or EREOES OF JUDGMENT AND ON THE PER>SONAL EQUATION. 
253 
groups as we are here using, we may safely group observations, and the differences 
between the constants calculated from the absolute formulm and from the grouped 
results will not exceed such errors as must arise from our statistics being a random 
sample and not embracing the entire “population” of errors. 
The interpretation of Table II., to which we shall frequently have occasion to refer, 
may be given here. Abiding by the ungrouped data and midtiplying by 1'734, we 
find for the observation strip of 32‘6 centims. the results : 
Observer. Mean. 
Professor Peaesox . . . + *1348 
Dr. Macdoxell. . . . — U9852 
Dr. Lee .— 7740 
Standard deviation. 
2-0620 
2- 0333 
3- 1585 
Thus on an average I was 1 -3 millims. ahead of the true position ; such a personal 
equation might arise from a reaction time. On the other hand, Dr, Macdoxell 
anticipated the position of the ray by 19-8 millims. on the average, and Dr. Lee by 
7-7 millims. Their personal equations cannot, therefore, be due to reaction time. 
Dr. Macdoxell is slightly steadier in his judgment than I am, and we are both 
considerably steadier than Dr. Lee. She and I have about changed our relative 
positions ; her steadiness is to mine in the ratio of about 40 to 32 in bisecting 
lines, but as 26 to 40 in judging of the position of a bright line on a scale. This 
change of position with regard to steadiness may be due to the different nature of 
the two series of experiments, or to the lapse of time, 4-5 years, between the two. 
Dr. Macdoxell with the largest personal equation is the steadiest of the three 
observers in his judgment. It is noteworthy that in both sets of experiments the 
observer with the largest personal equation judges most steadily. So far as our 
results reach, there appears to be no marked relationship between accuracy and 
steadiness of judgment. 
(7.) On the Constancfi of the Personal Equation. 
% 
The totals of our results were for the ungrouped returns added up first for every 
twenty-five to fifty trials, and this enables us to appreciate the degree of constancy 
in the personal equation when it is determined as it actually is, and probably must 
be in practice, from a comparatively few experiments. 
Table III. (p. 256) gives the changes in personal equation for the three observers as 
based upon every series of twenty-five bisections, and, further, the personal equation as 
based upon 25, 50, 75, 100, 125, ... 475, 500 experiments. These results are repre¬ 
sented graphically in Diagram 2. In this diagram 1 nnit of the vertical scale represents 
an error of only of the length of the line in placing its midpoint. It will be 
noticed that if we take 200 experiments, the variation in the value of the personal 
equation obtained by taking any larger number scarcely amounts to -gwofh of the 
