A term frequently used to signify a contagious disease, which destroys great numbers of either men or beasts.
Bills of Mortality, are accounts or registers specifying the numbers born, married, and buried in any parish, town, or district. In general they contain only these numbers; and, even when thus limited, are of great use, by showing the degrees of healthiness and prolificness, and the progress of population in the places where they are kept. It is therefore much to be wished, that such accounts had been always correctly kept in every kingdom, and regularly published at the end of every year. We should then have had under our inspection the comparative strength of every kingdom, as far as it depends on the number of inhabitants, and its increase or decrease at different periods. But such accounts are rendered more useful, when they include the ages of the dead, and the distempers of which they have died. In this case they convey some of the most important instructions, by furnishing us with the means of ascertaining the law which governs the waste of human life, the values of annuities dependent on the continuance of any lives, or any survivorships between them, and the favourable or unfavourable effects of different situations to the duration of human life. There are but few registers of this kind; nor has this subject, though so interesting to mankind, ever engaged much attention till lately. The first bills containing the ages of the dead were those for the town of Breslaw in Silesia. It is well known what use has been made of these by Dr Halley, and after him by De Moivre. A table of the probabilities of the duration of human life at every age, deduced from them by Dr Halley, has been published in the Philosophical Transactions, (see the Abridgement, vol. iii. p. 699.) and is the first table of that sort that has been ever published. Since the publication of this table similar bills have been established in a few towns of this kingdom; and particularly in London, in the year 1728, and at Northampton in 1735.
Two improvements of these registers have been proposed: the first is, That the sexes of all that die in every period of life should be specified in them, under the denomination of boys, married men, widowers, and bachelors; and of girls, married women, widows, and virgins. The second is, That they should specify the number of both sexes dying of every distemper in every month, and at every age. See the end of the 4th essay in Dr Price's Treatise on Reversionary Payments. Registers of mortality thus improved, when compared with records of the seasons, and with the circumstances that discriminate different situations, might contribute greatly to the increase of medical knowledge; and they would afford the necessary data for determining the difference between the duration of human life among males and females; for such a difference there certainly is much in favour of females, as will appear from the following facts.
At Northampton, though more males are born than females: and nearly the same number die; yet the number of living females appeared, by an account taken in 1746, to be greater than the number of males, in the proportion of 2301 to 1779, or 39 to 30.
At Berlin it appeared, from an accurate account which was taken of the inhabitants in 1747, that the number of female citizens exceeded the number of male citizens in the proportion of 459 to 391. And yet out of this smaller number of males, more had died for 20 years preceding 1751, in the proportion of 19 to 17.
At Edinburgh, in 1743, the number of females was to the number of males as 4 to 3. (See Maitland's History of Edinburgh, p. 220.) But the females that died annually from 1749 to 1758, were to the males in no higher proportion than 3½ to 3.
He that will take the pains to examine the accounts in Phil. Trans. Abr. vol. vii. part iv. p. 46, &c. will find, that though in the towns there enumerated, the proportion of males and females born is no higher than 19 to 18, yet the proportion of boys and girls that die is 8 to 7; and that, in particular, the still-born and chryson males are to the still-born and chryson females as 3 to 2.
In 39 parishes of the district of Vaud in Switzerland, the number of males that died during ten years before 1766 was 8170; of females 8167; of whom the numbers that died under one year of age were 1817 males and 1395 females; and under ten years of age, 3999 males and 2598 females. In the beginning of life, therefore, and before any emigrations can take place, the rate of mortality among males appears to material parts of them may be found in an essay by Dr Price on the Difference between the Duration of Human Life in Towns and in Country Parishes, printed in the 65th volume of the Philosop. Transf. Part II.
In the fourth essay in Dr Price's Treatise on Reversionary Payments and Life Annuities, the following account is given of the principles on which tables of observation are formed from registers of mortality; and of the proper method of forming them, so as to render them just representations of the number of inhabitants, and the probabilities of the duration of human life in a town or country.
In every place which 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 attain 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 show the exact number of inhabitants, and also the exact law according to which human life waxes 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 following tables. These numbers will, it has appeared, be the numbers of the living at 1, 2, 3, &c., years of age; and consequently the sum diminished 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. 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 a-
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**Table:**
| Under the age of one year, | 1000 to 1099 | |---------------------------|--------------| | From 1 to 3 years of age, | 1000—1022 | | 3—5 | 1042 | | 5—10 | 1074 | | 10—15 | 1080 | | 15—20 | 1097 | | 20—25 | 1283 | | 25—30 | 1161 | | 30—35 | 993 | | 35—40 | 1159 | | 40—45 | 1115 | | 45—50 | 1340 | | 50—55 | 1339 | | 55—60 | 1292 | | 60—65 | 1115 | | 65—70 | 1080 | | 70—80 | 1022 | | 80—90 | 1046 | | Above 90 | 1044 |
Registers of mortality on the improved plan before mentioned, were established in 1772 at Chester, and also in 1773 at Warrington in Lancashire; and they are so comprehensive and correct, that there is reason to expect they will afford much instruction on the subject of human mortality, and the values of lives.
