XLIV| lntnnlin-t'i,ni CCXV 



Hence the v.-iliu- of tli<- ronvl.-it.ioii riM-lli-i,-ni lor tin- deviations uf /^ and /, from 

 their secular trends is 



N 2-072,885 2-402,779 



*m$ 

 = -r>53, 



or, the correction is a very slight om . 



Many criticisms may be made of the above method; it is Dodoabtedlj nly a 

 suggestion, but it is, perhaps, the best we can at present use, if we wish to avoid 

 the great labour and rather uncertain results of smoothing or of h'tting high 

 order parabolae to give the secular trends. It depends upon three assumptions : 



2 



<r A "x o+'K {A'^JA^K} . /. 2 \ 

 (i) that the three ratios of = -- , = -- , - rAmVAtI1 r, to 4 - - 



ff AX *Ar {A M ;YA n 7} n + U 



approximate to finite limits; 



(ii) that we can obtain these limits by averaging when the values of the 

 above expressions begin to vary up and down ; 



(iii) that the series of correlations with geometrical decadence which give 



2 



the same deviation from 4 -- may be used to correct for the unascertained 



n+ 1 



correlations between non-corresponding values of X p , of Y p , and of X p with Y p . 



Illustration (iii). The following results were obtained by K. Pearson and 

 E. M. Elderton* for the relationship of death-rates, m t and w 2 , in the first and 

 second years of life for male and female infants : 



Male Female 



= -'696, --729, 



r5 = 7* A 8, n A , M = "679, "705, 



2 

 6 R,= V : 3-759,913, 3-734,666, 



5 #i = V' m ' = 3-756,029, 3-733,655, 

 AX 



a* 

 6 # 2 = A '"' a = 3-858,841, 3-844,977, 



= 3-847,871, 3-827,945. 



* Biometrika, Vol. x. pp. 488 506, and Vol. XIT. pp. 281 310. It had not occurred to me when 

 writing up the paper last referred to, that, while the hypothesis of geometrical decadence might be far 

 from true as expressing the intercorrelations of the non -corresponding A"s and PR, it might still serve 

 to make approximate corrections for such intercorrelationn. 



