Egon S. Pearson 
67 
The dates on which the series were carried out — the za — are given at the end 
of Table IX ; the distribution was more satisfoctory than that of the Trisections, 
and the significance of these two partial correlations will be referred to shortly. 
The variation in the means of the series is much smaller than in the case of 
the Trisections ; we have here a range from 2"93 to 2"80 ins. while in the other, 
from 2'70 to 2'34 ins.; in both cases the secular change is in the direction which 
lessens the measures, i.e. the marks on the forms in the later series were on the 
whole further to the observer's left hand than in the earlier series. Nor does 
experience appear to increase accuracy, for the true position of the half is at 2'97 
inches (and of the third at 2-51 inches). 
_ 11 13 15 17 19 
10 12 14 16 18 20 
Personal Equation — 
Ol der of Series. 
1 ~5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 
3^ 7 11 15 19 23 2 7 31 35 3 9 4 3 4 7 51 5 5 59 63 67 71 
Personal Equation. {Mean of 1st 50 observations of 
series) — Time {days from 13th June). 
Fig. 9. Bisection. Means of Groups 1 of each series plotted with Order of Series and Date of Series. 
Next considering the sessional change, the values of yt (defined on p. 47) have 
been plotted in Figure 10 ; the straight line " best " fitting these points is 
Tjt - 2-8816 = + -0003534 (t - '32) (xli), 
where t is the order of observation in a series, and the cocfiicient of correlation 
between J/t and t is + -5294 + -0137*. 
Using the relations of page 48, it is found that 
= •271 ±-018, Vl -7?-,, 
-963. 
and on comparing this latter value with that for the Trisections (-815) we see 
that in the present case the mean sessional change is of less significance. 
inches 
2-91 
290 
2 89 
2 8B 
287 
2 86 
2 85 
^ c Diagram of Mean Sessional Change 
- • 
Mean, at •J'Ssid inches 
-Regression /7^-'J-881(;= +-0(J03.'-)34 (/-f!'2) 
The value of the true half is '2'97 inches 
1 10 20 30 40 50 60 
Fig. 10. Bisection, t. Order of Observation in Series. 
It will be noticed in looking at Figure 10 that the points (t, J/t) appear to be 
subject to a fiiirly consistent periodic variation about the regression line, the 
* This correlation between the mean fth observation (y,) and t must be distinguished from the 
correlation between the tth observation {ij,) and t, which is + ■143, and as it should be, less than rj. 
5—2 
