The famous doctrine which ever since its enunciation has so powerfully influenced thought, not alone in the province of political economy, but in regions of even higher speculation, was formulated by Malthus in the proposition that, as shown by the growth of the North American colonies, the natural tendency of population is to double itself at least every twenty-five years, thus increasing in a geometrical ratio, while the subsistence that can be obtained from land “under circumstances the most favorable to human industry could not possibly be made to increase faster than in an arithmetical ratio, or by an addition every twenty-five years of a quantity equal to what it at present produces.” “The necessary effects of these two different rates of increase, when brought together,” Mr. Malthus naïvely goes on to say, “will be very striking.” And thus (Chap. I) he brings them together: “Let us call the population of this island eleven millions; and suppose the present produce equal to the easy support of such a number. In the first twenty-five years the population would be twenty-two millions, and the food being also doubled, the means of subsistence would be equal to this increase. In the next twenty-five years the population would be forty-four millions, and the means of subsistence only equal to the support of thirty-three millions. In the next period the population would be equal to eighty-eight millions, and the means of subsistence just equal to the support of half that number. And at the conclusion of the first century, the population would be a hundred and seventy-six millions, and the means of subsistence only equal to the support of fifty-five millions; leaving a population of a hundred and twenty-one millions totally unprovided for. “Taking the whole earth instead of this island, emigration would of course be excluded; and supposing the present population equal to a thousand millions, the human species would increase as the numbers 1, 2, 4, 8, 16, 32, 64, 128, 256, and subsistence as 1, 2, 3, 4, 5, 6, 7, 8, 9. In two centuries the population would be to the means of subsistence as 256 to 9; in three centuries, 4,096 to 13, and in two thousand years the difference would be almost incalculable.” Such a result is of course prevented by the physical fact that no more people can exist than can find subsistence, and hence Malthus’ conclusion is, that this tendency of population to indefinite increase must be held back either by moral restraint upon the reproductive faculty, or by the various causes which increase mortality, which he resolves into vice and misery. Such causes as prevent propagation he styles the preventive check; such causes as increase mortality he styles the positive check. This is the famous Malthusian doctrine, as promulgated by Malthus himself in the “Essay on Population.”