(15) To apply the preceding calculations to the use for which they were made; and to commence with the last, and, as it respects increase, the least favourable computation. Few, it is presumed, after what has been advanced, will assert that only one tenth part of the marriages of the United States are occasioned by emigration, at present; most certainly there are none who can suppose such was the case upwards of 200 years ago. But, one-tenth added to the number of marriages which occur in the table, as resulting from natural generation, and, in a manner which necessarily renders them the least productive, instead of increasing the number in existence at the end of the term by one tenth only, makes upwards of seven-fold that addition. The 9730 marriages which have occurred between the years 1 and 206, give, at the latter period, 1805 persons as in actual existence; 9% extra marriages added, as explained, produce by that time, 1400%, which, added to the former, make 3211. Even this evidently deficient computation proves, then, that emigration is "immaterial" to American increase, just so far as the difference between the numbers 180 and 321 may be so regarded.

(16) But the addition of this tenth, as given in the 10th column, is more conformable to the fact to be illustrated, though it will be still inadequate to present the result in its proper magnitude. Its effect, so calculated, is to add to the same 180 persons, who, as before stated, were the product of internal generation only, during the term in question, other 26618%, making the total 4471, or, between two and three times the natural amount of the population. According to this second method of computation, then, which is still, evidently, far within the truth in all respects, is emigration "immaterial"?

406

(17) Lastly, the effect, according to the 8th column, of an emigration which would add, during the 206 years, 211 marriages, to the 97 which take

place independently of it, and at the intervals and in the proportions already explained, would be that of raising the population from 1801, the number produced by "procreation only," to 81610; or, between four and five-fold: and, even in this last computation, the interpolated marriages, as referrible to American statistics, are manifestly too few, in some of the first, and in several of the last, sections, whatever may be the case respecting those in the intermediate ones.

(18) It is on the whole, therefore, quite clear that it would be easy enough to make such additions to the marriages in the table of natural increase, as given in the preceding chapter, as would, very accurately, double its numbers every twenty-five years; that such additions would not be required to be large; though, compared with those in the preceding table, they would have to be increased somewhat in a few of the last sections, which would certainly render them more consistent with the existing facts, in relation to America: but I shall pursue these computations no further, as, in the cavils that might be raised, about some of the facts which must be then distinctly advanced, the main design of the present argument might, in some measure, be lost sight of, which is, to demonstrate that comparatively small constant accessions to the population of a country have an effect upon its increase to an extent which could not be imagined, and, certainly, would not be credited, without their being demonstrated by actual calculation: and this, it is hoped, has now been satisfactorily done.

(19) Nothing then can be clearer than the conclusions suggested by the connected results of this and

the preceding chapter, or more fatal to the principle opposed throughout. The sole demonstration advanced. in proof of the existence of the geometric theory, even in its slowest ratio of increase, is avowedly derived from the progress of American population. That increase, as stated to us, may, under certain necessary limitations, already adverted to in a preceding part of this work, be taken as substantially correct; but whether it be almost wholly the result of internal generation, or greatly accelerated by external accessions, has been the sole question: and one which, it is hoped, is now finally answered. It has been demonstrated in the last chapter, as irrefragably as arithmetic can demonstrate any thing, that the very measure of prolificness assumed in behalf of American marriages, for the special purpose of proving the duplication contended for, as resulting from internal procreation only, would fall short of producing that effect, not by a slight deficiency, which it would have been unworthy of a work of this general nature to have noticed, but, in a couple of centuries only, in the overwhelming proportion of more than fifteen to one. That there is no possibility, consistently with the laws of Nature, of amending the calculation of that prolificness, so as to combine the ratio of American increase with the hypothesis that it proceeds from propagation only, is manifest: equally so is it, that there is only one remaining method of reconciling these otherwise discordant results; but, it is one which does so, clearly and adequately-it is by adverting to the fact, and its necessary consequences, which are known and proved to exist, and to have existed, and to the extent required, on the authority of every species of evidence of which the subject is susceptible, namely,-Emigration.

(20) Dr. Johnson, I think, observes, that the word

material," is often used in a sense in which it ought to be rejected; at all events, I hope I may conclude the examination which has been the subject of the present chapter, by expressing a persuasion that both the word, and the sense in which it is applied, will, in future, be discarded, in discussing the effect of emigration on the progress, past or present, of the population of America.

VOL. II.

H

98

CHAPTER VII.

OF THE POSSIBLE PROPORTION OF MARRIAGES IN DIFFERENT COMMUNITIES.

(1) THE main agent, which, in the geometric theory of population according to its advocates, has, to the exclusion of emigration, to reconcile the wide differences which exist in the increase of various countries, is what is now called the "preventive check ;" but the powers with which it is invested, are amply sufficient, were they real, to produce all such results, and still more astonishing ones; but, alas! the limits assigned for its operation involve impossibilities, still to repeat a term which cannot be well substituted, but which begins, I fear, to sound like tautology; I proceed, however, to justify its repetition, as applied to this part also of the system under examination.

(2) Previously to pointing out the essential error in the method by which the comparative prevalence of this check is at present supposed to be ascertained, I shall spend a few words (and many will not be required) in shewing the egregious mistake into which these writers have fallen regarding the possible number of marriages in different communities, and from which, they of course suppose they establish the existence, and calculate the effects, of the great regulator of their system. Now, without attending for the present to those particulars, which, it will be hereafter seen, limit the proportion, we will only state, that the utmost number of annual marriages (first ones, at least) which may take place in any community, cannot possibly exceed the number of those of