habitants at these ages; and consequently raises the deaths for allages above 20 considerably above their due proportion, whencompared with the number of deaths before 20. This is observa-ble in all the bills of mortality for towns with which we are ac-quainted, not excepting even the Breslaw bills. Dr. Ilalley takesnotice, that these bills gave the number of deaths between 10 and20 too small. This he considered as an irregularity in them ow-ing to chance ; and, therefore, in forming his table of observations,he took the liberty so far to correct it, as to render the proportionof those who die to the living in this division of life nearly thesame with the proportion which, iie says, he had been informeddie annually of the young lads in Christ-Church llospilal. Butthe truth is, that'this irregularity in the bills was derived from thecause we have just assigned. During the live years for which theBreslaw bills are given by Dr. Halley, the births did indeed a littleexceed the burials ; but it appears that this was the effect of some•peculiar causes that happened to operate just at that time: forduring a complete century from 1033 to 1734, llie annual mediumof births was 1089, and of burials 1250. This town, therefore,must have been all along kept up by a number of yearly recruitsfrom oilier places, equal to about a seventh part of the yearlybirths. It appears from the account in the Philos. Trans. Abr.voi. vii. no. 380, p. 40, &c. that from 1717 lo 1725, the annualmedium of births at Breslaw was 1252, of burials 1507; and thatthe greatest part of the births died under 10 years of age. proma table in Susmilch’s works, vol. i. p. 38, it appears that in realitytlie greater part of all that die in this town are children under liveyears of age. What lias been now observed concerning the periodof life at which people remove from the country to settle in towns,would appear sufficiently probable were there no such evidencefor it as lias been mentioned ; for it might he well reckoned thatthese people in general must be single persons in the beginning ofmature life, who, not having yet obtained settlements in the placeswhere they were bom, migrate to towns in quest of employments.It is proper next to endeavour to explain distinctly the effectwhich these accessions to towns must have on tables of observationformed from their bids of mortality. This is a subject proper tobe insisted on, became mistakes have been committed about it;and because also the discussion of it is necessary to shew how nearto truth the values of lives come as deduced from such tables.The following general rule maybe given on this subject: if aplace lias for a course of years been maintained in a slate nearlystationary, as to number of inhabitants, by recruits coming in everyyear, to prevent the decrease that would arise from the excess ofburials above the births, a table formed on the principle, “ thattlie number dying annually after every particular age, is equal to .the number of living at that age,” will give tlie number of inha-bitants, and tlie probabilities of life, too great, forall ages preced-ing that at which tlie recruits cease; and alter this it will givethem right. If the accessions are so great as to cause an increase intlie place, such a table will give tlie number of inhabitants and tlieprobabilities of life too little after tlie age at which tlie accessionscease; and too great if there is a decrease. Before that age itwill in both cases give them too great; but most considerably soin tlie former case, or when there is an increase. Agreeably totiiese observations, if a place increases not in consequence of ac-cessions from other places, but of a constant excess of the birthsabove tlie deaths, a table constructed on tlie principle that hasbeen mentioned will give (lie probabilities of life too low throughthe whole extent of life ; because in such circumstances the num-ber of deaths in tlie first stages of life must lie too great, in com-parison of tlie number of deaths in the latter stages; and more orless so as the increase is more or less rapid. The contrary in allrespects takes place where there is a decrease arising froiff tlie ex-cess of tlie deaths above the births. For example : Let us sup-pose that 244 of those born in a town attain annually to 20 yearsof age, and that 250 more, all likewise 20 years <A age, comeinto it annually from other places, inconsequence of which it hasfora course of years been just maintained in tlie number of its in-habitants’, without anv sensible increase or decrease : in these cir-cumstance's, the numtier of the living in the town at tlie age of 20will be always 244 natives and 250 settlers, or 494 in all ; andsince these arc supposed all to die in tlie town, and no more re-cruits are supposed to come in, 494 will be likewise the numberdying annually at 20 and upwards. In tlie same manner it will j

