On the fruitfulness of marriages.

annual deaths will much more nearly represent the true proportion of the born living to marry, than the marriages compared with the births."

The

1 Dr. Price very justly says (Observ. on Reserv. Pay. vol. i. p. 269, 4th edit.) "that the general effect of an "increase while it is going on in a country is to render "the proportion of persons marrying annually, to the an"nual deaths greater and to the annual births less than "the true proportion marrying out of any given number "born. This proportion generally lies between the other "two proportions, but always nearest the first." In these observations I entirely agree with him, but in a note to this passage he appears to me to fall into an error. He says, that if the prolificness of marriages be increased (the probabilities of life and the encouragement to marriage remaining the same) both the annual births and burials would increase in proportion to the annual weddings. That the proportion of annual births would increase is certainly true, and I here acknowledge my error in differing from Dr. Price on this point in my last edition; but I still think that the proportion of burials to weddings would not necessarily increase under the circumstances here supposed.

The reason why the proportion of births to weddings increases is, that the births occurring in the order of nature considerably prior to the marriages which result from them, their increase will affect the register of births much more than the contemporary register of marriages. But the same reason by no means holds with regard to the deaths, the average age of which is generally later than the age of marriage. And in this case, after the first interval between birth and marriage, the permanent effect would be, that the register of marriages would be more

On the fruitfulness of marriages.

marriages compared with the births, after a proper allowance has been made for second and third marriages, can never represent the true proportion of the born living to marry, unless when the population is absolutely stationary; but although the population be increasing or decreasing according to any ratio, yet the average age of marriage may still be equal to the average of death; and in this case the marriages in the registers compared with the contemporary deaths, after the correction for second and third marriages, will represent the true proportion of the born living to marry.'

affected by the increase of births, than the contemporary register of deaths; and consequently the proportion of the burials to the weddings would be rather decreased than increased. From not attending to the circumstance that the average age of marriage may often be considerably earlier than the mean age of death, the general conclusion also which Dr. Price draws in this note does not appear to be strictly correct.

The reader will be aware, that as all the born must die, deaths may in some cases be taken as synonimous with births. If we had the deaths registered of all the births which had taken place in a country during a certain period, distinguishing the married from the unmarried, it is evident, that the number of those who died married, compared with the whole number of deaths, would accurately express the proportion of the births which had lived to marry.

On the fruitfulness of marriages.

Generally however, when an increase of population is going forwards, the average age of marriage is less than the average of death, and then the proportion of marriages compared with the contemporary deaths, will be too great to represent the true proportion of the born living to marry, and to find this proportion, we must compare the marriages of any particular year with the deaths of a subsequent year at such a distance from it in the registers, as is equal to the difference between the average age of marriage and the average age of death.

There is no absolutely necessary connection between the average age of marriage and the average age of death. In a country the resources of which will allow of a rapid increase of population, the expectation of life, or the average age of death may be extremely high, and yet the age of marriage be very early, and the marriages then, compared with the contemporary deaths in the registers, would, even after the correction for second and third marriages, be very much too great to represent the true proportion of the born living to marry. In such a country we might suppose the average age of death to be 40, and the age of marriage only 20; and in this case, which however

On the fruitfulness of marriages.

would be a rare one, the distance between marriage and death would be the same as between birth and marriage.

If we apply these observations to registers in general, though we shall seldom be able to obtain accurately the true proportion of the born living to marry, on account of our not knowing the average age of marriage, yet we may draw many useful inferences from the information which they contain, and reconcile many of the difficulties with which they are accompanied; and it will generally be found, that in those countries where the marriages bear a very large proportion to the deaths, we shall see reason to believe that the age of marriage is much earlier than the average age of

death.

In the Russian table for the year 1799, produced by Mr. Tooke, and referred to p. 372, the proportion of marriages to deaths appeared to be as 100 to 200. When corrected for second and third marriages, by subtracting one sixth from the marriages it will be as 100 to 252. From which it would seem to follow that out of 252 births 200 of them had lived to marry; but we can scarcely conceive any country to be so healthy, as that 200 out of 252 should live to marry. If however we suppose what seems to be probable,

On the fruitfulness of marriages.

that the age of marriage in Russia is 15 years earlier than the expectation of life or the average age of death, then, in order to find the proportion which lives to marry, we must compare the marriages of the present year, with the deaths 15 years later. Supposing the births to deaths to be (as stated p. 372) 183 to 100, and the mortality 1 in 50, the yearly increase will be about of the population; and consequently in 15 years the deaths will have increased a little above .28; and the result will be, that the marriages compared with the deaths 15 years later, will be as 100 to 322. Out of 322 births it will appear that 200 live to marry, which from the known healthiness of children in Russia, and the early age of marriage, is not an improbable proportion. The proportion of marriages to births, being as 100 to 385, the prolificness of marriages, according to the rule laid down, will be as 100 to 411, or each marriage will on an average, including second and third marriages, produce 4.11 births.

The lists given in the earlier part of the chapter on Russia are probably not correct. It is suspected with reason, that there are considerable omissions both in the births and deaths, but particularly in the deaths, and consequently the proportion