Jedge; and they would afford the neceffary data 35 40 40 45 1161 25 30 45 50 50 55 60 65 65 70 80 90 Above 90 1044 Regifters of mortality on the improved plan above mentioned, were established in 1772 at Chester, and also, in 1773, at Warrington in Lancashire; and they are fo comprehenfive and correct, that there is reafon to expect they will afford much inftruction on the subject of human mortality, and the values of lives. But the country moft diftinguifhed in this refpect is Sweden; for in that kingdom exact accounts are taken of the births, marriages, and burials, and of the numbers of both fexes that die at all ages in every town and dif trict, and also at the end of every period of five years, of the numbers living at every age: and at Stockholm a fociety is eftablished, whose business it is to fuperintend and regulate the enumerations, and to collect from the different parts of the king. dom the regifters, in order to digeft them into tables of obfervation. These regulations were begun in Sweden in 1755; and, tables, containing the refult of them from 1755 to 1763, have been published in Mr Wargentin's memoir just referred to; and the moft material parts of them may be found in an effay by Dr Price on the Difference between the Duration of Human Life in Towns and in Country Parishes, printed in the 65th vol. of the Philof. Trans. part ii. (4.) MORTALITY, METHOD OF FORMING RE GISTERS OF. In the 4th effay in Dr Price's Trea tife on Reverfionary Payments and Life Annuities, the following account is given of the principles on which tables of obfervation are formed from registers of mortality; and of the proper method of forming them, fo as to render them juft reprefentations of the number of inhabitants, and the probabilitles of the duration of human life in a town or country. In every place which just fupports itself in the number of its inhabitants, without any recruits from other places; or where, for a courfe of years, there has been no increase or decrease; the number of perfons dying every year at any particular age, and above it, muft 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, muft, in fuch a fituation, be just equal to the whole number born every year. And for the fame reason, the number dying every year at one year of age and upwards, at two years of age and upwards, and so on, must be equal to the numbers that attain to thofe ages every year; or, to the numbers of the living at thofe ages. It is ob1042 vious, that unless this happens, the number of 1074 inhabitants cannot remain the fame. If the for1080 mer number is greater than the latter, the in-, 1097 habitants must decrease; if lefs, they muft in1283 creafe. From this obfervation it follows, that in 1000 to 1099 town town or country where there is no increase or decreafe, bills of mortality which give the ages at which all die, will show the exact number of inhabitants, and alfo the exact law according to which human life wattes in that town or country. 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 fecond column of the following tables. Thefe numbers will, it has appeared, be the numbers of the living at 1, 2, 3, &c. years of age; and confequently the fum diminished by half the number born annually will be the whole number of inha bitants. This subtraction is necessary for the following reafon. In a table formed in the manner here directed, it is fuppofed that the numbers in the 2d column are all living together at the beginning of every year. Thus the number in the 2d column opposite to o in the first column, the table fuppofes to be all juft born together on the first day of the year. The number, likewife, oppofite to 1, it fuppofes to attain to one year of age juft at the fame time that the former number is born. And the like is true of every number in the 2d column. Daring the courfe of the year, as many will die at all ages as were born at the beginning of the year; and confequently, there will be an excefs of the number alive at the begin ning 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 conftant ly alive together, is the arithmetical mean be tween thefe two numbers; or agreeably to the rule here given, the sum of the numbers in the 2d column of the table leffened by half the num ber of annual births. In fuch a fer.es of numbers, the excess of each number ábove that which im mediately follows it will be the number dying every year out of the particular number alive at the beginning of the year; and thefe excefies fet down regularly as in the 3d column of the table to which we have referred, will fhow the diffe rent rates at which human life waftes through all its different periods, and the different probabili ties of life at all particular ages. What has been now faid goes on the fuppofition, that the place whofe bills of mortality are given, fupports itfelf, by procreation only, in the number of its inhabitants. In towns this very feldom happens on account of the luxury and debauchery which generally prevail in them. They are, therefore, commonly kept up by a conftant acceffion of rangers, who remove to them from country pa rithes and villages. In thefe circumfta ces, in order to find the true number of inhabitants, and probabilities of life, from bills of mortality containing an account of the ages at which ali die, it is neceffary that the proportion of the annual births to the annual fettlers fhould be known, and alfo the period of life at which the latter remove. Both thefe particulars may be difcovered by the following method: If for a courfe of years there has been no fenfible increafe or decrease in a place, the number of annual fettiors will be equal to the exccfs of the annual bures above the annual births. If there is an incrcafe, it wil be greater than this excefs. If there is a decreafe, it will be lefs. The period of life at which there fettlers remove, will appear in the bills by an