262 
PROFESSOR K. PEARSON ON THE MATHEMATICAL THEORY 
present writer produces a correlation of judgments, for “ every one of the observers 
records the time of transit of faint stars later than that of bright stars.” Hence 
if a number of observations were made on stars of varying magnitude, the judg¬ 
ment being a function of the magnitude, we should have a series of correlated 
errors. Again it is quite possilde that the rate of transit of a bright line in our 
experiments might tend to correlate judgments, although the Cape observers did 
not find the personal equation to vary with stars of very different declination. It is 
not, however, contended that the correlation of jugdments is not due to one cause 
or another. The point of the present writer is this, that when every effort is made 
to eliminate large causes, such as varying brightness or rate of motion of the line 
in our own experiments, there still remains a multitude of small causes which 
produce correlation. It might be possible in an ideal series still further to 
eliminate some of these, but in practical observation we have to take a given 
phenomenon as it is, and we cannot possibly subtract from it the whole of its 
characteristic atmosphere. The next point to be noticed is, that whatever be these 
lesser causes of the characteristic atmosphere, e.y., possibility of judging better the 
position of a bright line when it is nearer to one or another part of its range 
of visibility, or of bisecting a line of one length better than of another length— 
they affect different observers in quite different manners. Unlike the brightness 
of stars, the fluctuations of personal equation due to these causes are in themselves 
personal. Dr. Macdonell and I have within the limits of error no correlation 
in our judgments of the position of a bright line. Dr. Lee and Dr. Macdoxell 
have a correlation as high as that of a measure made on a pair of brothers. In 
other words, correlation of judgments is a personal matter, just as personal equation 
itself We could no doubt increase it by introducing variety in the observed 
phenomena—degree of brightness, degrees of speed—hut beyond such causes capable 
of differentiation, there appear to be others, which I have classed as the influence 
of the immediate atmosphere, and which appeal to different personalities in different 
ways, and where there is a resemblance between certain features of two personalities 
produce correlation in their judgments. For example, A and B are alike in their 
sight, l^eing slightly short-sighted we will say, B and C are alike in their nervous 
temperament, being able to judge more correctly if the bell rings after the bright line 
has been visible a rather longer time. There is thus an element of personality the 
same in A and B and another the same in B and G. The result would be that A’s and 
B’s judgments would he correlated, and also B’s and C’s judgments would be correlated, 
but not necessarily A’s and C’s. Something like this probably is what actually occurs 
in the case of Dr. Macdonell, Dr. Lee, and myself But it would be practically 
hopeless to try and discover the common elements in our personalities, and what in 
the immediate atmosphere of the experiments affected such elements. Even if, in a 
long and laborious series of experiments and reductions, we could discover the subtle 
causes of our correlations or non-correlations, the results would be of small value. 
