70 On the Variations in Personal Equation 
residuals after the removal of the sessional term, will be very small indeed compared 
with the standard deviation of this difference, or 0-5. It is therefore suggested 
that in the combination of correlated observations, the average value of the 
jump in estimation between two successive judgments, is of more fundamental 
importance than a. As an example, consider the diagrams of the observations of 
Series X and Series XX in Figure 11 ; the correlation, pi, is very low in both 
cases, but it is suggested that the physiological significance of the difference 
in type between the two, lies in the fact that o-g for Series X is nearly twice as 
large as 0-4 for Series XX, rather than in the difference in the o-j's. Or again in 
the diagrams of the Trisection Experiment, Figure 6, I would emphasise the 
same point in a comparison of the difference between the two highly corre- 
lated Series VIII and XVI. 
Now returning to the coefficients of partial correlation 
, = + -529 + -109, 7-,.,. „ = - -.589 ± -099. 
With the interpretation suggested on p. 54 for these coefficients, we are led 
to a rather suggestive conclusion. If we are dealing with a number of series 
carried out at equal intervals of time in the course of one, or even perhaps two 
days, but effectively at one epoch when comparison is made with the long range 
of nearly 70 days covered by the Bisection Series, then the correlation between 
//• and y is positive, or the pencil mark in the later series tends to be made 
further to the observer's right than in the eai-lier series ; this change is in the 
same direction as the sessional change within a series. There is indeed a curious 
coincidence, on which of course no stress must be laid, 
, = + -529 + -109, r^,.f = + "5294 ± -0137. 
That is to say the correlation between the mean of a series and the order of 
that series when a number of series are done in close succession, is of the same 
sign and magnitude as the correlation between the mean tt\i observation and its 
order, t, in the series. But if we are dealing with all the pth series of sets which 
have been carried out on different days with varying and perhaps many days' 
interval between, then the coefficient r^^^y is negative, or the bisection-marks on 
the later days have on the whole a tendency to move to the left of the observer ; 
this is in the direction of the secular change. 
The conclusion which it seems possible to draw is this ; if a number of series 
are done at very short intervals, the interval of rest between the series will not 
be sufficient to break the effect of the sessional change ; but if a considerable 
interval elapses between the carrying out of the series, then the sessional change 
in one series has no influence on the judgments in the succeeding series, but a 
quite distinct secular change may be noticeable. In the Bisection Experiment 
both secular and sessional changes are very small, but they are acting in opposite 
directions. If these two changes are due to different physiological factors, it 
seems possible that it is the fact that they are acting in opposite directions in 
the Bisection Experiment which causes them to be of so much smaller magnitude 
than in the Ti'iscction Experiment, where they were acting in the same direction. 
