental ratios of the moments about the mean given by 
The result was as follows : 
A = -2726, /3, = 2-9739, Skewness = -3684 ± "0339, 
showing a very significant degree of skewness, and the freipicncy follows a Type I 
curve of limited range. 
The distribution of these 1000 observations made within a period of four con- 
secutive days, gives but another example of the frequent inapplicability of the 
Normal Error Law. 
Using the values of p^, o-j and a.., R/ is obtained from 
- (/3lO-lO-o) 
R/ = = + -5200 + -0156 (x) bis, 
/S(ar)2(a/) 
and the remaining values of R^', /i; = 2, ...13, by the approximate method of 
Problem 1, p. 41. Perhaps the chief source of error in the method is variation 
in Sic, which has been assumed constant; in this exjjeriment the range of S^ is only 
1"8 % compared with 3-6 for the Trisections and 2"5 % for the Bisections, and the 
results which are contained in the 6th row of Table XIV may be regarded, there- 
fore, with reasonable confidence. As before, for the higher values of k, 'R^' may be 
* Eleven definite iDterruptions in the ordinary routine of counting, due to a mistap on the key or a 
miscount of the 10 seconds, were recorded at the time of observation, but only three of these resulted 
in breaks of judgment ^ -07, the limiting value taken in the above investigation. 
