2S(i 
riiOFESSOR K. PEARSON ON THE MATHEMATICAL THEORY 
time from C to B were quite independent. Again, if the judgments of two observers 
be in Ijotli cases referred to a standard observer, then such relative judgments will be 
found to be correlated; and this is true, although if we could find the ahsolute errors 
of the two observers, we might discover that these errors were quite uncorrelated. 
We shall see illustrations below of the manner in which this spurious correlation almost 
imperceptibly creeps into any ordinary method of manipulating observations, and how 
very little attention has hitherto been paid to it. 
But apart from this spurious correlation the experiments described in this memoir 
seem to show that there exists almost invariably a genuine correlation between the 
judgments of independent observers. This may be due to two sources : (i.) Likeness 
of the environment in the case of each individual observation, which leads to likeness 
of judgment in the individual observers. One experiment may appear to be made 
under precisely the same conditions as a second, hut really it has a certain atmosj^here 
of its own which influences the olDservers in a like manner, (ii.) Likeness in the 
physical or intellectual characters of the oljservers leading to a likeness in their 
judgments of what took place. 
It is usual to suppose that the error made l)y an individual observer depends upon 
a great variety of smaU causes largely peculiar to that individual; or, if peculiar to 
the individual experiment, that they will affect different observers in different ways. 
Our ex|)eriments show such considerable correlation l^etween the judgments of 
individual observers, that I have been compelled to discard this view; I consider that 
very slight variations of the environment (foi‘ exanqjle, similar observations on stars of 
different N.P.D.) will be quite sufficient to produce correlated judgments; on the 
other hand, some slight similarity of eye-sight, of ear, of temperament, may be 
suflicient to associate the judgments of two observers. Whatever variety of small 
causes influence the judgment, it is clear that in actual practice they do not suffice 
to dominate some particular source of mental or physical likeness which leads to this 
correlation in judgments. 
Our first series of experiments show that the actual instantaneous environment is 
not necessarily the source of likeness in judgment. The same lines were not dealt 
with by the three observers at one and the same instant. Thus it is on some quite 
definite, but probably quite undiscoverable, likeness of temperament that we mnst 
largely rely to account for this correlation of judgment. 
To the naturalist, who has to observe, whether he Ije physicist, astronomer, or 
biologist, tins genuine correlation of judgments is of equal significance v'ith the 
“spurious” correlation, and, like the latter, almost invariably disregarded. A and B 
are two independent observers, making an experiment of the same character, or 
observing the same phenomena. As a rule theii' judgments, however, will not be 
independent. The importance of this conclusion in modifying the weight which must 
be given to a series of observations of the same phenomena made by two “indepen¬ 
dent ” observers will be manifest. Once we admit that the judgments of independent 