increafe 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 36 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 50, there is an afflux of people every year to London from the country, which oc cafions a great increase in the number of inhabitants at thefe ages; and confequently raifes the deaths for all ages above 20 confiderably above their due proportion, when compared with the number of deaths before zo. This is obfervable in all the bills of mortality for towns with which we are acquainted, not excepting even the Breflaw bills. Dr Halley takes notice, that these bills gave the number of deaths between 10 and 20 too small. This he confidered as an irregularity in them owing to chance; and, therefore, in forming his table of obfervations, he took the liberty fo far to correct it, as to render the proportion of thofe who die to the living in this divifion of life nearly the fame with the proportion which, he fays, he had been informed die annually of the young lads in Chrift-Church Hofpital. But the truth is, that this irregularity in the bills was derived from the caufe we have juft affigned. During the five years for which the Breflaw bills are given by Dr Halley, the births did indeed a little exceed the burials; but it appears that this was the effect of fome peculiar caufes that happened to operate juft 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, muft have been all along kept up by a number of yearly recruits from o ther places, equal to about a 7th part of the yearly births. It appears from the account in the Philo. Tran. Abr. 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 that the greateft part of the births died under 10 years of age, From a table in Sufmilch's works, vol. i. p. 38. it appears that in reality the greater part of ail that die in this town are children under five years of age. What has been now observed concerning the period of life at which people remove from the country to settle in towns, would appear fufficiently probable were there no fuch evidence for it as has been mentioned; for it might be well reckoned that thefe people in general must be fingle perfons in the beginning of mature life, who, not having yet obtained fettlements in the places where they were born, migrate to towns in queft of employments. It is proper next to endeavour to explain diftinctly the effect which thefe acceffions to towns must have on tables of obfervation formed from their bills of mortality. This is a fubject proper to be infifted on, because mistakes have been committed about it; and becaufe alfo the difcuffion of it is neceffary to show how near to truth the values of lives come as deduced from fuch tables. The following general rule may be given on this fubject. If a place has for a courfe of years been maintained in a ftate nearly stationary, as to number of inha bitants bitants, by recruits coming in every year, to pre vent the decreafe that would arife from the excefs of burials above the births, a table formed on the principle, "that the number dying annually after every particular age, is equal to the number 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 recruits ceafe; and after this it will give them right. If the acceffions are fo great as to caufe an increase in the place, fuch a table will give the number of inhabitants and the probabilities of life too little after the age at which the acceffions ceafe; and too great if there is a decreafe. Before that age it will in both cafes give them too great; but moft confiderably fo in the former cafe, or when there is an increase. Agreeably to thefe obfer. vations, if a place increases not in confequence of accellions from other places, but of a conftant excefs of the births above the deaths, a table conftructed on the principle that has been mentioned will give the probabilities of life too low through the whole extent of life; because in such circumftances the number of deaths in the first stages of life must be too great, in comparison of the number of deaths in the latter ftages; and more or lefs fo as the increase is more or lefs rapid. The contrary in all respects takes place where there is a decrease arifing from the excefs of the deaths above the births. For example: Let us fuppofe that 244 of those born in a town attain annually to 20 years of age, and that 250 more, all like wife 20 years of age, come into it annually from other places, in confequence of which it has for a courfe of years been juft maintained in the number of its inhabitants, without any fenfible increafe or decrease in thefe circumstances, the number of the living in the town of the age of 40 will be always 244 natives and 250 fettlers, or 494 in all; and fince thefe are fuppofed ail to die in the town, and no more recruits are fuppofed to come in, 494 will be likewise the number dy ing annually at zo and upwards. In the fame manner it will appear, on thefe fuppofitions, that the number of the living, at every age fubfequent to 20, will be equal to the number dying annual ly at that age and above it; and confequently, that the number of inhabitants and the decrements of life, for every fuch age will be given exactly by the table. But for all ages before 20, they will be given much too great. For let 280 of all born in the town reach ro; in this cafe 280 will be the true number of the living in the town at the age of ro: 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 divifion 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 decreafing means between 280 and (280 diminished by 36, or) 244. But in forming the table on the principle juft mentioned, 230 (the number above 20 dying annually in the town who were not born in it) will be added to each number in this feries; and therefore the table will give the numbers of the living, and the probabilities of life in this divifion of life, almost twice as great as they really