76 
On the Vai^iations in Pei^sonal Equatio7i 
so that the mean sessional change is of even less significance than for the Bisections. 
In fact it is clear from the diagram that the regression line (xxxviii) very nearly 
coincides with the line of mean judgment, 2/ = '919. 
'938 
■934 
■930 
■926 
■922 
■918 
■914 
■910 
■906 
■902 
"o Diagram of Mean ^ 
'^■c Sessional Change 
t 
. ft--..--/^- V- r/J- A 
', / \ .•'^ Mean, at "919 V 
* ;' " —Regression .y,- -^tlf = + -'>000731 (/-3'i) 
* The value of factor for a true 10 seconds is '080 
1 10 20 30 40 50 60 
Fig. 14. 10 Second Counting, t, Order of Observation in Series. 
The cr/s have been found for all the individual series, and using the values 
of >S]' and R/ given below, we have for the combined series 
8^ = 8,' V2(l -R7) = -0338. 
The method of correlation of Ranks gives 
r.^p^ = + -329 + -135, 
showing again that large variation is associated with high correlation. 
In Figure 16 are given eight representative series graphs which provide a good 
illustration of the variations in judgment. In the first two graphs (I and III), 
as is largo and there are many sudden fluctuations, but in the later series as is 
lower and very constant in value. What may be described as the smoothness 
in the change of judgment is in some cases particularly noticeable ; for example in 
the stretch between 
2/44 and y.,-., Series VI \ 
2/2 and 2/12, Series XII ^ . 
2/47 and 2/59, Series XV ) 
In making comparison with the similar diagrams for Trisections and Bisections 
allowance must be made for the differences in scale, but I think it is clear that this 
"smoothness" or gradual variation is a special feature of the 10 second counting; 
there is for instance no diagram of Trisections or Bisections which can compare 
with that of Series XVI of the counting, for high correlation combined with very 
gradual variation. But such a result is not unexpected, if the procedure of the 
experiment with the continuous counting be remembered. 
A further point of interest is to examine how far a sudden " break " or discon- 
tinuity in the length of estimate influences the succeeding judgments. Among the 
1000 observations forming the Groups 1 of the 20 series there are 61 "breaks" or 
differences between successive judgments of "07 or over (in terms of the factor e/p), 
