1815.] Population of the United Stales of America. 337 



I am indebted for the following curious speculation on this sub- 

 ject to John Leslie, Esq. F.R.S.E. Professor of Mathematics in 

 the University of Edinburgh. — T. 



The population of America at the different periods of life may 

 be nearly represented by the differences between the complimentary 

 spaces of a parabola. 



Thus, the population under ten 

 years of age may he represented by 

 the space A B F X, of which the 

 boundary X F is a portion of a para- 

 bola, X Z, whose vertex is Z. 



From the property of tiie curve, 

 D H is as D Z\ Therefore D H 

 X D Z is as D Z^ ; and therefore 

 any triHnear area, as D H Z, being 

 one-third of the rectangle D H x 

 D Z, is also as D Z\ Therefore A JB C D 



the area 



AF i! 

 BG 

 C H 

 DI 

 E IZ 



A Z3 



B Z3 



C Z3 



D Z3 

 EZ3 



B Z3 or as 



CZ3 



DZ3 



i;Z3 



03 



863 

 763 

 703 

 603 



413 



763 

 703 

 603 



413 



0° 



636056 

 438976 

 343000 

 216000 

 68921 



438976 

 343000 

 216000 



68921 







197080 



95976 

 127000 

 147079 



68921 



Aggregate Return of 

 Males and Females. 



If now we multiply these proportional areas by 10, and retain 

 the nearest figure in the place of thousands, they will stand as in 

 the second column below, while the gross return of population is as 

 in the first. 



Proportional 



Numbers on the 



Parabolic Theory. 



Under 10 years of age .. 1,970,000 1,970,000 



10— »« 897,000 960,000 



»«-2« 1,085,000 1,270,000 



2G— 45 1,089,000 1,471,000 



45 and upwards . . G91,000 689,000 



It appears, therefore, that in the first and last periods the areas 

 are very nearly proportional to the numbers ahve at those periods. 

 But in the second, third, and fourth, periods, these areas exceed 

 the return ; which excess increases from the earlier to the more 

 advant-ed ages ; so that the American population is increasing more 

 rapidly than the parabolic theory supposed. 



Vol. V. N" V. 



