.

(14) The preceding calculations, therefore, I repeat, exhibit very different proportions to those quoted from Euler, which are, "a mortality of 1 in 36, and the births to the deaths as 3 to 1," or, in other words, 1 birth in every 12, which, it is added, would double the population in the time specified, as has been known to have been the case in different countries. In the table, which hardly increases at that rate even exclusive of the deaths, no such proportions are found; there, on the whole average, there is only one birth in 18, and after the deaths of the recorded births are included, there is not one in 600! and the further the computation is carried, the less fluctuation is observable, and certainly no indication of material alteration in these proportions or of any acceleration in the increase. To augment the number in the column of the deaths, by transferring to it a part of that of the births in their infancy, it is evident would be fatal to the doubling in 12 years. How then are the proportions mentioned as those of Euler to be obtained, so as still to preserve the duplication which is its basis? In one method only, and that so as in some measure to reconcile the relative proportions in question to the laws of nature, though presenting them in a series of the grossest exaggerations; by increasing the number of births one-half, and assigning a third of the whole as the proportion of the born that do not live to marry most writers, including Dr. Franklin, fix that proportion at one-half; Mr. Malthus, I observe, at considerably more than two-fifths, under circumstances highly favourable to human increase. If we place these deaths in the octennial section in which they were born, considering the number that inevitably die in the first stages of infancy, it will allow some of them to survive to the age of puberty; and, lastly, the column of the population will have to receive these births for the

purpose of making the proper addition to its mean annual amount: the mean proportions of the last table will then be rectified as follows.

TABLE XVIII.

EXHIBITING THE MEAN PROPORTIONS IN A POPULATION DOUBLING EVERY 12 YEARS, IN WHICH THE BIRTHS ARE AS ABOUT 1 TO 12, AND THE DEATHS AS 1 TO 36.

(15) We have thus arrived, by exact calculations, at the particulars necessary in an entire population, to establish, from the given proportion of births and deaths, the rate of increase with which Mr. Malthus commences; and of which, he not only pronounces the possibility but the actual occurrence in repeated cases, and they are these:-All must marry, and at as early a period as twenty years of age; all the married must be fruitful, and to the extent of fifteen children each: of these fifteen children, as many as ten must live to marry, and at the same early age, and must in their turn be equally prolific; and so on. Every father, therefore, must be the parent of fifteen children in the first descent, of 165 in the second, of 1665 in the third; and if he could survive till he had seen the last complete their quota to this state of prolificness, he would reckon upon 16,665 great-great-grandchildren. Moreover, it must be observed, that these are the bare aver

age numbers demanded in order to this ratio of increase from every married individual. I leave to the reader's imagination how far, therefore, even this state of fecundity must be enlarged to make up for cases of positive or comparative sterility in the married, and for those marriages which would be dissolved by premature mortality, before they had produced the given number of children, all which occurrences, it must be borne in mind, are as common and as inevitable, in all communities, as death itself: he will not readily overrate the addition that must of necessity be made to the medium of fifteen children, in order to make up that average as resulting from the totality of cases.

(16) To those who are at all acquainted with the structure of a community, in regard to the ages and condition of the individuals of which it is necessarily composed, the foregoing demonstrations will appear superfluous. The bare terms in which the proposition is stated, namely, one birth in every twelve, are of themselves abundantly sufficient to refute it; it is, in fact, precisely coincident with the assertion that all married females shall, on the average, have fifteen children. The proportion involves a physical impossibility.

(17) The same author, still copying from others, without due examination, has mentioned in yet more confident terms a somewhat extended period of doubling; which, though rather less remote from possibility, is nevertheless very far removed from it. Alluding to the often recited increase in American population, he says, "It cannot be doubted that, in particular districts, "the period of doubling, from procreation only, has "often been less than fifteen years."

(18) This term is given forth with so much confi dence, is represented to be of such frequent occurrence and is so precisely limited to what is the only question

before us, that is, the natural increase of a community from procreation only, that I have been induced to examine it, also, with the attention necessary to ascertain the prolificness it demands. In assuming that what is meant by less than fifteen years, may perhaps be about fourteen, or rather, somewhere between fourteen and fifteen, I conceive I cannot be accused of misinterpretation; to find out, therefore, the circumstances necessary to realize this ratio of increase, I constructed several other tables, similar to the first of the preceding ones, when the following appeared to answer the purpose with sufficient exactness.

TABLE XIX.

SHEWING THE PROGRESS OF A POPULATION, DOUBLING BETWEEN EVERY 14 AND 15 YEARS.