would ascend to the size of Nebuchadnezzar's tree, shadowing all the beasts of the field, and sheltering the fowls of heaven in its branches, till at length it would darken the skies, and hide that sun which calls forth its busy fraternity to their annual labours. The calculations of this interesting insect would be not less true in the abstract, and not more false in their application, than that of the philosopher, who, with the page of history before him, where is recorded the existence of mighty and populous empires, not a vestige of which now remains, and others by whose ruins he is still surrounded, (not one of which met their fate from a want of food for their boasted numbers,) still raves about the geometric ratio of human increase1.

(8) Nor has this geometric ratio any existence when applied to the common pursuits of life. One of the authorities quoted in the first chapter of the work under examination, supposes, indeed, upon this principle, the possibility of the indefinite, or rather infinite multiplication of any particular race of men or vegetables, and applied, I think, the notion to other, and, as he thought, more practical as well as profitable purposes, the increase of money; calculating to a nicety what a farthing put out to interest at our Saviour's birth would have amounted to at his day, had it been properly husbanded. Nor did the idea exist with him in mere theory: he actually left in his last will and testament some, I forget how many, millions sterling to be applied as he directed at a given time after his death. The philosopher was quite as profound when he was penning his codicil as when engaged in proving that the world might be planted

1 I have observed, since I wrote this passage, that one of the profoundest writers on geography that has ever yet appeared, Malte-Brun, has explained, by

the same analogy, the rise, progress, and decay of the ancient races of man. -See Malte-Brun, Geog., 1. xcv., p. 72. 2 Dr. Franklin's Will, Works.

entirely with fennel :-the growth of Jack Hickathrift's bean, or any other nursery story, is as sober a supposition as either.

(9) False, however, and even ridiculous, as is the geometric ratio when any thing more than a mere abstract idea; and although, were it true, "the great "difference in the delivery of the mathematics, which "are the most abstracted of knowledges, and policy, "which is the most immersed'," is manifest; still the duty, interest, and policy of the country, it is now proposed, should be dictated by it; and in sober earnest we stand in no little danger, if the principle gain ground, of seeing one of the wildest of Swift's satirical rêveries actually realized amongst us. Under these circumstances, I hope I may hold the humble office of a "flapper" on the occasion, and so far recall these state mathematicians to matter of fact and common sense, as to shew them two practical problems, both of which are undeniably true, and either of them fatal to their theory; they are these:

First, Human increase, under the most favourable circumstances for its development, does not proceed in a geometrical ratio, but is constantly regulated on a totally different principle.

Second, Supposing such a ratio to exist, (which will be distinctly disproved,) still the longest of the terms upon which its supporters have founded their theory, even taking their own data, involves a series of physical impossibilities.

(10) For a full proof of these important positions, decisive indeed of the entire argument, I must again crave the reader to anticipate subsequent parts of this work. In regard to the first, and in proof that no

1 Bacon, Advancement of Learning, b. ii., p. 152.

2 Swift, Voyage to Laputa, Works vol. xiii., p. 145, et seq.

such duplication as the theory I am opposing ever has taken place, I have already referred to the Second Book of this treatise; that it never can, consistently with the established laws of nature, I hope is demonstrated, by every species of evidence of which the subject is susceptible, in the Fourth. In the opening chapters of the intermediate one, the second assertion is most distinctly substantiated, namely, that even the longest term assigned as the natural period of duplication in an unchecked population, is so far from being actually true, that it is not even possible, admitting the most favourable suppositions which have been brought forward in reference to human prolificness and longevity. My reason for postponing these proofs to a further stage of the argument is, that the different branches of it may be kept as distinct as may be, and thereby that tautology somewhat lessened, which it is not easy altogether to avoid in a work of this extended nature, at least with that share of time and attention that I have been able to devote to its composition and arrangement. I am not, however, unaware of the effect of continued repetition. Locke, I think, owed no little of his success in clearing away the metaphysical cobwebs of preceding times to it ; and, at all events, the practice has been avowedly resorted to by the author to whom I shall often address myself. In the choice of difficulties, I have, however, preferred separating the argument into two general divisions; the former of which will principally consist of proofs derived from general observation and experience; the latter, of those numerical calculations, by which it is arithmetically demonstrated. In subsequent parts of the work, then, the present subject will be resumed, when it will be fully proved, that the geometric ratio of human increase

has never yet been known to exist; that the periods in which its supporters assert that it doubles human beings, involve impossibilities; and, finally, that no such principle, however modified, constitutes the true law of population.

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64

CHAPTER IV.

OF THE THEORY OF HUMAN SUPERFECUNDITY;

ITS ARITHMETICAL RATIO.

(1) IF the geometric ratio, as applied to the increase of human beings, cannot bear a close investigation, the arithmetical one, as expressing the utmost possible augmentation of their sustenance, cannot sustain a single glance. So far from its being a "selfevident truth," as represented, it is an obvious fallacy, and one of the most glaring description; whether regarded theoretically or practically, whether submitted to the intellect of the philosopher, or the observation of the peasant, the error appears equally striking.

(2) The design of the theory under examination being to represent the utter insufficiency of the sustenance provided for the beings which the unrestrained laws of nature would certainly produce, two different ratios are employed, the geometric one, exhibiting the multiplication of those beings as proceeding, when unchecked, in an infinite series in which each successive term is double that of its preceding one; and the arithmetical, as shewing the means of subsistence when augmented to the utmost, advancing indeed, but so as to make each successive term exhibit a perpetually lessening proportion to the former. In this arithmetical series, the second term indeed doubles the first, but the third adds only a half to the second; the fourth, one third; the fifth, one fourth; the sixth, one fifth; and so on, till at the end of the few places,