254 
PEOFESSOR K. PEARSON ON THE MATHEMATICAL THEORY 
length of the line bisected. On the other hand, it must he noted that the fluctua¬ 
tions in the personal equation when we come to deal with series of 25 are much 
larger than the probable error of a random sampling. Tlie probable error of the 
personal equation of Dr. Lee, based on 25 experiments, is 'OOSSl, hut actually 
the personal equation as determined from two different sets of 25 experiments may 
amount to seven or eight times this amount. In other words, there is a significant 
difference in personal equation depending upon the individual 25 lines bisected 
Whether this significant difierenceds dne to the lengths of those lines, their exact 
position on the paper, or to the individual state of the observer, it may be hard to 
determine. It may even be due to slight variations in light occurring between one 
25 series of experiments and the next. But whatever be the single source or 
combination of sources to which these changes of personal equation are due, it 
seems to me that they are so insignificant and subtle that they will occur in almost 
every kind of physical measurement we may take. It would be idle to attempt 
indeed to discover and eliminate such sources, for while it might be possible after 
elaborate investigation to eliminate them in an especially devised series of experi¬ 
ments, this could not be done in practice, where we must take our observer’s 
experiments as they are given to us, and where we cannot possibly ensure uniformity 
in light, in mood, or health of observer, and as well as in all the features of the observed 
