forms us, in the very sentence quoted, "that there is "but one instance in which he had been enabled to "obtain the actual proportion of marriages to births "in the country," which, he says, was the parish of Hingham, in the state of Massachusetts; and as that place, according to his computation, contained an average population of 927 souls only, even were American parishes no larger than those of England, still the population must have been as thinly scattered as that of our villages. There, it appears, that, during the term of 54 years, there were 2247 births, and 521 marriages, giving, consequently, 4.312 births to each', instead of 4. Mr. Malthus's observation upon this piece of information, as we have already noticed, is this: "As, however, this proportion was taken principally from towns, it is probable that the births are given too low; and I think we may very safely "take five for the average of towns and country. Granting him even this proportion, unscrupulously as he has deduced it, and, likewise, that of 200 out of 351 of these births, as living to marry, it then follows that American marriages, one with another, produce nearly 2.85 children each, which survive to marry. Afterwards he calculates by a number of gratuitous assumptions, and, amongst the rest, by the very doubling which ought to have been first shewn possible, that 5.58 may be the prolificness of their marriages3: to give, then, the argument in favour of the geometric ratio, the benefit of the average of Mr. Malthus's suppositions, to the exclusion of Dr. Barton's recorded facts,-three children, which shall survive to marry, will be the proportion of American prolificness.

1 Transactions of the American Phil. Soc., vol. i., p. 30.

2 Malthus, Essay on Population, vol. i., p. 483.

a Ibid., p. 484.

! VOL. II.

E

(4) In assuming twenty-three as the age of marriage in an unchecked population, like that of America, I anticipate, by four years, the average period assigned by Mr. Malthus," as obtaining in this country, and by one year the age fixed upon by our ancestors as that of discretion in the male sex; the period of whose marriage, it needs not be remarked, determines the distance of the succession of the generations; nor have I done this arbitrarily. None of the actual proportions which I have had an opportunity of examining, including those of Dr. Barton, would allow of its being placed so early. Mr. Warden, one of the most confident assertors of the rapidity of American increase, and most sanguine anticipators of its consequences, distinguishing in this respect New Hampshire, says indeed, that "it is rare to see there an unmarried man of thirty';" he might, with equal truth, have asserted just the same thing regarding the bulk of the people in old Hampshire, or, indeed, of any other shire of the mother country: but, in regard to another state, and decidedly one of the most prosperous of the whole, he is more explicit, and remarks, that the period of marriage, for males, is from twenty-one to twenty-five, which gives, on the average, the very ages I have chosen: but, he adds, that in this state the natives are remarkable, even in America, "for their early maturity." That this period, therefore, is not anticipated in the other states, especially in the slave-holding ones, where concubinage prevails so lamentably, we may hold for certain; but, in order to prop up their theory, were the advocates of the geometric ratio, in spite . of all authority to the contrary, to demand a still greater degree of precocity than is thus allotted to the Americans by their own writers, it will be seen, in the

1 Warden, Statistical, &c. Account of 2 Ibid., vol. i. p. 501. the United States, vol. i., p. 386.

sequel, how little their supposition would favour human increase.

(5) In extending the period of life, as it respects the prolific part of the population, as far as 65 years, I have manifestly exceeded the truth in favour of their accumulation, and have even surpassed the pretensions of their own statistical writers in this particular.

(6) Upon these data, therefore, the most operative of which have been dictated to me by the advocates of the geometric theory, the following table has been constructed; and I do entertain a confident hope, that the trouble of extending it to a period almost co-extensive with the history of American colonization, and the scrupulous exactness which has been preserved throughout, may be recompensed by settling at least this question for ever. In its construction, I have again given away a great advantage to my argument, by contracting the term in which the births appear, to eight years, at least three short of the time which Nature would take to evolve the number assigned; and again, by invariably placing a surviving and prolific birth in the first year after marriage. Making the second the longer interval, will go but a very little way indeed in compensating for this liberality; but I have done thus, as in the preceding instances, purposely in order to obviate and silence any petty exceptions which, though not very easy to anticipate, may yet perhaps be taken, to weaken, if possible, the force of the demonstration, which, though not carried to its full extent, will be found overwhelming.

TABLE XXI.

SHEWING THE PROGRESS OF A POPULATION IN WHICH THE MARRIAGES TAKE PLACE AT 23; EACH HAVING, OUT OF 5,265 BIRTHS, THREE WHICH LIVE TO MARRY, ONE IN THE FIRST, AND THE REMAINDER IN THE FIFTH AND EIGHTH YEARS AFTER MARRIAGE, ALL SUCH SURVIVING TO THE AGE OF 65; THE EXISTING PROGENITORS OF THE TWO FIRST COUPLES BEING, THEREFORE, 2 INDIVIDUALS.