52 
On the Variations in Personal Equation 
equal, but though there is in general a considerable reduction, it is clear that 
neither a linear sessional change nor a parabolic one of the form represented by 
equation (xxx) account for the greater part of the correlation of successive judg- 
ments. 
The coefficients and also vary considerably from series to series, but there 
is no very marked progressive secular change. On the whole both and p/ are 
large when the standard deviation is large, and a measure of this correspondence 
will be given by the correlation of p and a. This can be obtained most readily, and 
with sufficient accuracy for the purpose, from the correlation of the ranks of these 
variates, by the method referred to in Biometrika, Vol. x. p. 416*. 
The results are 
correlation between and cTj + 52 ±11 = rpa, 
„ „ pi and ai + '60 + '10 =^r'pa- 
The difference is not significant, and we may draw the conclusion which could not 
have been assumed a priori, that the correlation of successive judgments is larger 
when the variations in judgment are larger, and that this relationship does not 
appear to be reduced when the large linear sessional change has been removed. 
Large values of o- might have implied erratic observation and small relation between 
TABLE IV. Constants of Individual Series {Trisection). 
(The definition of these constants is given on p. 35.) 
1 
2 
3 
4 
5 
6 
7 
8 
Series 
di 
h 
Pi' 
I 
2-6238 
+ 
•000673 
+ 
•2925 
+ 
•3008 
•06015 
•06093 
•0721 
II 
•7036 
•002964 
+ 
•4149 
+ 
•5485 
•08125 
■09182 
•0873 
III 
•6350 
•003626 
+ 
•3643 
+ 
■5560 
■08001 
■09561 
■0901 
IV 
•5114 
+ 
•001718 
•2521 
■0460 
•05356 
•05902 
■0854 
V 
■5309 
•001555 
+ 
•2520 
+ 
■3234 
■06853 
•07210 
■0839 
VI 
•5132 
•001529 
+ 
•2270 
+ 
■3390 
■05495 
•05921 
■0681 
VII 
•6448 
•004244 
+ 
•4918 
+ 
■6457 
■09322 
•111.54 
•0939 
VIII 
•5314 
•002788 
+ 
•5478 
+ 
•6089 
•11369 
•12060 
■1067 
IX 
■3404 
•004477 
+ 
•4979 
+ 
•7075 
•07935 
•10233 
■0783 
X 
•5590 
•000036 
+ 
•7151 
+ 
•7151 
•11141 
•11141 
•0841 
XI 
■4582 
■000972 
+ 
•7320 
+ 
•7381 
•08317 
•08435 
•0610 
XII 
•5014 
•002720 
+ 
•4851 
+ 
•6360 
•05923 
■07105 
•0606 
XIII 
•4752 
■003594 
+ 
•5101 
+ 
•6897 
•06409 
■08244 
•0649 
XIV 
•5000 
■003818 
+ 
•6433 
+ 
•7965 
•05993 
■08141 
•0519 
XV 
•4290 
■005588 
+ 
•6810 
+ 
•8568 
•07051 
■10711 
•0573 
XVI 
•4390 
■003071 
+ 
•6408 
+ 
•7412 
•06441 
•07819 
•0562 
XVII 
•4254 
•004369 
+ 
2569 
+ 
•6556 
•05840 
•08594 
•0713 
XVIII 
•3944 
•000580 
+ 
•2870 
+ 
•3144 
•04568 
•04644 
■0544 
XIX 
•3700 
•003236 
+ 
•4935 
+ 
•7219 
•05107 
•06920 
•0516 
XX 
2^3666 
•001725 
+ 
•2850 
+ 
•5072 
•03680 
•04443 
•0441 
Mean value ofb=- •002425. 
* The theory is based ou the hypothesis that the variates follow a normal distribution, and though 
tills may not be strictly true for the pi's and <j\s the method probably gives a sufiiciently accurate 
approximation to the value of their correlation. 
