290 lotka: a natural population norm 



In the numerical case here considered Tj^ = 0.01431, 



n = 0.01373. 



This gives, for the ratio ~zrr- the computed value 1.045, as against 



the observed value 1.054. 



III. Age-distribution at death. (3) we have for the total num- 

 ber of deaths between the age-limits and oo 



D = -Nb ^e-'^i){a)da (13) 



Similarly, between the age-limits a and (a + da) 



--^ da = — -- e-^"" p (a) da (14) 



da d 



Introducing a coefficient of age-distribution at death, defined in a 

 manner analogous to that applied to the living population, but 

 denoted by c'{a), this gives 



c'{a) = --e-"p(a) (15) 



d 



To find the proportion of deaths between the ages ai and az 

 we integrate 



\ c'{a) da = I e-^^ p (a) da (16) 



= -^[e-p(a)l"-f^ \^c{a)da (17) 



L J ai b iJ 0.1 



The last integral has already been computed in determining the 

 age-distribution in life, so that we can now readily calculate the 

 age-distribution at death. As a matter of fact, in the process of 

 computing the age-distribution in life many of the data required 



for computing e~'* p (a) 



aj 



by series are obtained, so that the work 



is largely disposed of. The computation was carried out for males 

 only. The results obtained are shown in Table V and figure 5. 

 Here again the agreement between the observed and calculated 

 values is very close. 



