Egon S. Pearson 
63 
the earlier to the later series ; in addition there was a remarkably constant 
sessional change within each series, this change being again a decrease from the 
earlier to the later observations. There was something in these changes almott 
analogous to an elastic strain, during the course of a series the estimation of a 
third drops, in the interval between the series there is a recovery, but not a 
complete recovery, for the first judgments in the succeeding series start at a 
little lower level than the first, but well above the last judgments in the series 
before ; this slight " permanent deformation " caused by the " strain " represented 
in the sessional change, results in the secular fall. The figure below gives an 
ideal representation of this. 
\ 1 
\ 1 
\ ' \ 
A_ / ^ 
\ / \ '\ A 
A, 
\ / 
\ / 
\ / 
\ / 
\ / 
B, 
\ ' \ ' T^— -A^ 
V \l \ ' 
\ / 
\ ' \ 
B. I V 
\ / 
\ / 
\ ' \ 
B, 
Fig. 7. 
sessional change in Series 1, 2 
ByA.„ 
Mi3Ig the resulting secular chauge 
etc. 
Br 
B, 
"recovery" during interval between Series 1 and 2, 2 .and 3 etc. 
Then combining the twenty series, in order to get more reliable results, the 
coefficients of correlation of successive judgments, R/j, were obtained ; owing to 
the secular and sessional changes these coefficients had very high values and as k 
increased, apparently tended to a limit at about + "60. By fitting the means of 
the series together, the secular change was eliminated, and a series of coefficients 
Ryt' obtained, which represented the average value of the correlation in a series ; 
owing to the sessional change the Ra:"s did not appear to tend to zero as k 
increased but to a limit at + 'lO or +*1.5. The correlation of successive values of 
the residuals, left after subtracting the ordinates of the straight line "best" fitting 
the first 50 observations of each series from the observations of that series, gave 
a set of coefficients Rjt", which fell off very rapidly and became negative when k 
equalled (3 or 7 ; the large negative values of the coefficients for the high values of 
k were probably due in part to the method of approximation used, and also to the 
fact that the straight line fitting the first 50 observations in a series did not 
represent satisfactorily the sessional change. 
The values of R^' calculated (up to k = 13), gave no evidence of any tendency 
to periodicity in this coefficient, although there was evidence of this occurring in 
some of the individual series ; periodicity in R^' would indicate marked variations 
of roughly the same period occurring at any rate in a large number of the series. 
