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]
[238-1] Thus, for instance, the sturgeon can, according to Leuckart, produce 3,000,000 eggs in a year. According to Burdach, the posterity of a pair of rabbits may be over 1,000,000 in four years; and that of a plant-louse, according to Bonnet, over a 1,000,000,000 in a few weeks. The prolificacy of a species of animals is wont to be greater in proportion as the structure-material (Bildungsmaterial) saved within a given time during the course of individual life, is greater, and as material wants during the embryonic period are limited; also (teleologically), in proportion as to the danger the individual is exposed to. Compare Leuckart in R. Wagner's physiolog. Wörterbuch,[TN 62] Art. Zeugung. Teleologically,[TN 63] Bastiat says: cette surabondance parait calculée partout en raison inverse de la sensibilité, de l'intelligence et de la force avec laquelle chaque espèce résiste à la déstruction. (Harmonies, ch. 16.)
[238-2] The researches of modern physiology make it probable that an ovum is detached from the ovaries at each period of healthy menstruation. (Bischoff, Beweis der von der Begattung unabhängigen periodischen Reifung und Lösung der Eier bei den Säugethieren und Menschen, 1844.) It is hardly possible to ascertain how many of these ova are capable of fecundation. Among the animals, on which the greater number of accurate observations have been made, that is in the case of horses, it has been found that, in the two districts of Prussia most favorably conditioned, of 100 mares that had been lined, 63.3 became pregnant, and 53.5 gave birth to live foals; in the rest of the Prussian monarchy, the births were only 46 per cent. Compare Schubert, Staatskunde, VII, 1, 98. In the Belgian haras (places for breeding horses), between 1841 and 1850, about 30 per cent. of the "leaps" proved fruitful, from 2 to 3 per cent. aborted, the rest were either probably or certainly unfruitful. (Horn., Statist. Gemälde, 171.) In the human species, also, the great number of first-born generated in the first weeks of marriage, bears witness to a high degree of procreative susceptibility.
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.
[238-3] See the exhaustive table in Euler, Mémoires de l'Académie de Berlin 1756, in Süssmilch, Göttl. Ordnung, I, § 160. Bridge has constructed the following formula: 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.
[238-4] Tucker, Progress of the United States, 89, ff. 98. Here deduction is already made of immigrants and their posterity, who after subtracting the loss by emigration back to the old country, amounted to over 1,000,000. It probably amounted to more yet. If, as Wappäus does (Bevölekerungsstatistik, 1859, I, 93, 122 ff.), we calculate the rate of increase per annum, we have an average during the first decade of 2.89, during the second of 2.83, the third of 2.74, the fourth of 2.52, the seventh of 2.39, the eighth (1860-70) of probably 2.25 per cent. On the still greater ratio of increase in earlier times, see Price, Observations on reversionary Payments, 1769, 4 ed. 1783, I, 282 seq., I, 260.
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).
[238-5] Immense increase of the Israelites in Egypt. (Genesis 46, 27; Numbers, 1.)
LIMITS TO THE INCREASE OF POPULATION.