ccxii Tables for Statisticians and Biometricians [XLIV 



for each pair of cases before determining the small type functions. Now for 



Bail and Coal Bail and Coffee Coal and Coffee 



r AX p AY p = + ' 383 ' 214 > ~ ' 204 ' 240 > -I" * 152 ' 245 > 



r A 5 ZpA 5 rp = + '402 -197, - -139 -232, + -163 '230. 



Most of these correlations do not differ significantly from zero, but retaining them 

 for the purposes of illustration we shall need 



Kail Coal Coffee 



q-A%, = 28-84 120-50 59'52 



<r A 5 Zp ~ 14-97 ' 62-80 ' 30-57 ' 



1-92652, 1-91879, 1-94701. 

 From these ratios and from the ratios of the corresponding correlation coefficients 



given above we deduce 



Bail and Coal Bail and Coffee Coal and Coffee 



Two of these values lie below, one above the range of values in Table XLIV for the 

 column n = 5. It is therefore not possible to express the relationship, if there be 

 any, in these cases between X p and Yp g by a geometrical decadence. An exami- 

 nation of the correlations r^s x A 5 r an( ^ r ti>K A 6 r sno \YS that, having regard to 

 their probable errors, they are wholly unreliable in at least four out of the six 

 cases. Twenty-eight individual indices for each variate are far from adequate when 

 we must proceed to sixth order differences before the constants approach stability. 



All we are justified in concluding from the above data is that while geometrical 

 decadence may be approximately true for the Rail and Coffee Indices, and to a 

 minor extent for the Coal Index, treated by themselves, it will not suffice at any 

 rate without the introduction of lag to modify the intercorrelations of Rail, Coal 

 and Coffee Indices with one another. 



Illustration (ii). The following data are taken from a paper by Dr Alice Lee* 

 dealing with Sir Arthur Newsholme's suggested influence of segregation on the 

 death-rate from phthisis. /$ = crude death-rate from phthisis = 10 5 x deaths from 

 phthisis -T- total population. I T = & measure of segregation = 100 x total paupers 

 -=- indoor paupers. These indices of Sir Arthur Newsholme were found by Dr Lee 

 in the case of England and Wales for the years 1866 1903 inclusive. For n=6 she 

 reached the results 



-^ = 3-729, "-f^ = 3-780, 



CT A fi / " A 6 / T 



while r A 7/ A 7/ = '539, 



.coo 

 A / A G 7 ~ dV'J' 



* Biometrika, Vol. x. pp. 538 and 546. 



