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this instance the utmost possible proportion of marriages under such circumstances; the preventive check, as it is called, having no existence whatsoever.

TABLE XVII.

IN WHICH THE PRECEDING ONE is divided into SectiIONS OF EIGHT YEARS, SHEWING THE ANNUAL PROPORTIONS OF THE MARRIAGES, BIRTHS, AND DEATHS, TO THE EXISTING POPULATION THROUGHOUT.

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(14) The preceding calculations, therefore, I repeat, exhibit very different proportions to those quoted from Euler, which are, "a mortality of 1 in 36, and the births to the deaths as 3 to 1," or, in other words, 1 birth in every 12, which, it is added, would double the population in the time specified, as has been known to have been the case in different countries. In the table, which hardly increases at that rate even exclusive of the deaths, no such proportions are found; there, on the whole average, there is only one birth in 18, and after the deaths of the recorded births are included, there is not one in 600! and the further the computation is carried, the less fluctuation is observable, and certainly no indication of material alteration in these proportions or of any acceleration in the increase. To augment the number in the column of the deaths, by transferring to it a part of that of the births in their infancy, it is evident would be fatal to the doubling in 12 years. How then are the proportions mentioned as those of Euler to be obtained, so as still to preserve the duplication which is its basis? In one method only, and that so as in some measure to reconcile the relative proportions in question to the laws of nature, though presenting them in a series of the grossest exaggerations; by increasing the number of births one-half, and assigning a third of the whole as the proportion of the born that do not live to marry most writers, including Dr. Franklin, fix that proportion at one-half; Mr. Malthus, I observe, at considerably more than two-fifths, under circumstances highly favourable to human increase. If we place these deaths in the octennial section in which they were born, considering the number that inevitably die in the first stages of infancy, it will allow some of them to survive to the age of puberty; and, lastly, the column of the population will have to receive these births for the

(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. Commencing 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 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

this instance the utmost possible proportion of marriages under such circumstances; the preventive check, as it is called, having no existence whatsoever.

TABLE XVII.

IN WHICH THE PRECEDING ONE IS DIVIDed into SectIONS OF EIGHT YEARS, SHEWING THE ANNUAL PROPORTIONs of the MARRIAGES, BIRTHS, AND DEATHS, TO THE EXISTING POPULATION THROUGHOUT.

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