Egon S. Pearson 
101 
confirmed in Experiment B, where it was found that there was evidence of a linear 
sessional change acting in the opposite direction to the secular change. A discussion 
of the values of the partial correlation coefficients Vxyz (personal equation and order, 
time constant) and r^cz.y (personal equation and time, order constant) suggested that 
if the interval between the successive series were made very short, it might not be 
sufficient to break the effect of the sessional change. The correlated variations 
which have been found to follow the law 'Ric'=qr'^, have been considered as in some 
way separate from and superimposed upon the other more steady changes. Starting 
from the tentative assumption that there is little or no paiiial correlation between 
the observer's true estimates at intervals greater than one — that is to say that the 
observer's judgment at any moment is only influenced by the judgment immediately 
preceding, and only through this and not directly by the earlier judgments — it has 
been shown that the constant q in the relation 
R/t' = (1-^v) bis 
can be accounted for by the presence of uncorrelated accidental errors which are 
superimposed on the correlated variations in the observer's true estimate. Without 
further investigation it would be difficult to distinguish between what may perhaps 
be termed the physiological and the psychological factors ; in the experiments that 
have been undertaken the variations in recorded judgment depend partly on the 
movements of the hand, so that the former factors are likely to have played some 
part as well as the latter. The successive recording motions of the hand may have 
been correlated as well as the variations in mental estimate. 
The importance of the results of course depends on how far they may be con- 
sidered as tyjjical of any practical series of observations made by the astronomer or 
the physicist. Experiments were admittedly chosen in which it was expected that 
the variations in judgment would be large, and for the experienced observer working 
at the type of observation in which he has had much practice, the errors would no 
doubt be smaller, but it seems to me likely that the phenomena which have been 
discussed will be present in the judgments of other observers even if on a smaller 
scale. Experience and accuracy may be gained by practice, but it does not follow 
that the correlation between successive judgments will disappear. The secular and 
sessional changes may be small, but if rough comparisons of only the yearly mean 
personal equations of different observers are made, the finer changes, which may 
be of considerable importance in a combination of observations, cannot be recognized. 
The Law of Normal Errors requires but two constants to describe adequately any 
series of observations : 
(1) the mean, 
(2) the standard-deviation, 
while the introduction of a third may be necessary if a gradual secular change in 
personal equation is noticed. But the more generalized Theory of Errors discussed 
in the preceding sections requires more detailed information and a greater number 
of constants to define the character of an observer's personal equation and variations 
in judgment. We shall require to know how the personal equation and the standard 
