Egon S. Pearson 
95 
series represented by Figure 4 may well be expected to hold approximately in the 
individual series. 
If then pk is constant for A; = 1, 2, ... 14 and equals j), we find readily from 
equations (lii) and (Iv) that 
h^'^- Pk=^- p, 
and hence (l - p) Rk' = qr^ or R/'= ^ -? r*. 
1 — p 
Making use of the numerical values = "1.524, f/ = "6817, ?•= 7105 we obtain 
finally 
R/ = -8043 (•7105)^- (Ivi), 
as the theoretical expression for the correlation of the successive residuals after 
the observations have been freed from secular and sessional change. This curve is 
the lower of the two curves drawn in Figure 8. The points which are there 
plotted about this curve are the points {k, R^")* obtained from equation (lii) 
(a) On the assumption that G-c = G^-= ... = = constant, 
= 1524, 
(c) Making use of equations (liv) and the tabled values of »SV. 
The close fit of the curve to these points shows that the manner in which the 
values of Rfc" fall off as k increases is not much affected by the different assump- 
tions regarding the relations of the »Vs and the Gk's made in the two cases f. 
Experiment B. 
Reference has been made on p. 71 to evidence for a slight periodicity in the 
observations of this Experiment, which gives rise to small but apparently signi- 
ficant negative values to R/, for k%l. Further investigation might enable a 
correction for this periodicity to be made, but at present it is not possible to 
express R^" with exactness in the form 
'Rk = qr''. 
For the purpose of comparison with the other experiments we can however 
obtain values of q and r which will give a rough fit for the first few values of R<;'. 
Thus if we take 
r = -72, q = -47 +, 
we get the values 
R/ = -34, r; = -24, r; = -18, r; = 13, 
which agree roughly with the actual values given in Table XI, namely 
R/ = -352, r; = -231, R/ = 183, R4' = -085. 
* In Figure 8 these points have been indicated by Rj.'" to distinguish them from the correlation 
coefficients of residuals after removal of linear sessional change, there denoted by Bj.". 
t The values of R^' calculated from equation (Ivi) and of and £.y calculated on the assumption 
of the constancy of Gjt are given in the 8th, 7th and 6th columns of Table XVIII. 
% r = -72 is the value of the mean of the ratios ~, , and ^\ , and using this value for r, 
g was taken as -47 by rough trial. 
