third was then above twenty-six years of age, and not above one eighth of them had reached forty-five.*

These facts show us how limited the number of the fathers of the new population could not but be. Not one half of the existing race could be so, even if all had married at sixteen ; not one third were alive to have offspring at the age of twentysix, and only one eighth at the mature period of forty-five. The mortality implied by these proportions is unfavourable to any large increase.

Ten years afterward, in the census of 1810, we find these relative amounts continuing much the same. Above one third were then under ten years; above half were under sixteen ; † not one third were above twenty-six; and not one eighth were above forty-five.‡

In the official census of the next decennial period, 1820, we find nearly the same proportions still subsisting. There also above one third of the males were under ten; not quite a moiety were under sixteen; above two thirds were under twentysix; and not one eighth were more than forty-five. What country in Europe presents to us a greater abbreviation of human life than these numbers-one eighth only above fortyfive!

* The numbers who had attained twenty-six, but were under fortyfive, were returned to be 478,520, leaving only 263,075, who were fortyfive years of age and upward, out of the 2,194,225.-Gen. View of Un. States, p. 53.

† In 1810, the free white males had increased to 2,988,141; of these, those returned as under ten were 1,035,278; those of ten and under sixteen were 468,183 more, making 1,503,461. The number of those who had reached sixteen, but were under twenty-six, was 547,597. Hence 2,051,058 males were under twenty-six years of age out of 2,988,141, or more than two thirds; for the two thirds would have been only 1,992,026. Hence fewer were twenty-six and above in 1810 than in 1800, as if human life had there rather lessened in duration during those ten years instead of increasing.

The males of twenty-six and under forty-five were found to be 572,347, and only 364,736 males were of forty-five and upward out of 2,988,141, which were not an eighth part, as this would have been 373,517; so that above seven eighths were under forty-five in 1810. The numbers returned in this census were of free white males :1st class, under 10

2d

66

of 10, under 16

of 16, under 26

1,345,220

612,535

776,150

766,083

495,065

-3,995,053

One third of these would have been 1,331,684; one half, 1,997,526'; two thirds, 2,663,368; and one eighth would have been 499,381.

The census of 1830 was taken with a different division of the ages; but the results are of a similar complexion. Here also nearly one third of the males were under ten years of age.* The next age distinguished was fifteen instead of sixteen; consequently those under fifteen did not amount to a moiety; and it is probable that those under sixteen were also less than half at this period.† Above five ninths, or nearly a ninth more than a half, were under twenty; consequently not four ninths of the males had reached twenty years of age.‡ Nearly three fourths were under thirty ; but above one seventh were above forty; and not one twelfth had reached fifty. The proportion of those who were sixty and above was not one twenty-fifth part ;** and those who

The summary of this census is given in the "General View of the United States," p. 55, and also in Flint's "Mississippi Valley," vol. ii., p. 214-229-thus: free white persons

Males under 5

66 of 5 and under 10

972,194

782,637

10 and under 15

671,688

575,614

952,902

592,596

369,370

230,500

134,910

58,136

15,945

1,993

100 and upward

274

-5,358,569 Flint, p. 228.

† One half would have been 2,679,284. Those enumerated as under fifteen amounted to 2,426,519; and if we take one fifth of those between fifteen and twenty as an average addition for those one year older, this would make the number under sixteen to be 2,541,642,

The males living under twenty were 3,002,133; five ninths would have been 2,976,988; those, then, of twenty and above were 2,381,581; four ninths would have been 2,381,591.

Those under thirty were 3,955,035; three fourths of the whole would have been 4,018,927; so that not one fourth were above thirty.

Those under forty were 4,547,631, and only 810,938 above thirtynine; one seventh would have been 765,509. If we add one tenth of those returned as between forty and fifty, for those who became forty, it would make those above forty to be 802,446.

¶ One twelfth would have been 446,547; the numbers returned of fifty and above were 441,758.

** The numbers under sixty were 5,147,311, leaving 211,258 for those of sixty and upward; one twenty-fifth part of all would have been 214,342.

were seventy were not quite a seventieth part of all their living males. Certainly, as far as the masculine elements of population go, their duration of life was too abridged for a series of four decennial periods to admit of anything like a geometrical augmentation. We may infer, that those who desire long life should not immigrate or settle in the United States; or, at least, not until some of their present habits of life are considerably altered; they will live longer in any part of Europe, except in some of its southern climates.+

The female world of the United States are not longer lived. In 1800, more than one third were under ten, and nearly a half under sixteen ;‡ and if we take the period from that year to forty-five, as the time during which the sex can be mothers, we find that not two fifths were of this age. So that these two fifths of the American females had to renew all the white population of both sexes in the United States; and, upon calculation, we perceive that they could not do this unless every one that could have a family was actually married, and each one so married had between six and seven children. They could not even replace themselves and the rest of their citizen contemporaries unless every one of those who in 1800 were marriageable presented, upon an average of all, above six and a half to the state. To produce any multiplication of the population beyond what it was, each of the then marriages must of course have on the average more than this proportion. But this proportion is beyond the usual rate of births to marriages even in North America, and therefore this fact

* Of seventy and upward, there were only 76,348 out of the 5,358,569; one seventieth part would have been 76,550.

