84 
On the Variations in Personal Equation 
100 
The factiir for a true 10 second interval would be 
10-2 
98, and was most 
nearly approached by the means of Series V, VII and IX, while in the case of 
XVII the mean estimation nearly reached the high value of 15 seconds. 
Distribution of Personal Equation in Estimating Seconds. 
2 00 
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1S 19 20 
PLACE OF SERIES IN ORDER 
Fig. 19. 
{h) TJie Combination of the Series. 
In combining the twenty series, D/,, Sk and R^. were calculated from the thirteen 
correlation tables of the observations of the combined series. Using the correlations 
and standard deviations of the separate series, R/ is obtained from 
2(/C>iO-i(T2) 
R/= — T^if— === + -19841 ± -02049 (x) bis, 
and 
V III 111 
^i' = -14101, S.; = -U056. 
Then using this value of R/, and the first difference correlation equations 
(Problem 1, p. 41), R/ can be calculated for k = 2,...12. The values of these 
quantities are given in the Table XVI below. 
