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have been all along kept up by a number of yearly recruits from other places, equal to about a seventh part of the yearly births.

What has been now observed concerning the period of life at which people remove from the country to settle in towns, would appear sufficiently probable, were there no such evidence for it as I have mentioned; for it might be well reckoned, that these people in general, must be single persons in the beginning of mature life, who not having yet obtained settlements in the places where they were born, migrate to towns in quest of employments.

Having premised these Observations, I shall next endeavour to explain distinctly, the effect which these accessions to towns must have, on Tables of Observation formed from their bills of mortality. This is a subject proper to be insisted on, because mistakes have been committed about it; and because also the discussion of it is necessary to shew, how near to truth the values of lives come as deduced from such Tables.

The following general rule may be given on this subject.

If a place has, for a course of years, been maintained in a state nearly stationary, as to

age. From a Table in Susmilch's works, Vol. I. p. 38, it appears, that, in reality, the greater part of all that die in this town are children under five years of age.

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number of inhabitants, by supplies or recruits coming in every year, to prevent the decrease that would arise from the excess of the burials above the births; a Table formed on the principle, “that the number dying annually, after "every particular age, is equal to the num"ber living at that age," will give the number of inhabitants and the probabilities of life, too great for all ages preceding that at which the supplies cease; and after this, it will give them right. If the accessions are

so great as to cause an increase in the place, such a Table will give the number of inhabitants and the probabilities of life, too little, after the age at which the accessions cease; and too great, if there is a decrease. Before that age it will in both cases give them too great; but most considerably so in the former case, or when there is an increase.

For example. Let us suppose, that 244 of those born in a town, attain annually to 20 years of and that 250 more, all age;

Agreeably to these Observations; if a place increases, not in consequence of accessions from other places, but of a constant excess of the births above the deaths; a Table, constructed on the principle I have mentioned, will give the probabilities of life too low through the whole extent of life; because, in such circumstances, the number of deaths in the first stages of life must be too great, in comparison of the number of deaths in the latter stages; and more or less so, as the increase is more or less rapid. The contrary, in all respects, takes place where there is a decrease, arising from the excess of the deaths above the births.

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likewise 20 years of age, come into it annually from other places; in consequence of which, it has for a course of years, been just maintained in the number of its inhabitants, without any sensible increase or decrease. In these circumstances the number of the living in the town of the age of 20, will be always 244 natives and 250 settlers, or 494 in all; and, since these are supposed all to die in the town, and no more recruits are supposed to come in; 494 will be likewise the number dying annually at 20 and upwards. In the same manner, it will appear on these suppositions, that the number of the living, at every age, subsequent to 20, will be equal to the number dying annually at that age and above it; and consequently, that the number of inhabitants and the decrements of life, for every such age, will be given exactly by the Table I have supposed. But for all ages before 20, they will be given much too great. For let 280 of all born in the town, reach 10. In this case 280 will be the true number of the living in the town, at the age of 10; and the recruits not coming in till 20, the number given by the Bills, as dying between 10 and 20, will be the true number dying annually of the living in this division of life. Let this number be 36; and it will follow, that the Table ought to make the numbers of the living at the ages between 10, and 20, a series of decreasing means between

280 and (280 diminished by 36, or) 244. But in forming the Table on the principle I have mentioned, 250 (the number above 20 dying annually in the town who were not born in it) will be added to each number in this series; and, therefore, the Table will give the numbers of the living, and the probabilities of life in this division of life, almost twice as great as they really are. This observation, it is manifest, may be applied to all the ages under 20.

It is necessary to add, that such a Table will give the number of inhabitants, and the probabilities of life, equally wrong before 20, whether the recruits all come in at 20, agreeably to the supposition just made, or only begin then to come in. In this last case, the Table will give the number of inhabitants, and probabilities of life, too great throughout the whole extent of life, if the recruits come in at all ages above 20. But if they cease at any particular age, it will give them right only from that age; and before, it will err all along on the side of excess; but less considerably between 20 and that age, than before 20--For example. If, of the 250 I have supposed to come in at 20, only 150 then come in, and the rest at 30; the numbers of the living will be given 100 too high at every age between 20 and 30; but as just shewn, they will be given 250 too high at every age before 20. In general, therefore, the number

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of the living at any particular age, must be given by the supposed Table, as many too great as there are annual settlers after that age: And, if these supplies come in, at all ages indiscriminately, during any certain interval of life; the number of inhabitants and the probabilities of life will be continually growing less and less wrong, the nearer any age is to the end of that interval.

These Observations prove, that Tables of Observation formed in the common way, from bills of mortality for places, where there is an excess of the burials above the births, must be erroneous, for a great part of the duration of life, in proportion to the degree of that excess. They shew likewise, at what parts of life the errors in such Tables are most considerable, and how they may be in a great measure corrected.

All this I shall exemplify and illustrate in the particular case of London.

The number of deaths, between the ages of 10 and 20, is always so small in the London Bills, that it seems certain few recruits -come to London under 20; or at least not so many as before this age are sent out for Leducation to schools and universities. After 20, great numbers come in till 30, and some perhaps till 40 or 50. The London Tables of Observation, therefore, being formed on the principle I have mentioned, cannot give the probabilities of life right

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