44 On the Variations in Personal Equation 
1st order product moment coefficient, for the m combined series*, of successive 
first differences at intervals of h is given by 
mn „i t=\ 
_ _l |s f- 6 + 1 Is f- 6 + 5±tlZLl^A| 
Or finally, 
,P, = (- R,_/' + 2R," - R,+;') 8"-^ -Qu-h" (xxvii). 
making the assumptions (a), (6), and (c) of p. 37, and where 
2. v/p is the standard deviation of the Vs. 
There will be similar corrected expressions for the standard deviations of the 
combined first differences. 
If we are justified in neglecting terms of the order of + h-, we may use the 
first difference equations, 
Rjt_i -I- 2Rj. — Hk+i 
~ 2(1- R,) 
-R,_/'-f2R,"-R,+/' /^,^i^2....-l 
.(xxviii), 
2(l-R/0 
where, as in Problem 1, the known R^'s will give the iR^'s, and it will only be 
necessary to calculate dii-ectly the one quantity R/', in order to obtain 
R,", R/' ... R,". 
Problem S. In the last illustration it may happen that while Qk + V is so 
small as to cause only a negligible error in the value of R," found from 
j3 — 1 -f 2Ri ' — Ra" 
litj = — 
2(1-R/') 
* ph is the slope of best fitting line in the pth Series. 
