XLIV] lutroilni'limi ocxiii 



588 



= : 78-729x3780 



= 3-471. 

 o 



But the value of 4 - - = 3714. 



n + I 



Thus we might expect a correlation to exist between X n and X n + t , and Y n and 

 F n+t ; but such a correlation is not evidenced by the value 3'471 for the ratio of 

 the difference products, for this is less than 3714. Accordingly we cannot assume 

 from this result that X p and Y p+l , when 8 is not zero, are correlated according to 

 geometrical decadence. 



Interpolating roughly into the Table we find for 7^ and 7 T respectively 



e' = --1009, e" = -'3583. 



Thus if we may judge by geometrical decadence there is a small negative correlation 

 between the phthisis death-rates for two successive years, and a somewhat larger 

 negative correlation between the pauper segregation rates. 



But the student needs to be warned that such values are only suggestive ; the 

 probable errors of short scries of these higher difference correlations are so large 

 that with the short series of indices generally available*, the results are very likely 

 to be erratic. Thus if we take the 7th and 8th differences we find 



-a = 3-802, -_j r = 3-843, 4-- - = 3750, 

 a \'I^ *tf/ T n + l 



and r A%,A7 T = '557, r A 7/^ A 7 /T = '539, 



and consequently 



2 

 Here all our three quantities exceed 4 -, and the correlation between A' 



71 + 1 



and Y p+ i, on the hypothesis of geometrical decadence, exceeds numerically 0*7, 

 while we found any geometrical decadence correlation impossible on the basis of 

 the 6th and 7th differences. 



This illustrates how difficult it may sometimes be to reach a valid conclusion 

 from the ratio of two successive difference values. 



The probable errors of the correlation coefficients of differences exceed '150, and 

 an examination of their valuesf indicates that 



is already practically stable when s = 2 ! 



* Yearly indices for social, economic, or hyi^ienic data are scarcely obtainable for as many as fifty 

 years. f /.'/o/m/r/A-,/, Vol. x. pp. 348 :M'.i. 