are. VOL. XV. PART I. This obfervation, it is manifeft, may be applied to all the ages under 20. Such a table will give the number of inhabitants and the probabilia ties of life equally wrong before 20, whether the recruits all come in at 20, agreeably to the fuppofition juft made, or only begin then to come in. In this laft cafe, 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 ceafe at any particular age, it will give them right only from that age; and before, it will err all a long on the fide of excefs; but lefs confiderably between 20 and that age than before 20. For example: if, of the 250 fuppofed to come in at 20, only 150 then come in, and the reft at 30; the num ber of the living will be given 150 too high at every age between 20 and 30; but, as just shown, they will be given 250 too high at every age before 201 In general, therefore, the number of the living at any particular age must be given by the supposed table as many too great as there are annual fettiers after that age; and if these fettlers come in at all ages indifcriminately, during any certain intera val of life, the number of inhabitants and the probabilities of life will be continually growing lefs and lefs wrong the nearer any age is to the end of that interval. Thefe obfervations prove, that tables of obfervation formed in the common way, from bills of mortality for places where there is an excess of the burials above the births, muft be erroneous for a great part of the duration of life, in proportion to the degree of that excefs. They fhow likewife at what parts of life the errors in fuch tables are most confiderable, and how bey may be in a great measure corrected. All this that be exemplified in the particu lar cafe of London. The number of deaths between the ages of 10 and 20 is always fo fmall in' the London bills, that it feems certain few res cruits come to London under 20, or at leaft not fo many as before this age are fent out for education to schools and universities. After 20 great numbers come in till 30, and fome perhaps till 40 or 50: but at every age after 50, it is proba ble that more retire from London than come to it. The London tables of obfervation, therefore, being formed on the principle already mentioned, cannot give the probabilities of life right till 40. Between 30 and 40 they must be a little too high; bu. more fo between 20 and 30, and most of all fo before 20. It follows alfo, that these tables must give the number of inhabitants in London much too great: The first of the following tables is formed in the manner here explained, from the London bills for 10 years, from 1759 to 1768, and adapted to 1500 born as a radix. The fum of the numbers in the 2d column, diminished by half the number born, is 25,757. According to this table then, for every 1000 deaths in London there are 25 as many inhabitants; or, in other words, the expectation of a child just born is 234; and the inhabitants are to the annual burials as 254 to 1. But it has appeared, that the numbers in the 2d column, being given on the fuppofition that all thofe who die in London were born there, must be too great; and we have hence a demonftration, that the probabilities of life are given in ૨૧ the the common tables of London obfervations too high for at least the first 30 years of life; and alfo, that the number of inhabitants in London must be less than 25 multiplied by the annual burials. The common tables, therefore, of London obfervations undoubtedly need correction, as Mr Simplon fuggefted, and in fome measure performed; though too imperfectly, and without going upon any fixed principles, or fhowing particularly how tables of obfervation ought to be formed, and how far in different circumftances, and at different ages, they are to be depended on. The way of doing this, and in general the right method of forming genuine tables of obfervation for towns, may be learned from the following rule: "From the fum of all that die annually, after any given age, subtract the number of annual fettlers after that age; and the remainder will be the number of the living at the given time." If, therefore, the number of annual fettlers in a town at every age could be afcertained, a perfect table of obfervations might be formed for that town from bills of mortality, containing an account of the ages at which all die in it. But no more can be learned in this inftance, from any bills, than the whole number of annual fettlers, and the general divifion of life in which they enter. This, however, may be fufficient to enable us to form tables that thall be tolerably exact. For inftance: Suppose the annual deaths in a town which has not increased or decreased, to have been for many years in the proportion of 4 to 3 to the annual births. It will hence follow, that of the perfons who die in fuch a town are fet tlers, or emigrants from other places, and not natives; and the fudden increase in the deaths after 20 will also fhow, agreeably to what was before obferved, that they enter after this age. In forming, therefore, a table for such a town, a quarter of all that die at all ages throughout the whole extent of life must be deducted from the fum of all that die after every given age before 20; and the remainder will be the true number living at that given age. And if at 20, and every age above it, this deduction is omitted, or the number of the living at every fuch age is taken the fame with the fum of all that die after it, the refult will be (fuppofing moft of the fettlers to come in before 30, and all before 40) a table exact till 20; too high between 20 and 30; but nearly right for fome years before 40; and after 40 exact again. Such a table, it is evident, will be the same with the table last described at all ages above 20, and different from it only under 20. It is evident alfo, that on account of its giving the probabilities of life too great for fome