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Observations on the proper Method of constructing Tables for determining the Rate of human Mortality, the Number of Inhabitants, and the Values of Lives in any Town or District, from Bills of Mortality in which are given, the Numbers dying annually at all Ages.
every place that just supports itself in the number of its inhabitants, without any recruits from other places; or where, for a course of years, there has been no increase or decrease, the number of persons dying. every year at any particular age, and above it, must be equal to the number of the living at that age.-The number, for example, dying every year, at all ages, from the beginning to the utmost extremity of life, must, in such a situation, be just equal to the whole number born every year. And for the same reason, the number dying every year at one year of age and upwards; at two years of age and upwards; at three and upwards, and so on; must be equal to the numbers that reach to those ages every year; or, which is
the same, to the numbers of the living at those ages. It is obvious, that unless this happens, the number of inhabitants cannot remain the same. If the former number is greater than the latter, the inhabitants must decrease; if less, they must increase. From this observation it follows, that in a town or country where there is no increase or decrease, bills of mortality which give the ages at which all die, will shew the exact number of inhabitants; and also the exact law, according to which human life wastes in that town or country.
In order to find the number of inhabitants; the mean numbers dying annually, at every particular age and upwards, must be taken as given by the bills, and placed under one another in the order of the second column of the 5th, 8th, &c. Tables in this volume. These numbers will, it has appeared, be the numbers of the living at 0, 1, 2, 3, &c. years of age; and, consequently, the sum, diminished by half the numbers living at age o, or by half the number born annually', will be the whole number of inhabitants.
This subtraction is necessary for the following reason. In a Table formed in the manner here directed, it is supposed, that the numbers in the second column are all living together at the beginning of every year. Thus; the number in the second column opposite to 0 in the first column, the Table supposes to be all just born together on the first day of the year. The number, likewise, opposite to 1, it supposes to attain to one year of age just at the same time that the former number is born.
habitants. In such a series of numbers, the excess of each number above that which immediately follows it, will be the number dying every year, out of the particular number alive at the beginning of the year; and these excesses set down regularly, as in the third column of the Tables to which I have referred, will shew the different rates at which human life wastes through all its different periods, and the different probabilities of life at all particular ages.
It must be remembered, that what has been now said goes on the supposition that the place, whose bills of mortality are given, supports itself, by procreation only, in the number of its inhabitants. In towns this very seldom happens, on account of the luxury and debauchery which generally prevail in them. They are, therefore, commonly kept up by a constant accession of strangers or settlers, who remove to them from country parishes and villages. In these circum
And the like is true of every number in the second column. During the course of the year, as many will die at all ages as were born at the beginning of the year; and, consequently, there will be an excess of the number alive at the beginning of the year, above the number alive at the end of the year, equal to the whole number of the annual births; and the true number constantly alive together, is the arithmetical mean between these two numbers; or, agreeably to the rule I have given, the sum of the numbers in the second column of the Table, lessened by half the number of annual births. See Essay I. page 9, &c.
stances, in order to find the true number of inhabitants, and probabilities of the duration of life, from bills of mortality containing an account of the ages at which all die; it is necessary that the proportion of the annual births to the annual settlers should be known; and also the period of life at which the latter remove.-Both these particulars may be discovered by the following method.
If for a course of years there has been no sensible increase or decrease in a place, the number of annual settlers will be equal to the excess of the annual burials above the annual births. If there is an increase, it will be greater than this excess. If there is a decrease, it will be less.
The period of life at which these settlers remove, will appear in the Bills by an increase in the number of deaths at that period and beyond it. Thus; in the London Bills, the number of deaths, between 20 and 30, is generally above double, and between 30 and 40, near triple the number of deaths between 10 and 20: And the true account of this is, that from the age of 18 or 20 to 35 or 40, there is a confluence of people every year to London from the country, which occasions a great increase in the number of inhabitants at these ages; and, consequently, raises the deaths for all ages above 20 considerably above their due proportion, when compared with the number of deaths before 20. This is observable in all the bills of mortality
mortality for towns with which I am acquainted, not excepting even the Breslaw Bills. Dr. Halley takes notice, that these Bills give the number of deaths between 10 and 20, too small. This he considered as an irregularity, owing to chance: and therefore, in forming this Table of Observations, he took the liberty so far to correct it, as to render the proportion of those who die to the living in this division of life, nearly the same with the proportion which, he says, he had been informed die annually of the young lads in Christ-Church Hospital. But the truth is, that this irregularity in the Bills was derived from the cause I have just assigned. During the five years for which the Breslaw Bills are given by Dr. Halley, the births did, indeed, a little exceed the burials; but, it appears, that this was the effect of some peculiar causes that happened to operate just at that time; for, during a complete century from 1633 to 1734, the annual medium of births was 1089, and of burials 1256. This town, therefore, must have
See Lowthorp's Abridgment of the Philosophical Transactions, vol. III. p. 670.
• See Dr. Short's Comparative History, p. 63.
It appears from the account in the Philosophical Transactions (Abridgement, vol. VII. No. 380, p. 46, &c.) that from 1717 to 1725, the annual medium of births at Breslaw was 1252, of burials 1507; and also, that much the greatest part of the births died under 10 years of