248 
rROFESSOR K. PEARSON ON THE ^lATHEMATICAL THEORY 
rectangles similar to the white strip on the black screen, and he drew across these 
“ recording” strips aline in the position he considered the line of light to have on the 
observation strip when the bell sounded. Every strip already used was covered up 
Ijefore a new observation was made, so that it might not influence the next judgment ; 
the lines were drawn from left to right and all measurements taken on the left-hand 
side of the strip. A facsimile of one of the sheets of observations accompanies this 
paper, and will give graphically an idea of the nature of the errors of judgment made. 
These errors were then scaled off to the nearest tenth of a millimetre, and formed the 
basis of the second series of errors of judgment. The line of light travelled down the 
strip, and if the estimated line is below the real line on the recording strip the error 
was considered positive. If the personal equation were solely due to reaction time, 
this positive error would represent a lag of the judgment, i.e., the biigiit line would 
be recorded as occupying a position posterior to what it really occiq^ied when the 
bell sounded. A glance at the observations, however, shows that reaction time must 
liave had very small Influence on the total magnitude of the personal equation ; two 
oljservers made rather large negative mean errors, and the tliird only a very small 
positive mean error. 
The experiments were carried out in about a week, not more than 2 hours being 
given to them at a time, to prevent over-fatigue. The observers were Dr. Alice 
IjEE, Dr. W. R. Macdonell, and myself Mr. K. Tressler kindly acted as adjuster 
of the scale. The observers were screened from each other, but the experiments 
being conducted in a long narrow room, the only one available. Dr. Lee was placed 
somewliat further from the oliservation strip than Dr. Macdonell or myself The 
only other differentiation between tbe observers, that I am aware of, was that I 
released the pendulum from its clamp with my left hand, drawing the recording line 
with my right; tlie bright line moved so slowly, however, that I was not at all 
conscious of being hurried, and, as a rule, I had my left hand on the table before the 
line of light had entered the strip. 
As the arrangement of the pendulum seems likely to be of service for similar 
observations, especially in tbe psycliological laboratory, it is figured on the opposite 
page. 
In this series of experiments, which will be termed the “ bright-line series ” to 
distinguish it from the “ bisection series,” x represents the error of judgment 
considered positive as defined above, and the subscripts 1, 2, 3 refer resjiectively to 
me, Dr. Macdonell, and Dr. Lee. Before entering into the details of these series, I 
shall consider some points beai'ing on the method of reducing material of this kind. 