But the country most distinguished in this respect is Sweden: for in that kingdom exact accounts are taken of the births, marriages, and burials, and of the numbers of both sexes that die at all ages in every town and district, and also at the end of every period of five years, of the numbers living at every age: and at Stockholm a society is established, whose business it is to superintend and regulate the enumerations, and to collect from the different parts of the kingdom the registers, in order to digest them into tables of observation. These regulations were begun in Sweden in 1755; and tables, containing the result of them from 1755 to 1763, have been published in Mr Wargentin's memoir just referred to; and the most greeably to the rule here given, the sum of the numbers in the second column of the table lessened by half the number of annual births.
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 table to which we have referred, will show 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, who remove to them from country parishes and villages. In these circumstances, 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 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 in the following method.
If for a course of years there have 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 be an increase, it will be greater than this excess. If there be 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 an afflux 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 for towns with which we are acquainted, not even excepting the Breslaw bills. Dr Halley takes notice, that these bills gave the number of deaths between 10 and 20 too small. This he considered as an irregularity in them owing to chance; and, therefore, in forming his 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 we 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 been all along kept up by a number of yearly recruits from other places, equal to about a seventh part of the yearly births.
It appears from the account in the Philosophical Transactions (Abridgement, vol. vii. No 382, p. 46, &c.), that from 1717 to 1725, the annual medium of births at Breslaw was 1232, of burials 1507; and also that much the greatest part of the births died under 10 years of age. From a table in Sufnich'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.
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 has been mentioned; for it might well be 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, it will be proper next to 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 show how near to truth the value of lives comes 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 number of inhabitants, by recruits coming in every year, to prevent the decrease that would arise from the excess 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 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.
Accordingly 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 that has been 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.
For example: Let us suppose that 244 of those born in a town attain annually to 20 years of age, and Mortality, and that 250 more, all 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. But for all ages before 23, 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 363; 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 just 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 supposed to come in at 20, only 150 then come in, and the rest at 30; the number of the living will be given 100 too high at every age between 20 and 30; but, as just shown, they will be given 250 too high at every age before 20. 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 settlers after that age; and if these settlers 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 show likewise at what parts of life the errors in such mortality tables are most considerable, and how they may be in a great measure corrected.
All this shall be exemplified 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 education to schools and universities. After 20 great numbers come in till 30, and some perhaps till 40 or 50; but at every age after 50, it is probable that more retire from London than come to it. The London tables of observation, 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; but more so between 20 and 30, and most of all so before 20. It follows also 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 1750 to 1768, and adapted to 1000 born as a radix. The sum of the numbers in the second column, diminished by half the number born, is 25757. According to this table, then, for every 1000 deaths in London there are 253 as many inhabitants; or, in other words, the expectation of a child just born is 253; and the inhabitants are to the annual burials as 253 to 1. But it has appeared, that the numbers in the second column, being given on the supposition that all those who die in London were born there, must be too great; and we have from hence a demonstration, that the probabilities of life are given in the common tables of London observations too high for at least the first 30 years of life; and also, that the number of inhabitants in London must be less than 253 multiplied by the annual burials. The common tables, therefore, of London observations undoubtedly need correction, as Mr Simpson suggested, and in some measure performed; though too imperfectly, and without going upon any fixed principles, or showing particularly how tables of observation ought to be formed, and how far in different circumstances, and in different ages, they are to be depended on. The way of doing this, and in general the right method of forming genuine tables of observation for towns, may be learned from the following rule:
"From the sum of all that die annually, after any given age, subtract the number of annual settlers after that age; and the remainder will be the number of the living at the given time."
This rule can want no explication or proof after what has been already said.
If, therefore, the number of annual settlers in a town at every age could be ascertained, a perfect table of observations 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 instance from any bills, than the whole number of annual settlers, and the general division of life in which they enter. This, however, may be sufficient to enable us to form tables that shall be tolerably exact. For instance: Suppose the annual deaths in a town which has not increased or decreased, to have Mortality been for many years in the proportion of 4 to 3 to the annual births. It will hence follow, that \( \frac{1}{4} \) of the persons who die in such a town are settlers, or emigrants from other places, and not natives; and the sudden increase in the deaths after 20 will also show, agreeably to what was before observed, 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 sum 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, the deduction is omitted, or the number of the living at every such age is taken the same with the sum of all that die after it, the result will be (supposing most of the settlers to come in before 30, and all before 40) a table exact till 20; too high between 20 and 30; but nearly right for some 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 also, that on account of its giving the probabilities of life too great for some years after 20, the number of inhabitants deduced from it may be depended on as somewhat greater than the truth; and more or less so, as the annual recruits enter in general later or sooner after 20.
