OF ERROES OF JUDGMENT AND ON THE PERSONAL EQUATION. 
‘237 
observers are correlated, then the determination of the amount of correlation becomes 
of vital importance. 
It has only been after further experiment, and after much seeking for possible 
sources of spurious correlation, that I have at last convinced myself of the reality of 
this genuine correlation in the judgments of independent observers. I cannot expect 
my readers to do so at once, but I believe that a careful examination of our experi¬ 
mental results will at least convince them that it is a factor of great importance in 
some, if not, as I believe, in all types of observation. As to the spurious correlation, 
it jdays such a large part in relative personal judgments, and is so ol)vious from the 
theoretical standpoint, that one can only wonder it has not hitherto l:)een regarded. 
The course Vhich I propose to follow in this memoir may be tlius summed up :— 
(a.) I shall introduce a more complete terminology than appears at present to 
exist for the theory of errors of judgment. 
(b.) I shall develop to some extent the current the(ny of ei'rors, and its application 
to personal equation. 
(c.) I shall next consider what modifications must ije made in this theory to allow 
for the correlation of the judgments of independent oljservers. 
(d.) I shall then discuss certain experimental investigations on personal equation, 
which demonstrate that (c.) and not (/>.) is the category imder which we must class 
errors of judgment. 
(e.) Lastly, I shall sum up the bearing of this discussion on our treatment of errors 
of observation, whether physical or astronomical. 
(2.) Terminology. 
If ^ be the actual value of some physical (piantity, whether it can be really 
determined or not, and Xj, be the values of it according to the judgments of two 
independent observers, whether formed by measurement, estimate, chronograjDhic 
record, or any other way, we shall speak of x^ — Xo — ^ as the absolute errors of 
judgment of the two observers, — which in many cases is all we can detei'inine, 
will be termed the relative error of judgment of the two observers. 
If a sufficiently large series of judgments be taken, then the mean values of Xj — ^ 
and Xj — ^ will be termed the absolute personal equations of the observers, and the 
mean value of x,, — x^ the relative personal equation of the two observers. We shall 
use the notation Ibr the absolute, for the relative personal equations of 
the two observers. 
Clearly ^> 2 , = ~ ip... 
If we form the standard deviations of the absolute judgments and o-q^, and of 
the relative judgments a-. 2 i = 0 - 12 , these will be measures respectively of the 
variability in judgment of either obsQrver absolutely, and of the variability of 
their relative judgment. 
