births! He had before been calculating, from other recorded particulars, a ratio of increase which would not double the population in less than twelve hundred years, and likewise gives us " other good observa"tions" of an intermediate nature; and at length "to

get out of this difficulty, and to temper these vast disagreements," he takes a medium of his own, the effect of which is to double the population, under existing circumstances, in 360 years, the conclusion to which he adheres. It must be further remarked, that though, in this calculation, he does not forget the checks, still he pronounces them to be, in their effect on the population during that period, "of no great matter to the whole nation1."

(5) But to remove all doubt or ambiguity as to the opinion of Sir William Petty on the subject, the term in question, ten years, is the one fixed upon by him in the same treatise as that in which "the people might have doubled;" when? during the first hundred years after the flood, and then only; as he trebles that term before the conclusion of the succeeding century, and at length enlarges it to twelve hundred years. His avowed object in asserting ten years as a possible term of human duplication, was to "justify the scriptures concerning the number of people in ancient time;" and he no more omitted in his calculation the astonishing longevity and prolificness of the period in question, as recorded in the Bible, than all other writers who, with a similar object, have availed themselves of the same facts. It is clear, therefore, that the age to which Noah arrived has as little to do with the present expectation of life, as it is termed, as the quotation from Sir William

1 Petty, Tracts, pp. 108-120.

Petty has with the period of doubling now-a-days, however free mankind might be from the checks so often alluded to. These remarks are made with a view of clearing that judicious writer from the absurdity thus imputed to him.

(6) Whatever might have been the opinion of Sir William Petty on this subject, it is clear that the author I am principally combating adopts one very similar to that attributed to him, and puts it forth under the sanction of a calculation of Euler's; though I think with as little reason as in the former case; the circumstance of that eminent mathematician having computed a table exhibiting the increase of human beings under different circumstances (a task, however, to which any arithmetician would have been fully competent) and terminating it with proportions which would double a population in 12 years, is no stronger a proof that he supposed that term to be the natural one, than that he so determined with regard to a period of 250 years with which he commences. Just as reasonably might we hold the interest tables of an accountant, calculated from an eighth to five and twenty per centum, to be valid proof of his belief that the interest of money vacillates between, and touches upon such extremes. He adds to this appeal to Euler's Table, these words: " and these proportions" (which double a population in 12 years) "are not only "possible suppositions, but have actually occurred "for short periods, in more countries than one." I proceed to disprove this supposed possibility altogether, which I hope to do in such a manner as will render any reference to these unmentioned countries quite unnecessary.

(7) I shall first premise that these doublings are of course meant to be represented as the result of

"procreation only," and, indeed, the one under consideration is so explained, viz. as produced solely by the excess of the births, compared with the deaths, of the entire community. Otherwise they would have no more to do with a general argument on the natural increase of population, than the annual reports of a foundling hospital, or the arrival of a cargo of convicts in New South Wales. And, again, by these 'possibilities" nothing further can be meant than the established average proportions of nature, placed under the most favourable circumstances. It would be futile and disingenuous in the highest degree, to select particular and extraordinary instances of longevity and fecundity, and transfer them, in such calculations as these, to an entire population; but the statement relieves itself from any such imputations by asserting the fact in question of a whole country, and of more countries than one. I beg leave to recall to the reader's recollection what has been said in a former section of this treatise, on the exactness and certainty of these operations of nature calculated on their totality, however dissonant they may seem, when individually taken; and how much more moderate are the average results, than the vague computations we generally form by contemplating particular instances; extraordinary cases being very naturally those which make the most powerful impression upon us, and are always the most present to our recollection.

(8) Previously to entering upon the calculations to which these supposititious doublings will be submitted, I shall notice two capital errors in the computations of those who have professed to prove their possibility, which have been necessarily fatal to the accuracy of their conclusions. The first is, making the prolific portion of the community (always a small

part of the entire number) the radix of all their calculations, to the total exclusion of the sterile and even effete part of it; (confining the use of the latter term to those who have ceased to be fruitful.) The second is, fixing upon the precise period when this small proportion of the whole number begins to be productive, as that from which to commence their doublings. This method, to be sure, fully answers their purpose in shewing an extraordinary rate of increase, which, having thus obtained, they transfer to an entire population; such a method of calculation is, however, utterly useless for any purpose whatsoever, least of all will it demonstrate the possibilities in question. It assumes that there are no aged persons in an entire community who have survived the reproductive period of life; that there are none weakly or deficient; and, moreover, that there are no infants or children more or less remote from the period of fruitfulness, of whom a considerable portion is never destined to attain to it. Such calculators generally commence with Melchizedeks; they present to us their prolific pairs unincumbered with father or mother; and, like ephemera, propagating as soon as they appear, and disappearing when they have ceased to propagate. It is quite

superfluous to dwell upon the absurdity of these suppositions, and yet it is from a series of impossibilities like these, that the "possibilities" about to be examined are made up.

(9) Bearing these necessary considerations in mind, I have, at some considerable pains, attempted to ascertain the degree of prolificness necessary, on the average, to effect this quick period of doubling which Mr. Malthus vouches to have taken place for short periods, in more countries than one. I have done this, not by reasonings, which surely ought never to

be admitted as evidence in questions which arithmetic can alone decide, but by constructing many different tables in order to trace the whole question clearly and distinctly, and as, I trust, without any risk of material errors: these have cost no little time; but I cannot conceive it wholly mispent in proving the utter absurdity of the preliminary suppositions on which the geometric ratio of human increase is professedly founded.

(10) The following table, then, will exhibit, soon after its commencement, for a long series of years, an increase in births, independently of extraneous accessions, amounting, very accurately, to a doubling in the period in question, once every 12 years, certainly not exceeding that ratio of multiplication. The results, only, are in this instance given, as it would have occupied too much space to insert the whole of the details; a course, however, which will be adopted in another and more important stage of the argument.

TABLE XVI.

SHEWING THE PROLIFICNESS REQUIRED IN ORDER TO DOUBLE A POPULATION IN 12 YEARS.