Vol. 8, 1922 
STATISTICS: A. J. LOTKA 
345 
2 These circumstances are : (a) an invariable life curve ("life table) ; (jb) an invariable 
ratio of male to female births; (c) an invariable rate per head of procreation at each 
year of age, for any given sex-and-age distribution in the population. 
3Lotka, Amer. J. Sci.; 26, 1907 {21); Ibid., 24 (199); /. Wash. Acad. Set., 3, 1913 
(241, 289). 
4 Sharpe, F. R., and Lotka, A. J., Phil. Mag., April 1911, 435. 
° A certain ambiguity is introduced here by the fact that, with /3(a) of. variable form, 
equation (4) might have more than one real root for r. In practice, however, in a human 
population at any rate, probably only one such root exists, or has any effect upon the 
course of events. 
