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On the fruitfulness of marriages.

rate of increase which may be obtained from other sources, it is clearly desirable to find in the registers a small, rather than a large proportion of births to marriages; because the smaller this proportion is, the greater must be the proportion of the born which lives to marry, and of course the more healthy must be the country.

Cromer observes that when the marriages of a country yield less than 4 births, the population is in a very precarious state, and he estimates the prolificness of marriages by the proportion of yearly births to marriages. If this observation were just, the population of many countries of Europe would be in a precarious state, as in many countries the proportion of births to marriages in the registers is rather below than above 4 to l. It has been shown in what manner this proportion in the registers should be corrected in order to make it a just representation of the prolificness of marriages, and if a large part of the born live to marry, and the age of marriage be considerably earlier than the expectation of life, such a proportion in the registers is by no means inconsistent with a rapid increase. In Russia it has appeared

Ueber die Bevolkerung der Europais. Staat. p. 91.

On the fruitfulness of marriages.

that the proportion of births to marriages is less than 4 to 1, and yet its population increases faster than that of any other nation in Europe. In England the population increases more rapidly than in France, and yet in England the proportion of births to marriages, when allowance has been made for omissions, is about 4 to 1, in France 45 to 1. To occasion so rapid a progress as that which has taken place in America, it will indeed be necessary that all the causes of increase should be called into action; and if the prolificness of marriages be very great, the proportion of births to marriages will certainly be above 4 to 1; but in all ordinary cases, where the whole power of procreation has not room to expand itself, it is surely better that the actual increase should arise from that degree of healthiness in the early stages of life, which causes a great proportion of the born to live to maturity and to marry, than from a great degree of prolificness accompanied by a great mortality. And consequently in all ordinary cases, a proportion of births to marriages as 4 or less than 4 to 1 cannot be considered as an unfavorable sign.

It should be observed that it does not follow that the marriages of a country are early, or that vol. ii.

On the fruitfulness of marriages.

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the preventive check to population does not prevail, because the greater part of the born lives to marry. In such countries as Norway and Switzerland, where half of the born live to above 40, it is evident that though rather more than half live to marry, a large portion of the people between the ages of 20 and 40 would be living in an unmarried state, and the preventive check would appear to prevail to a great degree. In England it is probable that half of the born live to above 35, and though rather more than half live to marry, the preventive check might prevail considerably (as we know it does, though not to the same extent as in Norway and Switzerland.

The preventive check is perhaps best measured by the smallness of the proportion of yearly births to the whole population. The proportion of yearly marriages to the population is only a just criterion in countries similarly circumstanced, but is incorrect, where there is a difference in the prolificness of marriages, or in the proportion of the population under the age of puberty, and in the rate of increase. If all the marriages of a country, be they few or many, take place young, and be consequently prolific, it is evident that to produce the same proportion of births, a smaller proportion of

On the fruitfulness of marriages.

marriages will be necessary; or with the same proportion of marriages a greater proportion of births will be produced. This latter case seems to be applicable to France, where both the births and deaths are greater than in Sweden, though the proportion of marriages is nearly the same or rather less. And when in two countries compared, one of them has a much greater part of its population under the age of puberty than the other, it is evident, that any general proportion of the yearly marriages to the whole population will not imply the same operation of the preventive check among those of a marriageable age.

It is in part the small proportion of the popu. lation under the age of puberty, as well as the influx of strangers, that occasions in towns a greater proportion of marriages than in the country, although there can be little doubt that the preventive check prevails most in towns. The converse of this will also be true, and consequently in such a country as America where half of the population is under sixteen, the proportion of yearly marriages will not accurately express how little the preventive check really operates.

But on the supposition of nearly the same natural prolificness in the women of most coun

On the fruitfulness of marriages,

tries, the smallness of the proportion of births will generally indicate, with tolerable exactness, the degree in which the preventive check prevails, whether arising principally from late, and consequently unprolific marriages, or from a large proportion of the population above the age of puberty dying unmarried.

That the reader may see at once the rate of increase, and the period of doubling, which would result from any observed proportion of births to deaths, and of these to the whole population, I subjoin two tables from Sussmilch, calculated by Euler, which I believe are very correct. The first is confined to the supposition of a mortality of 1 in 36, and therefore can only be applied to countries where such a mortality is known to take place. The other is general, depending solely upon the proportion which the excess of the births above the burials bears to the whole population, and therefore may be applied universally to all countries, whatever may be the degree of their mortality.

It will be observed, that when the proportion between the births and burials is given, the period of doubling will be shorter, the greater the mortality; because the births as well as deaths are in

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