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 is wholly superfluous to the argument.”[14] 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 progressively more and more difficult. And thus, wherever reproduction has had time to assert its power, and is unchecked by prudence, there must exist that degree of want which will keep population within the bounds of subsistence. Although in reality not more repugnant to the sense of harmonious adaptation by creative beneficence and wisdom than the complacent no-theory which throws the responsibility for poverty and its concomitants upon the inscrutable decrees of Providence, without attempting to trace them, this theory, in avowedly making vice and suffering the necessary results of a natural instinct with which are linked the purest and sweetest affections, comes rudely in collision with ideas deeply rooted in the human mind, and it was, as soon as formally promulgated, fought with a bitterness in which zeal was often more manifest than logic. But it has triumphantly withstood the ordeal, and in spite of the refutations of the Godwins, the denunciations of the Cobbetts, and all the shafts that argument, sarcasm, ridicule, and sentiment could direct against it, to-day it stands in the world of thought as an accepted truth, which compels the recognition even of those who would fain disbelieve it.