OF ERRORS OF JUDGMENT AND ON THE PERSONAL EQUATION. 
261 
It may be asked how, when as in practice we only know the relative judgments, 
are we to find out the degree of steadiness of the individual observers ? This is a 
very important problem, and the answer would be perfectly clear if the old theory 
on p. 240 of this memoir were correct. Unfortunately the correlation of judgments 
comes in, and deprives us of any means of judging from a knowledge of relative 
steadinesses what the absolute steadinesses are. Let me illustrate this ; The 
relative variabilities are greatest in the cases of 3-2 and 1-3, we might therefore 
suppose 3 to be least steady; the relative variabilities are least for 3-2 and 2-1, we 
might therefore suppose 2 to be most steady, and we should thus reach the actual 
scale of steadiness in absolute judgments—Dr. Macdonell, myself. Dr. Lee. 
But now turn from the bright-line experiments in Table VI. to the bisection experi¬ 
ments in Table I. The relative judgment standard deviations are greatest for 3-1 
and 1—2 and least for 2-3 and 3-1, we should therefore suppose that 1 was least 
steady and 3 most steady, or the order of steadiness 3, 2, 1, i.e., Mr. Yule, myself, 
Dr. Lee. But an examination of the absolute standard deviations sho’vvs us that the 
real order is quite different, being Dr. Lee, Mr. Yule, and myself In other words, 
no argument can be drawn, owing to the correlation in judgments, from relative to 
absolute steadiness. 
It seems therefore impossible without experiments ad hoc to determine which 
observer is steadiest in judgment from a knowledge of relative personal equations. 
We can only conclude that, at any rate in our own cases, the fluctuations in 
personal equation are such that, even in what are—for practical purposes—very large 
series, we cannot invariably assume them to be- due to random sampling. We 
cannot attribute sensible changes in our own case to practice or to fatigue, but the 
high correlation of judgments suggests an “ influence of the immediate atmosphere,” 
which may work upon two observers for a time in the same manner. 
( 8 .) Ou the Interdependence of Judgments of the same Phenomenon. 
(i.) The Bright-line Experiments. 
In the preceding paragraphs of this paper we have already had occasion to 
frequently refer to the correlation of the judgments of independent observers. 
Belations (vi.) of p. 240 are not fulfilled, nor even approximately fulfilled. For 
example, in Table II. we find 0-03 = 1'74, about, which is actually less than 0-^3 = D82, 
about, when, if the theory of p. 240 were correct, 0-33 = + cr,j 3 ^) ! An 
examination of Table II. show us substantial correlations in two out of the three 
cases between absolute judgments. Now it is well to put somewhat more definitely 
what is meant hy this correlation. Astronomers have already found that the 
brightness of a star influences the personal equation."^'" This in the language of the 
* ‘ Monthly Notices of the Roy. Astron. Soc.,’ vol. 60, November, 1899. 
