ccxvi Tables for Statisticians and Biovtietricians [XLI V 



Clearly we shall have 



whence we find with the above numerical values 



6 Z? 3 = 3-853,335 and 5 3 = 3'852,063 for males, 

 6 # 3 = 3-842,124 and 5 R 3 = 3'855,580 for females. 



Thus we see that 6 Ri, 6 Ri, 6 # 2 , 5^2, 6^3 and 5 -R 3 for both males and females exceed 



2 



the limiting value 4 -- r for seventh, sixth and fifth differences, and we are 

 + l 



compelled to suppose correlations to exist between X p (=mj) and X p Sy Y p (=mz) 

 and Yp s , and X p and Y p g . The existence of such correlations has been directly 

 verified*. Their values are somewhat erratic and soon become, having regard to 

 their probable errors, non-significant. Let us investigate what corrections would 

 be made on the crude mortality correlations, such as '696 and '729, if we 

 supposed the law of geometrical decadence to hold for the intercorrelations of 

 the X's together, of the Y's together, and of the X's and F's together. Even if 

 such correlations be not truly geometrically decadent, such an inquiry may aid 

 us in appreciating their general influence. 



We have twelve e's to find, namely for males : 6 6/ for 6 R it 6 ei for BJ R 1} 6 ei" for 

 6 .R 2 , 561" for 6 .R 2 and again 6 6i for 6 R 3 and 5 e! for 5 K 3 . From these we must again 

 deduce from Table XLIV the corresponding six values of the function 2< (n, e) 1, 

 in all cases using the appropriate column for n. We can, as soon as we have 

 recognised that all the .R-ratios are above the limiting value, proceed directly to 

 the determination of the 2<f>(n, e) 1 functions without computing the e's. But the 

 e's indicate a sort of average intensity for the X p and X p+s , the Y p and Y p+g , and 

 finally by aid of p Q = ^A n ZA n y f r ^ e -^P ari( ^ ^P+* correlations. 



Similarly for the females we shall have six corresponding e's and their allied 

 functions. We have 6 e 2 ', 5 e 2 ', 6 e 2 ", 5 e 2 ", 6 e 2 and 5 e 2 . 



We shall use linear interpolation only, and while working with the complete 

 number of decimals in the Table, state our final results to three decimals only. 

 We obtain the following results : 



Male 



(Values of 20 (n, e) - 1) 



6 e,' = - '267,856, 1-549,245, 



eei " = - -637,475-, 2-683,733, 



^ =--620,955, 2-619,391, 



5l ' = - -381,866, 1-799,045, 



56l " = _ -652,259, 2-611,364, 



=-'663,217, 2-649,204. 



Female 



(Values of 2<f> (n, e) - 1) 



6 e 2 ' =--133,576, 1-252,179, 



6 e 2 " = - -595,411, 2-522,016, 



6 e 2 =--585,882, 2-489,286, 



5 e a ' = - -303,108, 1-603,727, 



5<?2 " = _ -600,188, 2-431,553, 



5 e 2 =_ -672,220, 2'680,293. 



See note on p. ccxv. 



