On the fruitfulness of marriages. because in countries where the marriages are more prolific, the births generally follow at shorter intervals, and where they are less prolific at longer intervals; and with different degrees of prolificness, the length of the period might still remain the same.1 It will follow from these observations, that the more rapid is the increase of population, the more will the real prolificness of marriages exceed the proportion of births to marriages in the registers. The rule which has been here laid down, attempts to estimate the prolificness of marriages taken as they occur, but this prolificness should be carefully distinguished from the prolificness of first marriages and of married women, and still more from the natural prolificness of women in general, taken at the most favorable age. It is It is probable that the natural prolificness of women is nearly the same in most parts of the world; but 1 In places where there are many exports and imports of people, the calculations will of course be disturbed. In towns, particularly, where there is a frequent change of inhabitants, and where it so often happens that the marriages of the people in the neighboring country are celebrated, the inferences from the proportion of births to marriages are not to be depended on. On the fruitfulness of marriages. the prolificness of marriages is liable to be affected by a variety of circumstances peculiar to each country; and particularly by the number of late marriages. In all countries the second and third marriages alone form a most important consideration, and materially influence the average proportions. According to Sussmilch, in all Pomerania, from 1748 to 1756 both included, the number of persons who married were 56,956, and of these 10,586 were widows and widowers. According to Busching in Prussia and Silesia for the year 1781, out of 29,308 persons who married, 4,841 were widows and widowers, and consequently the proportion of marriages will be given full one sixth too much. In estimating the prolificness of married women the number of illegitimate births would tend, though in a very slight degree, to counterbalance the overplus of marriages; and as it is found that the number of widowers who marry again is greater than the number of widows, the whole of the correction should not on this ac 1 Gottliche Ordnung, vol. i. tables, p. 98. 2 Sussmilch, vol. iii. tables, p. 95. 3 In France before the revolution the proportion of illegitimate births was of the whole number. Probably it is less in this country. On the fruitfulness of marriages. count be applied; but in estimating the proportion of the born which lives to marry from a comparison of the marriages and deaths, which is what we are now about to proceed to, the whole of this correction is always necessary. To find the proportion of the born which lives to marry, we must first subtract one sixth from the marriages, and then compare the marriages of any year so corrected, with the deaths in the registers at such a distance from them, as is equal to the difference between the average age of marriage and the average age of death. Thus, for example, if the proportion of marriages to deaths were as 1 to 3, then subtracting one sixth from the marriages this proportion would be as 5 to 18, and the number of persons marrying annually the first time would be to the number of annual deaths as 10 to 18. Supposing in this case the mean age of death to be ten years later than the mean age of marriage, in which ten years the deaths would increase, then the number of persons marrying annually the first time, compared with the number of annual deaths, at the distance of the difference between the age of marriage and the age of death, would be as 10 to 20; from which it would follow that exactly half of the born lived to marry. On the fruitfulness of marriages. The grounds of this rule will appear from the following observations on registers in general. In a country in which the population is stationary, the contemporary deaths compared with the births will be equal, and will of course represent the deaths of all the born; and the marriages, or more properly the number of married persons compared with both the births and deaths, will, when a proper allowance has been made for second and third marriages, represent the true proportion of the born which lives to marry. But if the population be either increasing or decreasing, and the births, deaths, and marriages increasing or decreasing in the same ratio, then the deaths compared with the births, and the marriages compared with the births and deaths, will cease to express what they did before, unless the events which are contemporary in the registers are also contemporary in the order of nature. In the first place it is evident that death can not be contemporary with birth, but must on an average be always at such a distance from it, as is equal to the expectation of life, or the mean age of death. Consequently though the deaths of all the born are, or will be, in the registers, where there are no emigrations, yet, except vol. ii. C On the fruitfulness of marriages. when the population is stationary, the contemporary periods of births and deaths never show this, and we can only expect to find the deaths equal to the births, if the deaths be taken at such a distance from the births in the registers as is equal to the expectation of life. And in fact, thus taken the births and deaths will always be found equal. Secondly, the marriages of any year can never be contemporary with the births from which they have resulted, but must always be at such a distance from them as is equal to the average age of marriage. If the population be increasing, the marriages of the present year have resulted from a smaller number of births than the births of the present year, and of course the marriages, compared with the contemporary births, will always be too few to represent the proportion of the born which lives to marry, and the contrary will take place if the population be decreasing; and to find this proportion, we must compare the marriages of any year with the births of a previous year at the distance of the average age of marriage. Thirdly, the average age of marriage will almost always be much nearer to the average age of death than marriage is to birth; and consequently the annual marriages compared with the contemporary |