and negro total of 76,000,000. Indeed, if we take the total immigration
from 1820 to 1900, exceeding 19,000,000 people, and apply a slightly
higher than the average rate of increase from births, we shall find that
in the year 1900 one-half of the white population is derived from
immigrant stock, leaving the other half, or but 33,000,000 whites,
derived from the colonial stock.[124] This is scarcely more than
one-third of the number that should have been expected had the colonial
element continued to multiply from 1840 to 1900 as it had multiplied
from 1790 to 1840.

An interesting corroboration of these speculations is the prediction
made in the year 1815, thirty years before the great migration of the
nineteenth century, by the mathematician and publicist, Elkanah
Watson.[125] On the basis of the increase shown in the first three
censuses he made computations of the probable population for each census
year to 1900, and I have drawn up the following table, showing the
actual population compared with his estimates. Superintendent Walker, in
the essay above quoted, uses Watson's figures, and points out the
remarkable fact that those predictions were within less than one per
cent of the actual population until the year 1860, although, meanwhile,
there had come nearly 5,000,000 immigrants whom Watson could not have
foreseen. Thus the population of 1860, notwithstanding access of the
millions of immigrants, was only 310,000, or one per cent less than
Watson had predicted. And the falling off since 1860 has been even
greater, for, notwithstanding the immigration of 20,000,000 persons
since 1820, the population in 1900 was 75,000,000, or 25 per cent less
than Watson's computations.

POPULATION AND IMMIGRATION

------+------------+---------------+-------------+-----------
| POPULATION | WATSON'S | WATSON'S | FOREIGN
| (CENSUS) | ESTIMATE | ERROR |IMMIGRATION
| | | |FOR DECADE
------+------------+---------------+-------------+-----------
1790 | 3,929,214 | | |
1800 | 5,308,483 | | | 50,000
1810 | 7,239,881 | | | 70,000
1820 | 9,633,822 | 9,625,734 | -8,088 | 114,000
1830 | 12,866,020 | 12,833,645 | -32,375 | 143,439
1840 | 17,069,453 | 17,116,526 | +47,073 | 599,125
1850 | 23,191,876 | 23,185,368