j appear, on these suppositions, that the number of tlie living- atevery age subsequent to 20, will be equal to tlie number dyingannually at that age and above it; and consequently, that l*'j :number of inhabitants and (he decrements of life, for every suchage will be given exactly by tlie table. But for all ages befof e20, they will be given much too great. For let 2S0 of all born h’tlie town reach 10 ; in this , case 280 will be the true numbertlie living in tiie town at tlie age of 10 ; and tlie recruits not coin*ing in till' 20, the number given by the bills as dying between 1°and 20 will be the true number dying annually of tlie living 1)1this division of life. Let this number be 30: and it will followthat the table ought to make the numbers of die living at the agesbetween 10 and 20, a series of decreasing means between 280 and(280 diminished by 36, or) 244. But in forming the table on th°principle just mentioned, 250 (tlie number above 20 dying a °'nually in the town who were not born in it) will be added to eachnumber in tiiis series; and therefore tile table will give the linin'bersofthe living, and the probabilities of life in'tliis division oflife, almost twice as great as they really are. This observation*is manifest, may be applied to all the ages under 20. Such »table will give the number of inhabitants and the probabilities. 0 *life, equally wrong before 20, whether the recruits alt come in at20, agreeably to tlie supposition just made, or only begin then tocome in. In tills last case, tlie table will give the number of in-habitants and probabilities of life loo great throughout the wholeextent of life, if the recruits come in at all ages above 20. lint 1 *they cease at any particular age, it will give them rigid only fron>that age; and before, it will err all along on tlie side of excess*but less considerably- between 20 and that age than before 20-For example : if, of the 250 supposed to be in at 20, only D®then come in, and tlie rest at 30 ; tlie number of the livingbe given 100 too high at every age between 20 and 30 ; bub aSjust shewn, they will be given 250 too high at every age beloi’ 1 -20. In general, therefore, the number of theliving at any,parli< ulafage must be given by the supposed table as many too great a*there arc annual settlers after that age; and if these settlers co| otfin at all ages indiscriminately, during any certain interval of bli-the number of inhabitants and the probabilities of life will be con-tinually growing less and less wrong tlie nearer any age is to tl> 1 -end of that interval. These observations prove, that tables of ob*^servation formed in the common way, from bills of mortality i°Jplaces where there is an excess of the burials above the births, u" l>tlie erroneous for a great part of tlie duration of life, in proportionto the degree of that excess. They shew likewise at what p alliof life the errors in such tables are most considerable, and ho"*they may be in a great measure corrected. All this shall be ex-emplified in tlie particular case of London . The number of deat* lSbetween tlie 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 arc sent out for educa-tion to schools and universities. After 20 great numbers coine^ 11 *till 30, and some perhaps till 40 or 50 : but at every age after 5*Vit is probable that more retire from London than come to it.London tables of observation, therefore,' being formed on t*'°principle already mentioned, cannot give tilt: probabilities otfight till 40. Between 30 and 40 they must be a little loo bigi*'but more so between 20 and 30, and most of all so before 20. *

follows also, that these tables must give the number of inhabit:' 11 !*'in London much too great. The first of the following tables ' 9formed in the manner here explained, from the London bills \ of10 years, from’1759to 1708, and adapted to 1000 born as a radix-The sum of the numbers in the second column, diminished by ha*the number born, is 25,757. According to this table then, *°^every 1000 deaths in London (here arc 254 as many inhabitants *or, in oilier words, (lie expectation of a child just born is 25 j-; al,cthc inhabitants are to the annual burials as 25j- to 1. But it *' a3appeared, that tlie numbers in the second column, being given (,l>the supposition that all those who die in London were born the 1 ' 1 ’''must be too great; and we have hence a demonstration,., that o' 0probabilities of life are given in the common tables of Lon** 0 'observations too high for at least the first 30 years of life ; and a* 5 *that the number ot inhabitants in London must be less than 2?*multiplied by the annual burials. The common tables, tliereio^’of London observations undoubtedly need correction, as '*'•Simpson suggested, and in some measure performed; though 10 .

iinl 1<r1 '