OF EEEORS OF JUDGMENT AND ON THE PERSONAL EQUATION. 
•257 
Although the personal equations in Table IV. are based upon series varying in 
number from 26 to 37, the probable errors for thirty observations of the position of 
a bright line suffice to show that the fluctuations in the values of the personal equa¬ 
tions as given in Table IV. or in Diagram III., p. 270, are in many cases signiflcant. 
(b.) The probable errors for the personal equation in bisecting 250 lines show that 
there were signiflcant changes in the personal equations of the three observers 
between the first and second moiety of the experiments. While Dr. Lee (1) bettered 
her judgment by ’004, Mr. Yule (3) swung over from '001 to right of true midpoint 
to '010 to left of midpoint, and I had a worse judgment by '005 in the second 
moiety when compared with the first moiety of the results. 
In the case of the second series with the bright line. Dr. Macdonell (2) and I (1) 
have changes slightly for the better in our judgments between the 266 first experi¬ 
ments and the 253 second experiments; but having regard to the probable errors 
given for 260 experiments, it may be doubted whether these changes are signiflcant. 
Dr. Lee (3) has, however, a quite significant change for the worse. 
The fact that in some cases the personal equation grows less, in others greater, in 
the second half of the series seems to indicate that the changes in personal equation 
were by no means due to a secular improvement in judgment.* Nor do they admit 
of explanation on the assumption of increasing fatigue due to the exhaustion of the 
power of attention. It must be remembered that the experiments were spread out 
over a number of days, and this cause would only influence the latter experiments 
on each day. My worst experiments on the bright line are the Series 321-347 and 
504-520 (Observer (1) Column (a) Table IV.), but they are much above the average 
in goodness for Dr. Lee (Observer (3) Column (a)), and above the average for 
Dr. Macdoxell. Dr. Macdonell’s worst results are 186 to 239 (Observer (2) 
Column (a) ), and these, especially 213 to 239, are bad for Dr. Lee, but they are 
very good results so far as I am concerned. If any fluctuation was accordingly 
due to fatigue, it did not affect us alike. 
While these fluctuations in short series are significant, they by no means screen 
the general features of each observer’s individuality. Dr. Lee is clearly in the 
habit of bisecting straight lines at a point some or more to the right of the 
true point of bisection, while I place it with a sensibly less error to the left. She 
places a line of light moving downwards over a vertical strip ‘8 centim. above its 
true position, and I about '1 centim. below its true position at any instant. 
Dr. Macdonell, on the other hand, with the steadiest judgment of all three, 
displaces it 2 centims. above its true position.! The differences of personal equation 
in both series for all three observers are quite significant when compared with the 
* It should be noted that in the cases of Dr. Lee, Mr. Yule, and myself we have for years been 
accustomed to reading scales and judging proportional parts by the eye. 
t Table V., second series, gives lengths on recording strip. The actual values for observing strip are 
given on p. 253. 
VOL. CXCVIIL-A. 2 L 
