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

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(12) In the year 10, the number of the living will amount to 14%, (16% of the effete having died since the year one); from that period the table admits of nine of these doublings in the term of 12 years each, which bring us down to a little beyond 126. The geometrical progression would amount to 7577%, or (to omit the fractions in future) to 7577; but the actual number found in the table is 7463 only. Two years afterwards, viz. in 12, the numbers in existence are 16.8, which, doubled as before, give us for the year 127, 8601 persons, but the number in the table is 8368: two years further, and the 18.8 found in the year 14, when doubled nine times, amounts to 9625; but in the year 129, 9374 only appear. Again, in the year 16 there are 20.8, which, similarly doubled, would multiply to 10,649; there are 10,509 in the table. Com

mencing in like manner in several successive years afterwards, the numbers at each period thus doubled every 12 years, and those the table represents as actually existing, will be found very nearly balancing, till in some time afterwards the latter, I think, will rather exceed the former, in consequence, as I conceive, of the relation of the terms with the commencement of the series: then, again the geometric numbers would exceed. On the whole, therefore, we may assume that the table represents with sufficient exactness the increase of a population advancing in the rapid manner already mentioned; let us now, therefore, attend to the particulars of its construction, in order to determine the asserted possibility of such a multiplication in any country, under any circumstances whatsoever.

(13) This table, which, as before shewn, scarcely exhibits so rapid a rate of increase as that under consideration, is calculated on the following extraordinary data: First, all marry, and at the age of twenty; Second,

all the marriages are prolific, and to the astonishing extent of ten children each, one with another; Third, all these marriages are prolific the ensuing year, and thence in alternate years for eighteen subsequent ones, till the number of ten children each is produced; Fourth, none of these numerous offspring die unmarried, but, on the contrary, they all live to form that union at the same early age, and in their turn become equally prolific, a state of increase, in short, in which every individual in the third descent has one hundred, and in the fourth a thousand descendants, and so on through all succeeding generations; Lastly, must be added a fact relative to this calculation not a whit more surprising than those previously mentioned, there are to be no deaths in this miraculously multiplying community! Then we find that a doubling every 12 years is barely made up. Can an Can an alleged calculation of Euler's, or the vague appeal of Mr. Malthus to the experience of some unnamed country or countries, redeem this ratio of human increase, constructed as it must be upon such assumptions, from the derision it merits?

(14) But even the proportion of prolificness to the population in this extraordinary rate of increase falls vastly short of that demanded in the table to which Mr. Malthus appeals,-and of deaths, as before observed, there are none; but if we allow to each of our parents of ten children a life of sixty-five years duration, (the only rational supposition advanced), and then account for them as deaths, the results will be still wider from the suppositions in question. This will fully appear on a further examination of the preceding table, when divided into equal periods throughout, adding a column for the mean annual number of deaths in each; I shall likewise insert another, exhibiting in