28 
On the Variations in Personal Equation 
III. The Experiments. 
The present paper is based on the reduction of the following Experiments : 
A. Estimation of the value of a Third, or Trisection Experiment. 
B. Estimation of the value of a Half, or Bisection Experiment. 
C. Estimation of Time, by counting of Ten Seconds. 
D. Estimation of Ten Seconds without intermediate counting. 
E. Some repeated measurements of fine structure in a Stellar Spectrum, 
with a Zeiss Comparator. 
The first four Experiments were carried out by the writer in accordance with a 
uniform scheme ; each Experiment was divided into 20 series of 63 observations, 
making 1260 observations in all. Only one series (or 63 observations) was done 
at a sitting to avoid as far as possible the effect of fatigue ; in the case of 
Experiments A and B the sequence of the series was much broken, spreading 
over some weeks, but G and D were carried out within four consecutive days. 
The dates of the series are given with the detailed discussion of the observations 
below. 
(a) Experiments A and B. 
Figure 1 is a copy of one of the printed forms used for these experiments ; the 
longer line was used for A ; distance between inner edges of bounding marks 7'53 
inches ; the shorter line was used for B ; distance between inner edges of bounding 
marks 5'94 inches. 
The lines were on the same form simpl}' for convenience in printing, etc. and 
that not used was concealed while the observation on the other was being made ; 
a fresh line was used for each of the 1260 observations. In carrying out a series 
a pile of 63 forms was placed on a table slightly tilted up towards the observer, 
and straight in front of him, with a good light coming from the left-hand side, the 
pencil being in his right hand. He then made a short pencil stroke across the line 
at the point which he estimated was one-third way along the line from the left- 
hand end (Experiment A), or at the point which he considered to bisect the line 
(Experiment B). He then turned the form over, face downwards at his side, and 
proceeded to deal with the next form in the same manner, continuing until the 63 
were finished*. The pencil stroke was made after a rapid eye estimate, the aim 
being to record the first impression of third or half formed upon seeing the fresh 
line, and to avoid hesitation ; the average time taken in going through a series of 
63 observations was 5 minutes 40 seconds for Trisection, 5 minutes 22 seconds for 
Bisection, or 5'4 seconds and 5"1 seconds respectively between judgments. 
To avoid bias, it would have been desirable to complete all the observations of 
an experiment before commencing the measurement of any of the series, but 
* Actually in Experiments A and L'< 70 forms were marked in each series ; the first 7 were to enable 
the observer to "get his eye in," and the measures of them were not used at all in the reduction. 
