36 
Oil the Variations in Personal Equation 
In the reduction of the results of the experiments, unless it is necessary to 
specify a particular series, the prefix p before these constants will usually be 
omitted for brevity. 
{h) For the combined 20 series. 
D = mean of the whole 1260 (= 20 x 63) observations of an experiment. 
Dj; — mean of the 1000 observations in the combined ^th Groups of the 
20 series. 
S,. = standard deviation of the 1000 observations in the combined kth Group 
of the 20 series. 
Rt = coefficient of correlation between the 1000 observations in the 1st Groups 
and the 1000 corresponding observations in the k+ 1th Groups. 
^,7^^. = coefficient of correlation between the 1000 sth forward differences of the 
observations in the 1st Groups and the corresponding differences of the obser- 
vations in the k + 1th Groups. 
Ss = standard deviation of the 1000 tirst forward differences of the obser- 
vations in the 1st Groups. 
3. The Observations freed from the Secular Change. 
The " secular term " in the observation considered as a member of the kth 
Group is pd-k. Thus the mean of the 1000 observations in the kth. Groups each 
freed from its secular term will be zero. 
>S'i.' = standard deviation of the 1000 observations (freed from secular term) in 
the /i;tli Groups. 
Rfc' - coefficient of correlation between the 1000 observations in the 1st Groups 
and the 1000 corresponding observations in the k + 1th Gi-oups (all freed from 
secular term). 
4. 'Ihe Observations freed from both Secidar and Sessional Change. 
y ~fp (^) curve representing the sessional change in the pth Series, 
so that fp (t) is the " sessional term " in pyt, the tth observation in the 2Jth Series. 
yl'f = the residual left after removing the secular and sessional terms from pyt. 
Sic" = standard deviation of the 1000 F's in the ^:th Groups. 
R/;" = coefficient of correlation between the 1000 F's in the 1st Groups and 
the corresponding 1000 F's in the k+ 1th Groups. 
jjOt = the part of pYt representing the actual estimate which the observer 
wishes to record. 
p/3t = the part of pYt representing a complex of accidental errors superimposed 
on pOfj in the process of record. 
Gk = standard deviation of the sessional terms in the 1000 observations of the 
kth Groups. 
Fi; = 1st order product moment coefficient about the mean of these sessional 
terms in the 1st Groups and the corresponding terms in the k 1th Groups. 
