Critical, Historical, and Miscellaneous Essays; Vol. 2 / With a Memoir and Index

by Baron Thomas Babington Macaulay Macaulay

“It may at once be denied,” says he, “that human increase proceeds geometrically; and for this simple but decisive reason, that the existence of a geometrical ratio of increase in the works of nature, is neither true nor possible. It would fling into utter confusion all order, time, magnitude, and space.”

This is as curious a specimen of reasoning as any that has been offered to the world since the days when theories were founded on the principle that nature abhors a vacuum. We proceed a few pages farther, however; and we then find that geometric progression is unnatural only in those cases in which Mr. Malthus conceives that it exists; and that, in all cases in which Mr. Malthus denies the existence of a geometric ratio, nature changes sides, and adopts that ratio as the rule of increase.

Mr. Malthus holds that subsistence will increase only in an arithmetical ratio. “As far as nature has to do with the question,” says Mr. Sadler, “men might, for instance, plant twice the number of peas, and breed from a double number of the same animals, with equal prospect of their multiplication.” Now, if Mr. Sadler thinks that, as far as nature is concerned, four sheep will double as fast as two, and eight as fast as four, how can he deny that the geometrical ratio of increase does exist in the works of nature? Or has he a definition of his own for geometrical progression, as well as for inverse proportion?

Mr. Malthus, and those who agree with him, have generally referred to the United States, as a country in which the human race increases in a ‘geometrical ratio, and have fixed on twenty-five years as the term in which the population of that country doubles itself. Mr. Sadler contends that it is physically impossible for a people to double in twenty-five years; nay, that thirty-five years is far too short a period,—that the Americans do not double by procreation in less than forty-seven years,—and that the rapid increase of their numbers is produced by emigration from Europe.

Emigration has certainly had some effect in increasing the population of the United States. But so great has the rate of that increase been that, after making frill allowance for the effect of emigration, there win be a residue, attributable to procreation alone, amply sufficient to double the population in twenty-five years.

Mr. Sadler states the results of the four censuses as follows:—

“There were, of white inhabitants, in the whole of the United States in 1790, 3,093,111; in 1800, 4,309,656; in 1810, 5,862,093; and in 1820, 7,861,710. The increase, in the first term, being 39 per cent.; that in the second, 36 per cent.; and that in the third and last, 33 per cent. It is superfluous to say, that it is utterly impossible to deduce the geometric theory of human increase, whatever be the period of duplication, from such terms as these.”

Mr. Sadler is a bad arithmetician. The increase in the last term is not, as he states it, 33 per cent., but more than 34 per cent. Now, an increase of 32 per cent, in ten years, is more than sufficient to double the population in twenty-five years. And there is, we think, very strong reason to believe that the white population of the United States does increase by 32 per cent, every ten years. Our reason is this. There is in the United States a class of persons whose numbers are not increased by emigration,—the negro slaves. During the interval which elapsed between the census of 1810 and the census of 1820, the change in their numbers must have been produced by procreation, and by procreation alone. Their situation, though much happier than that of the wretched beings who cultivate the sugar plantations of Trinidad and Demerara, cannot be supposed to be more favourable to health and fecundity than that of free labourers. In 1810, the slave trade had been but recently abolished; and there were in consequence many more male than female slaves,—a circumstance, of course, very unfavourable to procreation. Slaves are perpetually passing into the class of freemen; but no freeman ever descends into servitude; so that the census will not exhibit the whole effect of the procreation which really takes place.

We find, by the census of 1810, that the number of slaves in the Union was then 1,191,000. In 1820, they had increased to 1,538,000. That is to say, in ten years, they had increased 29 per cent.—within three per cent of that rate of increase which would double their numbers in twenty-five years. We may, we think, fairly calculate that, if the female slaves had been as numerous as the males, and if no manumissions had taken place, the census of the slave population would have exhibited an increase of 32 per cent, in ten years.

If we are right in fixing on 32 per cent, as the rate at which the white population of America increases by procreation in ten years, it will follow that, during the last ten years of the eighteenth century, nearly one-sixth of the increase was the effect of emigration; from 1800 to 1810, about one-ninth; and from 1810 to 1820, about one-seventeenth. This is what we should have expected; for it is clear that, unless the number of emigrants be constantly increasing, it must, as compared with the resident population, be relatively decreasing. The number of persons added to the population of the United States by emigration, between 1810 and 1820, would be nearly 120,000. From the data furnished by Mr. Sadler himself, we should be inclined to think that this would be a fair estimate.