Egon S. Pearson 
75 
giving partial correlation coefficients 
rxy.z = + -022 ± -151, = - -271 ± -140. 
The secular change corresponds to a gradual decrease in estimate thi'oughout 
the course of the experiment; the value of the factor e/p for a true 10 second 
estimate would be = "98, and this was closely approached by the means 
of the first three series, which were carried out on the first day, shortly after trial 
counts had been made with a watch. No further check with a watch was made 
during the succeeding days, and the length of estimation decreased and finally 
appears to have reached a fairly steady value at about "88. The mean for the 
20 Series was -9186, or a count of 9'87 seconds. 
TABLE XII. 
Constants of Individual Series (Counting Seconds). 
Series 
Pi 
Date (1920) 
Time at Start 
I 
■9786 
•04030 
+ -5283 
■0391 
13 December 
( 2.30 p.m. 
II 
1-0140 
•04331 
+ ^4988 
•0434 
n 
)» 
3.15 p.m. 
III 
•9998 
•03844 
+ ■0625 
■0526 
( 3.45 p.m. 
IV 
•9446 
•03732 
+ -4027 
•0408 
14 December 
•10.15 a.m. 
V 
•9128 
•03394 
+ ^4378 
•0360 
» 
11.20c\.m. 
VI 
•9090 
•03015 
+ ^5437 
•0288 
12.0 noon 
VII 
1^0070 
•03981 
+ •3819 
•0443 
2.30 p.m. 
VIII 
•9012 
■02488 
+ -4550 
•0260 
J) 
3.5 p.m. 
IX 
•8886 
•03934 
+ -4326 
•0419 
15 December 
3.35 p.m. 
X 
•9030 
■02851 
+ ^5439 
•0272 
'lO.Oa.m. 
XI 
■9130 
•02982 
+ •5326 
■0288 
5» 
11 
10.35 a.m. 
XII 
•8774 
•01852 
+ -2850 
■0221 
11.10 a.m. 
XIII 
■9046 
•02402 
+ ^4894 
■0243 
11 
11.50 a.m. 
XIV 
■9464 
•02903 
+ ^5085 
■0288 
11 
2.30 p.m. 
XV 
•8880 
•04162 
+ ^7589 
■0289 
11 
16 December 
3.5 p.m. 
XVI 
■8812 
•04947 
+ ^8549 
■0266 
ho.Oa.m. 
XVII 
•8828 
■03945 
+ ^6566 
•0327 
11 
10.30 a.m. 
XVIII 
•8872 
•02750 
+ ^5406 
•0264 
] 11.5 a.m. 
XIX 
•8468 
■02486 
+ •I 266 
■0329 
11 
11.35 a.m. 
XX 
•8864 
■03345 
+ ^6369 
•0285 
11 
I12.IO p.m. 
Probable Errors of 
Coefficients of Corre- 
lation calculated from 
50 pairs of the vari- 
ates. 
p 
P.E. 
■80 
+ ^0343 
•70 
+ •0486 
•60 
+ ^0610 
•50 
+ •0715 
•40 
+ ^0801 
•30 
+ ^0868 
•20 
+ -0916 
•10 
+ ^0944 
•00 
+ -0954 
With the interpretation of p. 54, the insignificant value of the coefficient 
'>^xy.z> suggests that for a number of series done in quick succession, there will be 
no change in personal equation ; we shall therefore not expect to find any large 
general sessional change in the series. The diagram of mean sessional change is 
given in Figure 14, where yt is plotted to t. 
The equation of the straight line best fitting the points is 
yt - -919 = + -0000731 - 32) (xxxviii), 
and has been drawn in Figure 14. 
Using the relations and interpretation of page 48, it is found that 
7)y, = -212 + -018 and VF- = '977, 