↑ In arriving at this conclusion, Mr. Turner has forgotten the influence of immigration. It is well known that a very large proportion of immigrants, probably nine in ten, are young men and women; either unmarried, or, if married, with very young children. It is comparatively rare to see an immigrant of forty years old or upward.-Am. Ed.

In the census of 1800, the white females were returned to be 2,115,431. Of these, 726,774 were under ten; 323,906 were of ten and under sixteen, making, together, 1,050,680; one third of the whole would have been 705,143; one half, 1,057,715.

The numbers of females stated to have been above fifteen and under forty-five were 809,760; two fifths would have 846,172.

All the free white population in 1800 composed, in both sexes, 5,309,758 persons. Now, for 809,760 mothers to produce a new generation of the same number, to take the place of the old one, without any augmentation of it, each of these must have above 6 children on an average, as 809,760 multiplied by 64 gives but 5,263,440.

VOL. III.-F

concurs, with the shortened lives of the male sex, to make a doubling in twenty-five years physically impossible.

In the census of 1810, the females who then could be mothers could only replace their contemporaries and themselves by every one having five children; for there, above one third were under ten,* nearly one half were under sixteen,† and not two fifths were between fifteen and forty-five.‡ For those who only could be mothers to renew the existing population, every one must have above five children. Similar results arise from the population of 1820,|| and likewise in the altered scale of 1830. In the last, nearly one third

In the census of 1810 the white females were returned to be 2,873,950; of those under ten years were 981,426; one third would have been 957,983.

Under sixteen were 1,429,748; one half would have been 1,436,975. Of sixteen and under forty-five were 1,105,824; two fifths would have been 1,149,580.

The whole white population of 1810 were :

Males.
Females

2,988,141
2,873,950

-5,862,091

Now five times 1,105,824, the number of women between fifteen and forty-five, would be 5,529,120; so that every marriageable female must have, upon an average of all, above five children each, in order to reinstate only the number of the then existing generation, without any increase.

The census of 1820 returned 3,866,657 free white females, of the following ages :

Under 10

of 10 and under 16

of 16 and under 26

of 26 and under 45

1,280,550

605,348

781,371

736,600
462,788

¶ In the census of 1830, we find the free white females to have been

were under ten; nearly four ninths were under fifteen ;* not much more than one fourth were above thirty † more than one seventh were above forty;‡ not one twelfth were fifty ;§ and only between a twenty-fifth and twenty-sixth attained sixty; less than one in seventy-one had become seventy years of age. Their vital duration was a little longer than that of the male sex. But we may submit it to the judgment of our statistical calculators, whether it is possible, with these established relative proportions of the different living ages of our North American contemporaries, that they could, from their own nativities alone, enlarge their population in a geometrical ratio. Instead of this, I cannot avoid thinking, from all the above circumstances, that if there had been no immigrants to them, the United States would not have done more in the thirty years we have been surveying than keep up their own population, or but very gradually increase it.

Both Mr. Malthus and his followers have made a distinction between the multiplying ratio of the older states of America and their new or back settlements; because, on the comparison of their numbers in the latter at different dates, a greater increase was visible than in the former. But here again the effect of immigration has been mistaken for that of natural birth; the new states have not swelled into their enlarged numbers from the successive reproductions of their original inhabitants. There has been, and is still, a constant influx of new comers; the travellers into America

* Under ten were 1,671,753. One third would have been 1,722,433. Under fifteen were 2,310,816; four ninths of all would be 2,296,576.

↑ The females under thirty were 3,824,191; three fourths would have been 3,875,472. Those of thirty and above were 1,343,108; taking from these one tenth of the next class as the number who reached thirty, those above thirty would be 1,287,552. One fourth would have been 1,291,824,

The number under forty was 4,379,756; and those of forty and above were 787,543. If we take off one tenth of the next class as those attaining forty, the number above that age would be 752,001. One seventh would have been 738,185.

Of fifty and above were only 432,118 out of the 5,167,299; deducting one tenth of the next class for those who reached fifty, those above that age would be 409,826. One twelfth would have been 430,608.

Those under sixty were 4,958,109; adding to these one tenth of the next class for those who were sixty, those above sixty would be only 196,104, One twenty-fifth would have been 206,692.

Under seventy were 5,088,975. One tenth of the next class would make those who attained seventy 5,094,778. Those above seventy would be 72,521. One in seventy-one would have been 72,778,