years after 20, the number of inhabitants deduced from it may be depended on as fomewhat greater than the truth; and more or less fo, as the annual recruits enter in general later or fooner after 20. Let us now confider what the refult of these remarks will be, when applied particularly to the London bills. It must be here first obferved, that at least one quarter of all that die in London are fupplics or fettlers from the country, and not natives. The medium of annual burials for 10 years, from 1759 to 1768, was 22,956; of births 15710. The excels is 7246, or near a third of the burials. The fame excess during 10 years be fore 1750 was 10,500, or near half the burials. London was then decreafing. For the last 12 or 15 years it has been increafing. This excefs, therefore, agreeably to the foregoing obfervations, was then greater than the number of annual fettlers, and it is now lefs. It is however here suppofed, that the number of annual fettlers is now no more than a quarter of the annual burials, in order to allow for more omiffions in the births than the burials; and alfo, in order to be more fure of obtaining refults that shall not exceed the truth. Of every 1000 then who die in London only 750 are natives, and 250 are recruits, who come to it after 18 or 20 years of age; and, confequently, to obtain from the bills a more correct table than the first of the following tables, 250 must be fubtracted from every one of the num ber in the 2d column tili 20; and the numbers in the 3d column must be kept the fame, the biils always giving these right. Atter 20, the table is to be continued unaltered; and the refult will be, a table which will give the numbers of the living at all ages in London much nearer the truth, but ftill fomewhat too high. Such is the 2d of the following tables. The fum of all the numbers in the 2d column of this table, diminished by 500, is 20,750. For every 1000 deaths, therefore, in London, there are, according to this table, 20,750 living perfons in it; or for every fingle death 20 inhabitants. It was before shown, that the number of inhabitants in London could not be fo great as 25 times the deaths. It now appears (fince the numbers in the 2d column of this table are too high) that the number of inhabitants in London cannot be fo great as even 20 times the deaths. And this is a conclufion which every one who will beftow due attention on what has been faid, will find himfelf forced to receive. It will not be amifs, however, to confirm it by the following fact, the knowledge of which is derived from the particular enquiry and information of Mr Harris, the late ingenious mafter of the royal mathematical fchool in Chrift-Church hofpital. The average of lads in this fchool has, for 30 years past, been 831. They are admitted at all ages between 7 and 11; and few ftay beyond 16: they are therefore in general, lads between the ages of 8 and 16. They have better accommodations than children commonly have; and about 300 of them have the advantage of being educated in the country. In fuch circumftances, it may be well reckoned, that the proportion of children dying annually must be less than the general proportion of children dying annually at the fame ages in London. The fact is, that for the latt 30 years 12 have died annually, or one in 703. According to Table II. one in 73 dies between 10 and zo, and one in 70 between 8 and 16. That table, therefore, probably gives the decrements of life in London, at thes ages, too little, and the numbers of the living too great: and if this is true of these ages, it must be true of all other ages under 20; and it follows demonftrably, in conformity to what was before fhown, tl it more people fettle in London after 20 than the 4th above fuppofed; and that from 20 to at least 30 or 35, the numbers of the living are given too great great, in proportion to the decrements of life. In this table the numbers in the ad column are doubled at 20, agreeably to what really happens in London; and the fum of the numbers in this column diminished by half the whole number of deaths, gives the expectation of life, not of a child juft born, as in other tables, but of all the inhabitants of London at the time they enter it, whether that be at birth or at 20 years of age. The expectations, therefore, and the values of London lives under 20, cannot be calculated from this table. But it may be very eafily fitted for this purpose, by finding the number of births which, according to the given decrements of life, will leave 494 alive at 20; and then adapting the intermediate numbers in fuch a manner to this radix, as to preferve all along the number of the living in the fame proportion to the numbers of (5.) MORTALITY.—TABLE I. the dead. This is done in the 3 of the following tables and this table may be recommended as better adapted to the prefent ftate of London than any other table. The values of lives, however, deduced from it, are in generai nearly the fame with those deduced by Mr Simpfon from the London bills as they ftood 50 years ago; (See ANNUITIES, Sec. II. Table IV.) the main difference is, that after 52, and in old age this table gives them fomewhat lower than Mr Simpson's table. The difference between the rate of human mortality in great towns and in country parishes and villages, may be found from various tables in Sir J Sinclair's Statistical Account of Scotland; as well as from the the rev. D. Wilkie's table and calculations for the county of Fife, inferted under the article ANNUITIES, Sec. III. (6.) MORTALITY.—TABLE II. till the age of 19. Showing the probabilities of life in London, on Showing the true probabilities of life in London the fuppofition that all who die in London were born there. Formed from the bills for 10 years, from 1759 to 1768. Perfons living Decr. of Life. 62 132 63 125 64 118 01234 750 I 240 510 99 4 65 66 III 5 Awwww. Decr. of Life. 67 |