period in question, to which, according to the preceding computation, one fourth more, or 5000, would be added, as the effect of emigration. And it will be fully seen in the course of this work that no less an accession could have reconciled the fact of American increase to the physical laws of our nature.

(17) But the effect of such an accession would be still greater than it might be supposed to be from the mere relative addition it makes to the number of the marriages. This fact will be more fully demonstrated hereafter; in the mean time I will select, in proof of it, only one calculation from many that I had constructed, conceiving that even this is, in a great measure, superseded by a clearer method of computing the effect of emigration as given in the succeeding Book of this Treatise. The assumed proportions, that of the marriages, 1 in 1081; that of their annual prolificness, 4.38 births each (implying a higher degree of individual prolificness); and, lastly, of the deaths, one half the number of the births 3, are founded on data given

2

1 Thus, in the town of Portsmouth, U.S., the weddings were in 1808 and 1809, 125; the population in 1810, 6934; the former to the latter were therefore not quite 1 in 110 annually calculated on the inhabitants a year or two afterward.

In the town of Salem, which it was said contained in 1782 about 9000 inhabitants, the marriages were, in 1781, 70, and in 1782, 84, averaging, therefore, nearly 1 in 117 annually. Brissot, Travels in the United States, pp. 362, 363, 364.

In Philadelphia, the proportion, as reported in 1818, was still smaller.

According to Dr. Barton, however, the marriages were, in the parish of Hingham, 1 in less than a hundred; viz. above 1 in 97; calculated on a period of 54 years, and including, of course, the weddings of emigrants. But as he only guesses at the population during this period, his computation is unsatisfactory. Transactions, American

Phil. Soc., vol. iii., p. 30.

The average for the towns of Portsmouth, (U.S.), Salem, and Hingham, Massachusetts, will be 1 marriage in every 108 of the entire number of the inhabitants; which will be adopted in the ensuing calculation.

2 In the town of Salem there were, in 1781 and 1782, 385 births, illegitimates included, and 154 marriages, or 4.55 to each. Brissot, Travels in the U. States.

In the town of Portsmouth, during 8 years, from 1804 to 1811 inclusive, there were 514 marriages and 2197 births, giving a proportion of 4.27 of the latter to one of the former.

In Hingham, as given by Mr. Barton, the same proportion was for 54 years as 4.32 to 1.

The mean proportion of the three places is 4.38 to 1.

3 The proportion given by Mr. Barton, Mr. Warden, vol. iii., p. 231, and Baron Humboldt.

in the notes; and they will be shewn to be more favourable to the increase of population than the general laws of Nature warrant.

(18) The following table exhibits the increase of a population, the movements of which should be thus regulated, amounting to 108.00 individuals; and, therefore, starting with one marriage, 4.38 births, and 2.19 deaths.

TABLE XIV.

SHEWING THE INCREASE OF A COMMUNITY IN WHICH THE MARRIAGES ARE AS 1 IN 108 INDIviduals, the Births 4.38 tO EACH MARRIAGE, AND the Deaths half the number of the Births.

(19) The preceding table might have been calculated with more mathematical exactness by another method, but it would not have exemplified the progress of population thus increased, so familiarly; it is, however, quite accurate enough for the purpose of shewing that it would take a period of nearly 35 years to double a population, in which the marriages are as 1 in 108, the births double the number of deaths, and 4.38 to each marriage. In this table, it will be perceived, that the births are to the population as 1 in every 24.65, and the deaths 1 in 49.3; whereas Warden himself estimates the deaths in the United States at 1 in 40; and though he conceives the births to be twice as numerous, all the facts we are in possession of contradict him. In the places before referred to in the notes, the births give, in no instance, so great a proportion. In a statistical account of the State of New York, I find them amounting to 1 in 26.77. It is needless to say how much all the proportions in the table exceed those which prevail in Europe'.

(20) The following table exhibits the effect which a stationary number of emigrants would have upon the increase of population, commencing with so low a proportion as a two hundredth part of the native inhabitants; supposing that only of that proportion directly caused a marriage each, and that the remainder were composed of a promiscuous number of both sexes, and of all ages.

"Depuis le 40 degré de latitude jusqu'au 65, c'est-à-dire, sur une ligne qui s'étend de Lisbonne à Stockholm, en embrassant une étendue de mille lieues environ, et sur une population de 65 millions d'individus, qui habitent le Portugal, le royaume de Naples, de France, l'Angleterre, la Prusse, le Danemark,

et la Suède, la proportion des décès est de 1 sur 40.3;

par

Celle des naissances, de 1 sur 30.1; Celle des mariages, de 1 sur 123.3, Et la fécondité de 4 enfans mariage."-Benoiston de Chateauneuf, Bul. Univers. Géog. et Statistique, vol vi., p. 169.

1

TABLE XV.

EXHIBITING THE EFFECT OF EMIGRATION ON THE INCREASE OF POPULATION.