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84 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."

It is not worth while to dwell upon the fallacy involved in the assumption of geometrical and arithmetical rates of increase, a play upon proportions which hardly rises to the dignity of that in the familiar puzzle of the hare and the tortoise, in which the hare is made to chase the tortoise through all eternity without coming up with him. For this assumption is not necessary to the Malthusian doctrine, or at least is expressly repudiated by some of those who fully accept that doctrine; as, for instance, John Stuart Mill, who speaks of it as "an unlucky attempt to give precision to things which do not admit of it, which every person capable of reasoning must see wholly superfluous to the argument." The essence of the Malthusian doctrine is, that population tends to increase faster than the power of providing food, and whether this difference be stated as a geometrical ratio for population and an arithmetical ratio for subsistence, as by Malthus; or as a constant ratio for population and a diminishing ratio for subsistence, as by Mill, is only a matter of statement. The vital point, on which both agree, is, to use the words of Malthus, "that there is a natural tendency and constant effort in population to increase beyond the means of subsistence."

The Malthusian doctrine, as at present held, may be thus stated in its strongest and least objectionable form:

That population, constantly tending to increase, must, when unrestrained, ultimately press against the limits of subsistence, not as against a fixed, but as against an elastic barrier, which makes the procurement of subsistence