fore, the term assumed as the duration of life throughout. The correctness of every part of the calculation, to the least fraction, is therefore substantiated.

(9) Before applying this table to the purpose contemplated in its construction, I shall repeat, that though the proportions assigned by Dr. Franklin, which are certainly extravagant enough, are taken, still they are so applied as to exceed, and indeed violate the law of Nature, as well as that of probability, in favour of population. This is remarked, in order to prevent the cursory reader from falling into a contrary apprehension, when he is made aware of the results. That the interval of prolificness is somewhat too short, I am perfectly persuaded; but, not to dwell upon that circumstance, it will not be denied that in admitting the first year after marriage as constantly prolific, I give an unnatural advantage to the scheme of multiplication put forth, and a far greater and more unreasonable one in making that year invariably produce a surviving and prolific birth, instead of giving it alternately to that and the 16th year after marriage; which, as half the births in Dr. Franklin's scheme do not survive to marry, the plainest rule of the doctrine of chances certainly demands. How influential this clearly necessary rectification would be on the increase manifested in the table needs not to be pointed out; the calculation would certainly have been so constructed, but its importance was not sufficiently adverted to until after the table was finished: the error on the side of excess can now only be remedied by deducting no inconsiderable proportion of the increase from the numbers generated by the somewhat erroneous mode of computation already explained. To all these instances, in proof that every disadvantage is voluntarily encountered in rebutting the possibility of

the period of doubling, now under examination, must be added the fact, that I shall assume twenty years as that term, whereas Dr. Franklin contends for its being less" than twenty.'

(10) But all these rectifications will appear minute, and wholly unnecessary, when the plain facts, thought thus somewhat overrated, are confronted with Dr. Franklin's hypothesis. Using then this table as the foregoing ones, let us commence at the period when the first couples have produced half their children, namely, in the year 6; from thence to its termination there are ten of these periods of duplication, of 20: years each, bringing us down to the year 206. Now the ten individuals found in the former year, six, ten. times doubled, amount to 10,240, which we are assured would be produced in considerably less than that time. Our population, however, in the table, though all marrying at 20, and all the married having four children, which themselves survive, to marry and become equally fruitful, (leaving out such who die in infancy and unmarried, at both extremities of the table, and throughout, as totally uninfluential on the relative numbers,) surviving to the age of 65 years each, has advanced to 1665% only, not one-sixth part of the augmentation required. If we proceed to the next period, in which the primary population is augmented, the 10th year, the 12 individuals then found, doubled nine times, for the table admits in this instance of no further term, come to 6144, which, on the hypothesis under examination, ought to be found in: the year 192; instead of which, 10891 would be the relative number in actual existence. From the year: 14, the geometrical number would, in 194, be 7168, -the actual one is 1208. Even were we to com-. mence with the year 1, at the moment of the marriage:

of our first couples, 10 doublings of the then existing individuals would give 7168, whereas in 201, there are 1462 only. Nay, were we to proceed upon the principle of our modern writers upon population, and, rejecting all others, calculate from the breeders only at the beginning of the term, and triple their numbers at the end of it, by then admitting age and infancy into the reckoning, still Dr. Franklin's "reckoning, even allowing its basis to be borne out by facts, would be false in the proportion of 4096 to 1462.

(11) But it is unnecessary to pursue the examination any further; I shall, however, remark, in conclusion, that the facts on which he erects his supposition about American doubling, are as palpably erroneous as the calculation he founds upon them. The assertion, that marriages take place there, on the average, at 20, is hardly credible; that they produce eight children each, one with another, not at all so; while the statement that one marriage takes place annually, in every fifty persons, is, as will be seen, palpably impossible. In short, his calculations on this subject are far wilder than those developed in his codicil, in which he bequeaths, at a given period, upwards of four millions sterling to the inhabitants of Boston and the State of Massachusetts, and another four millions odd, to the State of Pennsylvania and the city of Philadelphia: these legacies are arithmetically possible, upon the wretched and ruinous principle of political economy, which he seemed early to have imbibed and recommended, but the ratio of human increase is not so; and still the "philosophers of Europe" continue to appeal to his notions on the subject, which, erroneous as they are, have this apology, that they were advanced for a very different purpose from that of checking the numbers of mankind.

47

CHAPTER IV.

OF THE POSSIBLE PERIODS OF HUMAN DUPLICATION,
CONCLUDED.

(1) I HAVE given more attention to the preceding conjectures, or rather assertions, regarding the rapid periods of doubling hitherto examined, than they of themselves merited, because, as it appears to me, they are brought forward by the anti-populationists for a very special purpose, namely, that of introducing with greater effect and investing, with more apparent certainty, that ratio of human increase, for which, as with one consent, they contend; so that astronomers are less unanimous concerning the cycles of our planet, than they are about the natural progress of its population. If the reader can be but possessed with the idea that mankind may double in 10 years, or in 123, or in less than 15 years, from procreation only, and that some of these extraordinary rates of increase have not only been realised at various periods, and in different places, but are still "short of the utmost power of population," the theory which allows the human race twice the average of these terms, in which to double their numbers, presents itself to him as having the highest claims to confidence, and comes recommended by a very large degree of apparent moderation. It is evidently announced with a view to produce this impression. "But," says the most confident of these writers, "to be perfectly

sure that we are far within the truth, we will take the "slowest of these rates of increase; a rate in which "all concurring testimonies agree, and which has been

repeatedly ascertained to be from procreation only; it may be safely pronounced, therefore, that population, 'when unchecked, goes on doubling itself every 25 years, or increases in a geometric ratio1."

(2) Justice to the important matter in dispute compels me to deny every part of this statement. That mankind multiply in any geometric ratio whatsoever, remains to be disproved; when a contrary principle, more consistent with the wisdom and benevolence of GOD, and the well being of mankind, will be developed and established: that the one in question has never been" ascertained" at all, unless mere unsupported and reiterated assertion can be so reckoned, I challenge any one to shew; in the mean time, I shall proceed to prove, that what all these "concurring testimonies agree" to assert, is utterly irreconcileable with facts.

(3) But in approaching more nearly the confines of possibility, it is obviously necessary to be less extravagant in our suppositions regarding the circumstances which contribute to human increase; still, however, adopting such as are most favourable to it, and that are known to exist in countries where population is the most unrestrained and encouraged. And in doing this, to avoid all cavil or suspicion, I shall even here again' adopt the plain data on which these doublings profess to be built. Mr. Malthus, referring to a paper in the Transactions of the Philosophical Society of Philadelphia, by Mr. Barton, notices that, according to thenumbers given, the births in America are as 4 to a marriage; but adds, " as, however, this proportion was "taken principally from towns, it is probable that the "births are given too low;" which observation is another instance of the grievous misquotations in which, our author constantly indulges. Barton expressly in-,

Malthus, Essay on Population, p. 5.