Egon S. Pearson 
83 
giving partial correlation coefficients 
rxz.y = + -570 ± -102, r^,,,, = - '470 ± -118. 
These latter coefficients suggest that the secular change for observations spread 
over a number of days will be a lengthening in estimation, but that, if a number 
of series are done in rapid succession, the tendency will be for a shortening ; in 
fact we should expect the sessional change to be in the opposite direction to the 
secular, as for the Bisections. 
1 24 
1 20 
1 16 
n2 
108 
1 04. 
I 00 
,1 Diagram of Mean Sessional Change 
1 10 20 30 40 50 60 
Fig. 18. 10 Second Estimation, t. Order of Observation in Series. 
The values of have been plotted in Figure 18; the best fitting line has not 
been calculated, but it would certainly correspond very closely with the mean, 
y — 1'1333. There is in fact apparently no mean sessional change, though the drop 
in the last eight values of yt may be significant, and a mark of the tendency 
suggested by the negative value of r^,/.^. 
In Figure 19 the centres of the small circles represent the positions of the 
means ^f the 63 observations of each series; these points have been fitted with 
the cubic 
X = 1-093971 + -0221 16 ( 10 5) + -001 174 {y - 10-5)---0002002 (y- 10'5)'. . .(xli), 
which is the middle of the three carves. There is evidence of a slight secular 
change, the length of the estimation increasing towards the end of the experiment. 
If however it is remembered that the 20 series were carried out in 4 days, it will 
be seen that there is in general a decrease in estimation in the course of the 5 series 
done in any one day. It is this daily drop that the coefficient rxy^^{ = - -470) is 
picking out. Now in addition to the secular change in pez'sonal equation, the 
figures in Table XV suggest that there is also a secular change in standard devia- 
tion. The vertical lines on each side of the series-means in Figure 19 equal in 
length the corresponding standard deviations, or o-j's. These values of have been 
fitted with the cubic 
x = -1 29006 + -001072 {y - 10-5) -h -000302 {y- 10-5)^+ -0000214 ( y - 10-5)^ . .(xhi), 
and the other two curves in the diagram have ordinates equal to x + x and x — x', 
so that the distance between the central curve and either of the outer curves, gives 
the smoothed value of the standard deviation at the point. The diagram provides 
a generalised repi-esentation of a secular change in personal equation and standard 
deviation. 
6—2 
