314 



POPULATIONS 



from 1790 through 1940 fit the smoothed 

 curve with a high degree of fidelity. They 

 show that the population has increased from 

 3,929,000 persons in 1790 to 131,410,000 

 persons in 1940; an increase exceeding 33.4 

 times. (The calculated values are, respec- 

 tively, 3,730,000 and 132,756,000.) 



A word is here appropriate about the use 

 of the logistic curve in the prediction of 

 future population size. In 1920 Pearl and 

 Reed reported a curve that described the 

 United States population through the 1910 

 census. It is of interest to compare this lo- 



106) predicts for the same year an asymp- 

 totic population of about 184,000,000 per- 

 sons. This difference of 13,274,000 indi- 

 viduals results from the inclusion of three 

 more observed points (the 1920, 1930, and 

 1940 censuses) in the computations. Thus 

 there is danger, as common sense dictates, 

 in accepting an extrapolation too literally. 

 On the other hand, extrapolation is un- 

 doubtedly of more value than pure guess- 

 work. * 



Figure 107, adapted from Pearl and 

 Gould (1936), is a logistic curve fitted to 



2800 



Fig. 



1650 1700 '50 1800 '50 1900 '50 2000 '50 2100 



YEARS 



107. The logistic curve fitted to an interval of recorded data from the population of the 

 world. (From Pearl and Gould.) 



gistic with Figure 106, which is corrected 

 by the actual observations through 1940, 

 and to examine the difference between the 

 two. The first curve missed the counted 

 population by "16 parts in a thousand in ex- 

 cess in 1920; by 2.5 parts in a thousand in 

 defect in 1930, and by S7.3 parts in a thou- 

 sand in excess in 1940. The error in 1940 

 is of perhaps about the same order of mag- 

 nitude as that probably inherent in the 

 count itself. But it is considerably larger 

 than that made by the curve in either 1920 

 or 1930." The first curve predicted an 

 asymptotic population of about 197,274,000 

 persons in 2100. The second c"»-ve (Fig. 



known census data for the world from the 

 seventeenth century to 1931-1932. The 

 observed points cover roughly one-half the 

 total span of the curve. The lower asymp- 

 tote occurs at about year 1650, at which 

 ** Should the reader wish to pursue further 

 this question of prediction, his attention is 

 called to the paper of Whelpton (1936), which 

 approaches the question from a different point 

 of view. Here the author attempts to arrive at 

 the future course of the population, not through 

 the use of a theoretical function such as the 

 logistic curve, but through certain assumptions 

 about reproduction and mortality and then 

 ( >lc'iIatintT empirically the population increase 

 on the basis of these assumptions. 



