Egon S. Pearson 
25 
may be possible to construct a more generalised theory of errors of judgment 
than that which has hitherto been adopted, and although the practical corrections 
which such a theory will impose may not be large, yet a more detailed knowledge 
of the nature of the variations and perhaps some insight into the psychological 
and physiological factors which underlie them, will give the observer a clearer 
idea of the precautions to be taken to avoid error and a greater justification for 
confidence in his results. 
II. Generalised Theory of Personal Equation. 
Before proceeding to the reduction of the Experiments which have been carried 
out, I will consider whether it is not possible to make a very general, and yet 
simple, analysis of personal equation. Let us suppose that we have a large number, 
iV^, of observations, which have been made in separate groups, or at what may be 
termed separate sessions. For the astronomer, a session will be a night's work ; 
for the physicist or psychologist, one continuous set of readings or observations. 
Any particular observation y may be designated (1) by t, a function of the time 
when it was recorded, measured from some fixed epoch, or (2) by the number of 
the session in which it was made, and t, the time of record measured from the 
coTnmencement of that session. E.g. an observation made in the pth session may 
be written either as i/^ or j,yf. We will suppose that the secular change can be 
represented by the function </> (t), but in addition to this change there may 
be another of a different t3'pe which may be termed the sessional change, and 
will be represented by the function The fundamental difference between 
a secular and sessional change is this : if there is a break of some hours or perhaps 
days between two series of observations, the sessional change of the first scries 
will have no influence on the judgments of the second series, while the secular 
change will continue from series to series. The sessional change is thus peculiar 
to its own session or series of observations, although it is very possible that the 
same type of change may be repeated in session after session ; it may be a change 
resulting simply from fatigue or pei'haps from more complex causes. Figure 3 
(p. 4G) provides a good illustration of secular and sessional changes ; the centres of 
the small circles represent the mean values of twenty different series of observations, 
and it will be seen that the general tendency is for a drop in mean judgment 
from left to right of the diagram ; this is the secular change. The sessional 
changes are represented by the continuous lines drawn through the centres of 
the circles, and the slope of these lines is on the whole seen to be very constant 
throughout the twenty series. In this case the secular and sessional changes are 
acting in the same direction, but they may well act in opposite directions. 
We have thus seen that an observation y may be expressed in the form 
2/ = </.(t)+./;(o + f, (i), 
where Yt is the residual after the removal of secular and sessional changes. The 
duration of the session is likely to be so short compared with the period over 
which the secular change is measured, that t may be taken as practically constant 
