ECtON S. Pearson 
35 
where 0 (r^,) represents the secular term which we take as constant for aill the 
observations of the ^th Series, and fp{t) gives the sessional change, then 8^' will 
be the standard deviation of the 1000 residuals in the twenty 1st Groups, Sk' of 
the 1000 residuals in the twenty kth. Groups, etc., so that 
the mean of the residuals being zero, and m = 20, n = 50 again ; while the corre- 
lation of the successive residuals at intervals of k, after the removal of secular and 
sessional terms, or R^." will be given by 
--2i(F,F,+,) 
R-t = oTT^TT (Xll). 
Table of Constants. 
In the following table definitions are given of the most important of the 
constants referred to in the preceding section and of others to be introduced 
in the sequel. 
1. The ^th Group of the /)th Series consists of the 50 observations 
As each Series consists of 63 observations, there are 14< Groups in each of the 
20 Series, 
n will often be used for 50, the number of observations in a Group, 
m „ „ 20 „ „ Series. 
2. The crude Observatioiiti. 
(a) For the jjth Series. 
d -= mean of the whole 63 observations. 
pdk = mean of observations in kth Group. 
pO-/; = standard deviation of observations in kth Group. 
pPk = coefficient of correlation between corresponding observations of Groups 1 
and k+1, i.e. between p-iji and pi/k+\, plIi and ^T/t+o, etc. 
pCTs = standard deviation of the first forward differences of the observations in 
Group 1, i.e. of py,- py^, py, - py^.-.py,^ - py,o- 
p6 = slope of the straight line y — pdi = — '^ ^) ^^'^^"^'^ "best" the 
50 observations py^, py.2, ... pyt, ••• i)yn of Group 1. 
pCTj;' = standard deviation of residuals left after the ordinates of this " best " 
fitting straight line have been subtracted from the observations of Group k. 
pPk = coefficient of correlation between these residuals of Group 1 and Group 
k+\. 
