POPULATION OF THE UNITED STATES. 



5i 



Observed 

 Year. Population. 



1790 3,929,000 



1800 5,308,000 



1810 7,240,000 



1820 9,634,000 



1830 12,866,000 



1840 17,069,000 



1850 23,192,000 



1860 31,443,000 



1870 38,558,000 



1880 50,156,000 



1890 62,622,000 



The smallness of the discrepancies and the consequent close agree- 

 ment of the formula with the observations show that the growth of the 

 population has been a regular and orderly one. There are, however, 

 two residuals which have abnormally large values. The census of 1860 

 shows a population of 975,000 larger than the computed value, while 

 that of 1870 falls 754,000 below that of the computed value. 



The explanation of these discrepancies is not far to seek. The 

 devastating effect of the war would show itself in the census of 1870 

 and succeeding years. The effect would be to give 1870 a smaller ob- 

 served value than would be expected. This is precisely what we find 

 to be the case, the census of that year falling 754,000 short of the com- 

 puted value. An abnormally small value in 1870 would, of course, 

 have its effect on the population of succeeding decades and would also 

 give an apparent difference of opposite sign to the observed population 

 in 1860. 



There is, however, good reason to believe that the population in 

 1870 as determined by the census was much smaller than the actual 

 population at that time. Mr. Robert Porter, in Census Bulletin ISTo. 

 12, October 30, 1890, makes the statement that the census of 1870 was 

 grossly deficient in the Southern States and that a correct and honest 

 enumeration would have shown at that time a much larger population 

 than that actually returned by the Census Bureau. There are, of course, 

 no means of ascertaining exactly the extent of these omissions, but 

 there is no question that the population as computed by the formula for 

 1870 is far nearer the truth than the value given by the census for that 

 year. 



However this may be, it is evident that the formula represents the 

 general law of growth which held between 1790 and 1890 with an ac- 

 curacy almost comparable with that of the census determinations them- 

 selves. The question of immediate interest, however, is not whether 

 the growth of population during the last century can be represented by 

 a mathematical formula, but it is that which stands at the beginning 



