32 On the Variations in Personal Equation 
which is moved horizontally in a greased slot by pressure with the hand ; the 
measurer looks through one eyepiece and pushes the slide until the feature on the 
plate of which he is wishing to measure the position, comes under a cross wire in 
the focus of the eyepiece ; then looking through a second eyepiece at the scale 
attached to the slide, he takes the reading, the last two figures of which are read 
from a graduated wheel attached to a micrometer screw-head. In making a measure- 
ment there are therefore two adjustments : 
(1) The setting of the marking in the plate under the cross wire in the first 
eyepiece. 
(2) The shifting of two very close parallel wires by a micrometer screw in the 
second eyepiece, until a line of division on the scale appears to lie exactly in the 
centre between them. 
Far the greater source of error arises from the hrst setting, particularly if the 
marking on the plate is not clear cut. In taking a series of measurements, the 
observer should always move the slide from the same direction- — that is he should 
always push it or always pull it, until he thinks that the marking is bisected or 
" edged " by the cross wire, and then he should stop ; if he obviously overshoots 
the mark he should start again, and not hesitatingly move the slide backwards 
and forwards in search of what he thinks may be the best setting. By shifting the 
slide into position from the same direction, the measures may be all subject to a 
fairly constant personal equation due to " over push " or " under push," " over 
pull " or " under pull " of the slide, but this effect may be eliminated by reversing 
the plate in the instrument, making a fresh series of measures, and taking the 
mean of the two. In this particular set of readings the slide was always " pulled " 
into its final position. 
{d) It is hoped that the results of some further experiments of a different type 
in estimating length which were kindly undertaken for me by Mr E. A. Milne of 
Trinity College, and Mr L. J. Comrie of St John's College, Cambridge, will be 
included in a future paper. 
IV. Terminology. 
Experiments A, B, C and D were arranged in accordance with a uniform 
scheme, each Experiment being divided into 20 " series " consisting of 63 obser- 
vations. The series will be designated by the Roman numerals I, II... XX in the 
order in which they were carried out, and the 63 observations* in a series by the 
letters 
y-i, ■■•yt--- ym- 
In dealing with each Experiment one of the first objects will be to ascertain 
whether there is any correlation between successive judgments, and the manner in 
which this correlation, if existent, fells off as the interval between the judgments 
correlated is increased. To obtain these coefficients of correlation it is necessary 
* The first 7 observations, see footnote, p. 28, being always disregarded. 
