The number of free colored persons in 1850 was 428,637; in 1840, 386,345. The increase of this class has been 42,292 or 10.95 per cent.
From 1830 to 1840, the increase of the whole population was at the rate of 32.67 per cent. At the same rate of advancement, the absolute gain for the ten years last past, would have been 5,578,333, or 426,515 less than it has been, without including the increase consequent upon additions of territory.
The aggregate increase of population, from all sources, shows a relative advance greater than that of any other decennial term, except that from the second to the third census, during which time the country received an accession of inhabitants by the purchase of Louisiana, considerably greater than one per cent. of the whole number.
The decennial increase of the most favored portions of Europe is less than one and a half per cent. per annum, while with the United States it is at the rate of three and a half per cent. According to our past progress, viewed in connection with that of European nations, the population of the United States in forty years will exceed that of England, France, Spain, Portugal, Sweden, and Switzerland combined.
In 1845, Mr. William Darby, the Geographer, who has paid much attention to the subject of population, and the progress of the country; having found that the increase of population in the United States for a series of years, had exceeded three per cent. per annum, adopted that ratio as a basis for calculation for future increase. He estimated the population of 1850 at 23,138,004, which it will be observed is considerably exceeded by the actual result. The following are Mr. Darby's calculations of the probable population of the Union for each five years up to 1885:
| 1850 | 23,138,004 | 1870 | 40,617,708 |
| 1855 | 26,823,385 | 1875 | 47,087,052 |
| 1860 | 31,095,535 | 1880 | 54,686,795 |
| 1865 | 35,035,231 | 1885 | 63,291,353 |
If the ratio of increase be taken at three per cent. per annum, the population duplicates, in about twenty-four years. Therefore, if no serious disturbing influence should interfere with the natural order of things, the aggregate population of the United States at the close of this century must be over one hundred millions.
The relative progress of the white and colored population in past years, is shown by the following tabular statement, giving the increase per cent. of each class of inhabitants in the United States for sixty years.
| Classes. | 1790 to 1800 | 1800 to 1810 | 1810 to 1820 | 1820 to 1830 | 1830 to 1840 | 1840 to 1850 |
| Whites | 35.7 | 36.2 | 34.19 | 33.95 | 34.7 | 38.28 |
| Free col. | 88.2 | 72.2 | 25.25 | 36.85 | 20.9 | 10.9 |
| Slaves | 27.9 | 33.4 | 29.1 | 30.61 | 23.8 | 28.58 |
| Total col. | 32.2 | 37.6 | 28.58 | 31.44 | 23.4 | 26.22 |
| Total pop. | 35.01 | 36.45 | 33.12 | 33.48 | 32.6 | 36.25 |
The census had been taken previously to 1830 on the 1st of August; the enumeration began that year on the 1st of June, two months earlier, so that the interval between the fourth and fifth censuses was two months less than ten years, which time allowed for would bring the total increase up to the rate of 34.36 per cent.