Egon S. Pearson 
85 
The fall in is small, and although there is considerable irregular variation 
from R7 onwards, it appears that R^. will not vanish as k increases, but approach a 
constant value in the neighbourhood of + -35. This can be tested ; we have from 
the equations (vi) to (x) 
'RkS^S'k+, + - 2 - d,) (Dk+i - dk+i) 
R, = -— "' ■ (xliii), 
V (_ III J )» ) 
TABLE XVI. 
Constants of Combined Series (Estimating Seconds). 
k=i 
2 
3 
4 
0 
6 
7 
8 
9 
10 
11 
12 
13 
1-1421 
1-1440 
1^1415 
M413 
1-1421 
1-1423 
1-1416 
1-1402 
1-1395 
1-1391 
1-1382 
M378 
M351 
Sk 
-1749 
± -0026 
•1749 
± -0026 
•1759 
± ^0027 
•1761 
± ^0027 
•1764 
± -0027 
-1760 
± -0027 
-1754 
± -0026 
-1757 
± -0026 
-1763 
± -0027 
-1756 
± -0026 
•1760 
± -0027 
•1767 
± ^002 7 
•1773 
±•0027 
R«; 
+ -4825 
± -0164 
-4269 
±•0174 
•3965 
±•0180 
•3913 
±•0181 
-3764 
±-0183 
-3755 
±-0183 
•3983 
±•0180 
-4045 
±•0178 
-3488 
±•0187 
-3691 
+ -0184 
•3524 
±•0187 
•3831 
±•0182 
Sk 
-14101 
± -00213 
•14056 
±•00212 
Rk' 
+ -19841 
± -02049 
+ •1123 
±•0211 
+ •0652 
±•0212 
+ ^0570 
± ^0212 
+ -0338 
± -0213 
+ -0332 
± -0213 
+ ^0693 
±•0212 
+ -0798 
±-0212 
- -0056 
± 0213 
+ -0267 
±0213 
+ ■0017 
±■0213 
+ •0501 
±■0213 
iRk 
- -4463 
- ^0243 
- ^0243 
+ -0094 
- -0135 
- -0229 
+ •0160 
+ -0598 
- -0734 
+ -0357 
- •0458 
. ,S'fi = »S','v'2(l-Bi') = ^1785. 
and as the sessional change for the series is very small, we may make the approxi- 
mation 
S (A - d,) (A+1 - 4+0 = S ( A - d,y = 2 ( A+i - 4+0^ for all values of k, 
m m III 
and in view of the constancy of Sk, 
Si = S'k+i for all values of k. 
Then on the assumption that there is no significant periodic variation in the 
observations, 
Hk 0 as k increases, 
- 2 (A - d,y 
and from (xliii) R^. — = + -.354. 
s,'"-+^^(D,-d,r 
III m 
The correlations R^' become rapidly insignificant ; the values tabulated are of 
course subject to the errors of the method of approximation, but as in the case of 
the 10 second Counting Experiment, these should not be large owing to the 
constancy of Sk*. The points {k, Hk) and {k, Rk) are plotted in Figure 20 ; the two 
curves there drawn will be referred to in Section XI below. 
■*■ The difference between Si and .S'i:j is one of only. 
