lotka: a natural population norm 



289 



VITAL STATISTICS.— A natural population norm.' II. 

 Alfred J. Lotka. Communicated by G. K. Burgess. 



II. Proportion of sexes. In addition to the features discussed 

 in part I of this paper, Table III also shows the calculated and 

 observed ratio of the total number of females to that of males 

 in the population. The calculated figure is obtained as follows: 



Let Bra be the total number of male birth per annum, and Nm 

 the total number of males in the population. Let B{, N{ similarly 

 refer to females. Then b^, hi, the male and female birthrates 

 per head per annum, are defined respectively by 



&m = 





Hence 



N^ 

 N^ 





B^ h 



(8) 



(9) 



Bi 



Now — , the proportion of female births to male births, is 



Bra 



a characteristic constant of the population, and in the case under 



1 



consideration its value was 



1 . \joo2i 



bjn, b{ we have by (4) and Table I 



Hence (9) becomes 



Ni 



= 0.9632. For the values of 



= 41.35 - 1312r^ + 



44.62 - 1467rf + 



(10)^ 



A. 



= 0.9632 



= 1.0395 



44.62 - 1467rf 

 41.35 - 13"l2r„, 



1 - 32.878rf ) 

 r^31.729r„i 



(11) 



ri2) 



1 See this Journal 3: 241-248. 1913. 



- The convergence of the series (10) is such that in the computation of 6 and of 

 c (a) seven terms had to be retained; but the quotient (12) is much more rapidly- 

 convergent, so that only two terms are here required. 



