population are of course chiefly of the positive kind, and arise from the diseases occasioned by squalid poverty, by damp and wretched cabins, by bad and insufficient clothing, by the filth of their persons, and occasional want. To these positive checks have, of late years, been added the vice and misery of intestine commotion, of civil war, and of martial law. CHAP. CHAP. XI. 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 prolifickness 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 dif ficulties which appear in many registers, if we attend to the following 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 almost always given too great. In the enumeration which lately took 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, prevail in other countries. To form a judgment of the prolifickness 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 has 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 the period, and of course the real prolifickness of those marriages. If the population be stationary, the number of births to be added would exactly equal the number to be subtracted, and the proportion of births to marriages, as found in the registers, would exactly represent the real prolifickness 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 prolifickness 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 prolifickness 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 mar riages 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 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 33 years. In instances of the most rapid increase it will rather exceed the births of the next 31 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, 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. b According to the rate of increase which has lately been |