duce the food for a family, joined to the ignorance and barbarism of the people, which have prompted them to follow their inclinations with no other prospect than an immediate bare fubfiftence, have encouraged marriage to fuch a degree, that the population is pushed much beyond the industry and prefent refources of the country; and the confequence naturally is, that the lower claffes of people are in the moft depreffed and miferable state. The checks to the population are of course chiefly of the pofitive kind, and arife from the difeafes occafioned by squalid poverty, by damp and wretched cabins, by bad and infufficient clothing, by the filth of their perfons, and occafional want. To thefe pofitive checks have, of late years, been added the vice and mifery of inteftine commotion, of civil war, and of martial law.

СНАР.

CHAP. IX.

On the fruitfulness of Marriages.

Ir would be extremely defirable, 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 folution, but we shall make fome approximation towards it, and be able to account for fome of the difficulties which appear in many registers, if we attend to the following confiderations.

It should be premised however, that in the registers of most countries there is some reason to believe, that the omiffions in the births and deaths are greater than in the marriages; and confequently, that the proportion of marriages is almost always given too great. In the enumeration which lately took place in this country, while it is fuppofed with reason, that the registry of marriages is nearly correct, it is known with certainty, that there are very great omiffions in the births and deaths; and it is probable,

that

that fimilar omiffions, though not perhaps to the fame extent, prevail in other countries.

To form a judgment of the prolifickness of marriages, taken as they occur, including fecond 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 fuccceding 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 prolifickness of thofe marriages. If the pulation be stationary, the number of births to

po

be added would exactly equal the number to be fubtracted, and the proportion of births to marriages, as found in the registers, would exactly reprefent the real prolifickness of marriages. But if the population be either increafing or decreafing, the number to be added would never

be

be equal to the number to be fubtracted, and the proportion of births to marriages in the registers would never truly represent the prolifickness of marriages. In an increafing population the number to be added would evidently be greater than the number to be fubtracted, and of course the proportion of births to marriages, as found in the registers, would always be too fmall to represent the true prolifick nefs of marriages, And the contrary effect would take place in a decreafing population. The question therefore is, what we are to add and what to fubtract, when the births and deaths are not equal.

The average proportion of births to marriages in Europe is about 4 to 1. Let us fuppofe for the fake of illuftration, that each marriage yields four children, one every other year. In this cafe it is evident, that whereever 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 fame manner, the

In the ftatistical account of Scotland it is faid, that the average distance between the children of the fame family has been calculated to be about two years.

marriages

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 confidered 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 cafes of flow increase, approach towards the births of the next 4 years. The mean therefore may be taken at 3 years." Confequently 34 if we fubtract the births of the first 3 years of the period, and add the births of the 3 years fubfequent to the period, we fhall have a number of births nearly equal to the births produced by all the marriages included in the period, and of courfe the prolifickness of these marriages. But if the population of a country be increasing re-. gularly, 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 fame proportion to all the births of any other period of the fame extent, taken a certain number of years later, as the births of

a

According to the rate of increase which is now taking place in England, the period by calculation would be about 3 years.

any