OF EEEOES OF JUDGMENT AND ON THE PEESONAL EQUATION. 
291 
physical quantity, appear to be “ sympathetic.” Thus there may arise a very con¬ 
siderable correlation of judgments between two observers assumed a priori to observe 
independently. 
(c.) In addition to this psychological or organic correlation occurring in the case of 
absolute judgments, there is a spurious correlation which arises when two observers 
are referred to either a third observer as standard or to a common time or space 
element in each measurement as unit. 
[(I.) Errors of judgment whether relative or absolute far from universally exhibit 
the normal distribution of frequency. It is necessary to generalise this law of 
distribution, and this can only he done by supposing some or all of the axioms on 
which the normal law is based to he modified until we have a sufficiently general 
theoretical distribution, which will enable us to look upon the great l)ulk of observa¬ 
tional errors as random samplings from the theoretical frequencies. 
Even then we may expect occasionally outlying observations due to mistakes of 
record, or the interference of special causes of i.solated occurrence, to render our 
distribution as a random sample improbable. But this raises the question of the 
rejection of improbable observations, which is common to any theory of distribution. 
Practically it would seein : 
(1.) That the correlation of judgments is a necessary factor in our appreciation of 
personal equation. The weiglit to he given to a combined observation, or to the 
combination of observations of two observers, depends upon a knowledge oi this 
factor. 
(ii.) That we should attempt not only to find the jDersonal equation of two 
observers, but also the variations and correlation of their judgments. For this 
purpose it may be needful to make experiments cmI hoc, mimicking the actual 
observations to be made as closely as possible, for there appears no method of 
determining these quantities from the relative as distinguished from the aljsolute 
judgments. 
(iii.) That the existence of this correlation in judgments appears to vitiate very 
largely the existing theory of the probability of testimony; that theory ought to he 
extended by the introduction of what we may term the psychological element; an 
element which many may more or less unconsciously have found wanting, when they 
considered the weight whicli had to he given on the mathematical theory to the 
testimony of “ independent ” witnesses of the same series of events."^ 
(iv.) That great care should he used in applying the current theory of errors to 
observations until it has been shown that within the fluctuations of random sampling 
these observations really follow the normal law. If they do not, then the physical 
* If Dr. Lee and Dr. ^Iacdoxell assert that a liriglit line was in certain positions when tlie bell 
rang, their united testimony is very far from having the weight it wonld have on the old mathematicad 
theory that they are independent witnesses, and yet they record perfectly “independently.” 
2 P 2 
