6oO , TRANS. ST. LOUIS ACAD. SCIENCE. 



fluctuating than in older and longer settled countries. Since, 

 however, the only trustworthy means of predicting the popula- 

 tion for the future consists in reasoning from the law of growth 

 in the past, it has seemed to me an interesting question to see 

 how nearly the data already at hand could be represented by 

 a mathematical function. 



The data available for this discussion, up to December 1S90, 

 are contained in the ten enumerations of the census from 1790 to 

 18S0 inclusive. The results of these enumerations are given in 

 the following table. The population there given is exclusive of 

 the inhabitants of Alaska and of Indians on reservations. 



Year. Population. 



1790 3.929'2i4 



iSoo 5'3oS.483 



1810 7,239,881 



1820 9,633,822 



1830 I2,S66,020 



1840 17,069,453 



1850 23,191,876 



1S60 3i'443.32i 



1870 38,558,371 



1880 50,155.783 



A preliminary plat showed that these values could be approxi- 

 mately represented by a parabola, and would be closely repre- 

 sented by an equation of the form : — 



P=:A-}-B/f + Cz;2-|-D/;3 



where P represents the population and / the time from some as- 

 sumed epoch. 



Expressing the population in millions and fractions of a million, 

 and the time {t) in decades (census years) counting from 1S40, 

 the observations furnish the following 10 equations of condition 

 for determining the constants A, B, C and D : 



