88 
On the Variations in Personal Equation 
or pull of the slide at the right moment. It is possible that unconscious "over-pulls" 
or "under-pulls" may go in runs together, but the measures seem to show that 
this is not the case, and that the correlation of successive judgments is due rather 
to correlated changes of mental estimate than to those of a more physical character. 
If it were more difficult to bisect a maximum, if there were greater opportunity for 
variation, it is probable that there would be a congelation of successive judgments, 
and this is perhaps illustrated by the case of Series VIII, which has the largest 
standard deviation ("0041) and also a correlation (p^ = + "227 + "091) possibly 
significant. 
The result of IX suggests that there is a correlation between successive settings 
of the micrometer wires in the second eyepiece ; this correlation would of course 
enter into the results of I — VIII, but the standard deviation of IX ("0004) is so 
small that the effect will be insignificant where the variations in slide settings are 
large. 
As a matter of practical application these results serve to emphasise the 
importance of the routine of measurement usually adopted ; if, for example, it is 
proposed to take four readings of each of a number of markings on a plate, the four 
readings should not be made in succession, but all the markings should be measured 
once, and then perhaps a short interval taken before the second measuring is made, 
and so on. This method should eliminate the error in the mean of several measure- 
ments of a marking, which may arise from a correlation of successive judgments, as 
well as errors due to change in temperature of instrument or plate, etc. 
XI. Analysis of the correlation between successive judgments. 
(a) Tlie Tlteory of correlated Estimates and accidental Errors. 
It has been seen that in the case of the Bisection and Timing Experiments 
when the secular term was removed the coefficients of correlation of the successive 
judgments, or the constants R^', diminished to approximately zero values as k, the 
interval between the judgments correlated, was increased. In the Trisection Ex- 
periment, owing to the marked sessional change which was repeated in practically 
all the series, Ryt' appeared to approach a value of +"16 and not zero as ^' was 
increased ; the sessional change in this case appeared to be of parabolic rather than 
linear form, and it seemed possible that if the ordinates of the " best " fitting 
parabola of each series were removed from the observations, the coefficients of corre- 
lation of the residuals, or the Rjt"'s, would tend to zero as k increased, as in the 
case of the other three experiments in which there was no large sessional change. 
The points representing the values of R^' which have been plotted in Figures 8, 
12, 17 and 20 appear on the whole to lie so nearly on a smooth curve, that it is of 
no little interest to inquire whether we can obtain equations to such curves based 
on some definite theory of the physiological factors underlying the variations in an 
observer's judgment. 
