BOOK V.. On Population.

ON POPULATION.

CHAPTER I.

THEORY OF POPULATION.

SECTION CCXXXVIII.

INCREASE OF POPULATION IN GENERAL.

That amid the thousand dangers which threaten the existence of the individual the species may endure, the Creator has endowed every class of organic beings with such reproductive power, and so much pleasure in propagating their kind, that if the action of these were entirely unrestricted, it would soon fill up the earth.[238-1] In the case of the human race, also, the physiological possibility of propagation has very wide limits.[238-2] It would be nothing extraordinary that a healthy pair, living in wedlock from the 20th to the 42nd year of the woman's life, that is, during the whole time of her full capacity to bear children, should rear six children to the age of puberty. This would, therefore, suffice to treble the population in a single generation; provided that all who had grown up should marry. According to Euler,[238-3] when the births were 5 per cent. and the deaths 2 per cent., the population doubled in not quite 24 years; when the increase was 2-1/2 per annum, in 28 years; when 2, in 35 years, and when 1-1/2 per cent. in 47 years.

The United States furnish us with a striking illustration of this doctrine, and on the grandest scale. There the natural increase of the white population, from 1790 to 1840, was 400.4 per cent.; that is in the first decade 33.9 per cent. of the population in 1790; in the second 33.1, in the third 32.1, in the fourth 30.9, in the fifth 29.6 per cent.[238-4] [238-5]

On the other hand, the healthy male semen ejected during a single act of coition contains innumerable germs, a very few of which are sufficient to produce fecundation. (Leuckart, loc. cit, 907.) According to Oesterlen, Handbuch der medicischen Statistik, 1865, 196, from 10 to 20 per cent. of all marriages were childless. In the United Kingdom, Farr, report on the Census of 1851, estimated that in a population of 27,511,000, there were 1,000,000 childless families, when the term is allowed to embrace widows and widowers as well as married couples.]

Log. A = Log. P + n x Log.(1+(m-b)/mb). Here P stands for the actually existing population, 1/m = the ratio between the annual mortality and the number of the living, 1/b, the ratio of the number of annual births to the number of the living, n the number of years, A, the population at the end of three years, the quantity sought for.]

It was nothing unheard of to see an old man with a living posterity of 100. (Franklin, Observations concerning the Increase of Mankind, and the Peopling of New Countries, 1751.) It is said that in the region about Contendas, in Brazil, there were on from 70 to 80 births a mortality of from 3 to 4 per annum (how long?), and an unfortunate birth (unglücklichen) was scarcely ever heard of. Mothers 20 years of age had from 8 to 10 children; and one woman in the fifties had a posterity of 204 living persons. (Spix und Martius, Reise III, 525).]