Egon S. Pearson 
55 
as the sessional change, for it has been supposed that this latter occurs only during 
the course of a sitting, and is broken by the interval of rest in between. On the 
other hand if we take all the jjth series of the various days, then r^^^y (the partial 
correlation of personal equation and time, order being constant) gives the relation 
between change in personal equation and time, taken over a long period. 
The long break in the middle of the Trisection Experiment takes away any 
real significance from the difference between (— '•'559) and r^c^^y (+ '049) for the 
twenty series, and in the case of the last fourteen series these coefficients are equal 
(—•143 and —-138), because the intervals between the series were nearly uniform. 
In the Timing FCxperiments, C and D, the arrangement of the series in groups on 
consecutive days leads to considerably more interesting results*. 
A comparative measure of the consistency of the consecutive judgments in the 
different series, is the standard deviation of first differences, or 
— - = '-1^/2(1-^0 
approximately. The values of this expression are given in the 8th column of 
Table IV. 
Now suppose we compare the constants in Table IV, the dates and remarks at 
the end of Table I and the diagrammatic representation of seven of the series given 
in Figure 6. The first series to be remarked on is IV ; most of the series were 
carried out at the beginning of the morning before any other work, and it is possibly 
the fact that IV was done soon after a spell of measuring spectrograms with a Zeiss 
comparator that explains the exceptional values of and p/, namely pi = — '0460, 
Pi = — '2521. The o-^, or standard deviation of 1st differences, is no higher than for 
the other series done at about the same time (in May), and the o-j is lower. 
The first graph in Figure 6 gives the diagram of this series ; the rapid fluctuations 
in judgment about a very steady, if slowly changing, personal equation may perhaps 
have some physiological significance. In the second and thii'd graphs of Figure 6 
are represented two of the four Series VII — X which were done when the 
observer was not very fit; they have large values for a^, and the o-^'s are large 
compared with those of the ten series which follow, showing that the judgments 
were rather erratic; the correlation is however high. In VIII there is a great 
jump between the 44th and 45th judgments, from 2'22 to 2li6, and the gradual 
drop down, which follows, to 2'20 (for the 52nd judgment) is a good example of 
a way in which successive judgments are correlated. In Series XI (not repre- 
sented among the graphs) there appears to be a periodic variation, for the 
correlation falls steadily from = + '7381 to |0,o — — "4428. 
XIII, XV and XVI are typical highly correlated series with lai-ge sessional 
changes ; the cr^'s as well as the a^s, are considerably smaller than in the series 
VII — X. In examining the fourth to sixth graphs we notice what may be called 
the large scale correlated variations superimposed upon the linear sessional change ; 
* See pp. 70, 75 and 83, and below. 
