ESSAY, &c. BOOK II. CHAPTER IX. On the Fruitfulness of Marriages. IT would be extremely desirable to be able to deduce from the rate of increase, the actual population, and the registers of births, deaths, and marriages, in different countries, the real prolificness of marriages, and the true proportion of the born which lives to marry. Perhaps the problem may not be capable of an accurate solution, but we shall make some approximation towards it, and be able to account for some of the difficulties which appear in many registers, if we attend to the fol. lowing considerations. It should be premised however, that in the registers of most countries there is some reason to believe, that the omissions in the births and deaths are greater than in the marriages; and consequently, that the proportion of marriages is al most always given too great. In the enumeration vol. ii. b On the fruitfulness of marriages. which lately took place in this country, while it is supposed with reason, that the registry of marriages is nearly correct, it is known with certainty, that there are very great omissions in the births and deaths; and it is probable that similar omissions, though not perhaps to the same extent, prcvail in other countries. To form a judgment of the prolificness of marriages, taken as they occur, including second and third marriages, let us cut off a certain period of the registers of any country, 30 years for instance, and inquire what is the number of births which have been produced by all the marriages included in the period cut off. It is evident, that with the marriages at the beginning of the period will be arranged a number of births proceeding from marriages not included in the period; and at the end, a number of births produced by the marriages included in the period, will be found arranged with the marriages of a succeeding period. Now if we could subtract the former number, and add the latter, we should obtain exactly all the births produced by the marriages of the period, and of course the real prolificness of those marriages. If the population be stationary, the number of births to be added would exactly equal the num On the fruitfulness of marriages. ber to be subtracted, and the proportion of births to marriages, as found in the registers, would exactly represent the real prolificness of marriages. But if the population be either increasing or decreasing, the number to be added would never be equal to the number to be subtracted, and the proportion of births to marriages in the registers would never truly represent the prolificness of marriages. In an increasing population the number to be added would evidently be greater than the number to be subtracted, and of course the proportion of births to marriages, as found in the registers, would always be too small to represent the true prolificness of marriages. And the contrary effect would take place in a decreasing population. The question therefore is, what we are to add and what to subtract, when the births and deaths are not equal. The average proportion of births to marriages in Europe is about 4 to 1. Let us suppose for the sake of illustration, that each marriage yields four children, one every other year. In this In the statistical account of Scotland it is said, that the average distance between the children of the same family has been calculated to be about two years. On the fruitfulness of marriages. case it is evident, that wherever you begin your period in the registers, the marriages of the preceding eight years will only have produced half of their births, and the other half will be arranged with the marriages included in the period, and ought to be subtracted from them. In the same manner, the marriages of the last eight years of the period will only have produced half of their births, and the other half ought to be added. But half of the births of any eight years may be considered as nearly equal to all the births of the succeeding 3 years. In instances of the most rapid increase it will rather exceed the births of the next 3 years, and in cases of slow increase approach towards the births of the next 4 years. The mean therefore may be taken at 3 years. Consequently if we subtract the births of the first 3 years of the period, and add the births of the 33 years subsequent to the period, we shall have a number of births nearly equal to the births produced by all the marriages included in the period, and of course the prolificness of these marriages. 1According to the rate of increase which is now taking place in England, the period by calculation would be about 3 years. On the fruitfulness of marriages. But if the population of a country be increasing regularly, and the births, deaths, and marriages continue always to bear the same proportion to each other, and to the whole population, it is evident that all the births of any period will bear the same proportion to all the births of any other period of the same extent, taken a certain number of years later, as the births of any single year to the births of a single year taken the same number of years later; and the same will be true with regard to the marriages. And consequently to estimate the prolificness of marriages we have only to compare the marriages of the present or any other year with the births of a subsequent year taken 33 years later. We have supposed in the present instance, that each marriage yields four births; but the average proportion of births to marriages in Europe is 4 to 1, and as the population of Europe is known to be increasing at present, the prolificness of marriages must be greater than 4. If allowing for this circumstance we take the distance of 4 years instead of 3 years, we shall probably be not far from the truth. And though undoubtedly the riod will differ in different countries, yet it will not differ so much as we might at first imagine; pe |