(12) The following table, having been constructed previously to the preceding calculation, regarding the proportion which 10,000 emigrants would add to American marriages, they were, in two of the columns, taken at a tenth only, and that proportion extended to the entire term, in two different methods, both of which, as will be apparent on the slightest examination, must give results erring greatly in deficiency. The first, which equally distributes the sum of that tenth throughout the whole period, (which is divided into short and equal terms,) evidently falls far short of the relative number of weddings, which must have taken place in consequence of emigration, in the earlier periods of American colonization, and must likewise greatly underrate those which have been added in the later ones, from the same cause; as, if the preceding computations be correct, it would allow only between three and four thousand emigrants as the amount of the annual accessions for the last 44 years. The other, which adds one tenth to every marriage throughout, while it gives so much smaller a part of those accessions which certainly took place in the first periods of American history, still does not come up to the proportion that is allowed, on all hands, to prevail at present, and would give, on the average of the last 44 years, less than 8000 annual emigrations. Both methods, therefore, are necessarily very deficient in representing the results which emigration must certainly have produced on the population; but even that which is the farthest from the reality will give an addition, as will be shortly seen, any thing rather than "immaterial.” (13) But the addition to the marriages of America, as produced by emigration, must be made on a principle dissimilar to both the preceding ones, in order to manifest and confirm the real fact regarding these accessions. If we fix upon so low a proportion as one tenth of the marriages as produced by these foreign additions at the present time; which, as has been before observed, supposes them to amount to less than 8000 annually, (I perceive I have given only in one of the columns in the last three sections of the ensuing table,) the farther we trace back the history of the colonies, the smaller is their population, and the proportion of emigrant marriages must consequently greatly enlarge, till at length we arrive at a period, when nearly all of them must have been thus occasioned, and finally the whole of them, literally speaking, were the union of parties born elsewhere. In conformity with this undeniable fact, I have, therefore, lastly calculated the effect of an addition of emigrant marriages, regulated on this principle, commencing with as low a proportion as part of the whole, and continuing that backwards for three sections, and afterwards for two successive sections each, increasing it to do, b, 1, 1, 4, 4, t,, t, and in the first two, adding an equal number. I am not so sure that this may not overrate the proportion of marriages thus occasioned, in some periods of the table, as I am that in others, and particularly in the beginning and end of the whole term, that proportion is greatly underrated; but, again disclaiming any pretence to scrupulous exactness on this occasion, this method also will exemplify, and perhaps more correctly than the others, the effect emigration has unquestionably had upon American population; as it is evidently calculated on a principle more consistent with its history. I have only further to remark, that should the demonstrators of the geometric theory select short periods from any of these calculations, and especially from that last mentioned, by which to shew these accessions as immaterial, I shall not only rebut the induction, by repeating what has been already advanced in proof of the erroneousness of such a method, but retract all that has been allowed, for the sake of argument, respecting the limited extent of emigration, and demand, as I am fully warranted in doing, for years together, many times the amount at which it has been stated. (14) The ensuing table, calculated on the basis of the last in the Third Chapter, presents, in the first column, equal divisions of nine years each, except, ing the last, which has eight only: the second, the middle year of each, which, deducted from 206, the last date in the table, gives, of course, the remaining years, during which the increase on any additions that are to be made to the marriages must be calculated; and the terms, thus obtained, appear in the third column. In the fourth are given, in their respective terms, the actual marriages which occur in the before mentioned table, as resulting from the two original couples. In the fifth, is found the increase on those marriages, according to the same table, for a period equal to the term expressed in the third column, and which constantly extends to the end of the calculation. In the sixth column are placed the fractional proportions of the marriages arising from emigration, compared with the rest; commencing, as before explained, with the supposition of their being equal, and of their diminishing, till, at the termination, they are abated to, which proportions are reduced in the seventh column to actual numbers. In the eighth, is the increase upon these additions, computed, for the terms specified, according to the table. In the ninth column, a less addition is made to the marriages, amounting, on the whole, to only one tenth part of the entire number; and this addition is equally distributed throughout the several divisions, without any reference to the marriages that otherwise take place in eachthe proportion in the last being reduced so as to correspond with its shorter duration. The tenth column gives the effect of such accessions on the natural increase. The eleventh column makes only the same total addition to the marriages, as the former, but does so by increasing, by, the number of marriages as they occur in the table. The twelfth, and last, gives the results of this method also. |