54 
On the Variations in Personal Equation 
we have for the regression straight line o{ x on y 
X - 2-4976 = - -01351 (// - 10-5) (xxxii), 
and for the regression of x on z 
X- 2-4976 = - -00233 {z - 53-05) (xxxiii), 
and these lines have been drawn in the diagram. 
The corresponding coefficients of correlation between (1) personal equation and 
order, (2) personal equation and time, and (3) time and order, a meaningless 
coefficient but required to find the partial correlations, are 
(1) r,,, = - -800 + -054, 
(2) r.,, = - -692 + -079, 
(3) = + -882 + -033, 
and the partial correlations are 
rvv..---559 ± -104, 
= + -049 ± -150. 
But the intei-val between the May and July sei'ies was so large, that the series 
should perhaps be considered as forming two groups, one of six and the other of 
fourteen. Taking the last fourteen series, we have the regression lines 
- 2-4596 = - '01346 {y - 7-5), 
the Series VII being given the order 1, VIII, 2 etc., and 
,r - 2-4596 = - -01048 - 6-64), 
z being the days between 10th July and date of Series. These lines have also been 
drawn on the diagrams. 
The correlations are 
(1) r,,, = --674 + -098, 
(2) = - -673 + -099, 
(3) = + -956 + -010, 
giving partial correlations i-^,,.^ = — -143-^ -177, 
,-,.,. , = - -138 ± -177. 
The point of interest is this : there is a secular change in personal equation 
from series to series ; is this change more closely related to the number of series 
or sessions that have gone before (that is, almost, to the experience gained), or is 
it due to some change with time in the observer's outlook ? Suppose that it was 
arranged to carry out observations on a number of different days with varying 
intervals of time between them, and that on each day a certain number of different 
series of observations or sessions were undertaken at regular intervals of perhaps 
an hour or less ; any series could then be classified as the j>th series of the qih 
day. Then ?Vy ^ (the partial correlation of personal equation and order, time being 
kept constant) would give a measure of the relationship between change in personal 
equation and order of series in any one A-aj. This will not necessarily be the same 