Let us now consider what the result of these remarks will be, when applied particularly to the London bills.
It must be here first observed, that at least one quarter of all that die in London are supplies or settlers from the country, and not natives. The medium of annual burials for 10 years, from 1759 to 1768, was 22,956; of births 15,710. The excess is 7,246, or near a third of the burials. The same excess during 10 years before 1750 was 10,500, or near half the burials. London was then decreasing. For the last 12 or 15 years it has been increasing. This excess, therefore, agreeably to the foregoing observations, was then greater than the number of annual settlers, and it is now less. It is however here supposed, that the number of annual settlers is now no more than a quarter of the annual burials, in order to allow for more emigrations in the births than the burials; and also, in order to be more sure of obtaining results 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, consequently, in order to obtain from the bills a more correct table than the first of the following tables, 250 must be subtracted from every one of the numbers in the second column till 20; and the numbers in the third column must be kept the same, the bills always giving these right. After 20, the table is to be continued unaltered; and the result will be, a table which will give the numbers of the living at all ages in London much nearer the truth but still somewhat too high. Such is the second of the following tables. The sum of all the numbers in the second 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 persons in it; or for every single death 20\(\frac{1}{4}\) inhabitants. It was before shown, that the number of inhabitants in London could not be so great as 25\(\frac{1}{4}\) times the deaths. It now appears (since the numbers in the second column of this table are too high) that the number of inhabitants of London cannot be so great as even 20\(\frac{1}{4}\) times the deaths. And this is a conclusion which every one, who will bestow due attention on what has been said, will find himself forced to receive. It will not be amiss, however, to confirm it by the following fact, the knowledge of which is derived from the particular inquiry and information of Mr Harris, the late ingenious master of the royal mathematical school in Christ-Church hospital. The average of lads in this school has, for 30 years past, been 831. They are admitted at all ages between 7 and 11; and few stay beyond 16: they are therefore, in general, lads between the age of 8 and 16. They have better accommodations than it can be supposed children commonly have; and about 300 of them have the particular advantage of being educated in the country. In such circumstances 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 same ages in London. The fact is, that for the last 30 years 11\(\frac{1}{4}\) have died annually, or one in 70\(\frac{1}{4}\).
According to Table II. one in 73 dies between 10 and 20, and one in 70 between 8 and 16. That table, therefore, probably gives the decrements of life in London, at these 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 demonstrably, in conformity to what was before shown, that more people settle in London after 20 than the fourth above supposed; and that from 20 to at least 30 or 35, the numbers of the living are given too great, in proportion to the decrements of life.
In this table the numbers in the second column are doubled at 20, agreeably to what really happens in London; and the sum of the numbers in this column diminished by half the whole number of deaths, gives the expectation of life, not of a child just 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 easily 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 such a manner to this radix, as to preserve all along the number of the living in the same proportion to the numbers of the dead. This is done in the third of the following tables; and this table may be recommended as better adapted to the present state of London than any other table. The values of lives, however, deduced from it, are in general nearly the same with those deduced by Mr Simpson from the London bills as they stood forty years ago; the main difference is, that after 52, and in old age, this table gives them somewhat lower than Mr Simpson's table. The fourth and fifth of the following tables, compared with the two last, will give a distinct and full view of the difference between the rate of human mortality in great towns and in country parishes and villages.
TABLE ### Table I
Showing the Probabilities of Life in London, on the supposition that all who die in London were born there. Formed from the Bills for 10 years, from 1759 to 1768.
| Ages | Persons living | Decr. of Life | Ages | Persons living | Decr. of Life | Ages | Persons living | Decr. of Life | |------|---------------|--------------|------|---------------|--------------|------|---------------|--------------| | 0 | 1000 | 240 | 31 | 494 | 9 | 62 | 132 | 7 | | 1 | 760 | 99 | 32 | 395 | 9 | 63 | 125 | 7 | | 2 | 661 | 42 | 33 | 386 | 9 | 64 | 118 | 7 | | 3 | 619 | 29 | 34 | 377 | 9 | 65 | 111 | 7 | | 4 | 592 | 21 | 35 | 368 | 9 | 66 | 104 | 7 | | 5 | 569 | 11 | 36 | 359 | 9 | 67 | 97 | 7 | | 6 | 538 | 10 | 37 | 350 | 9 | 68 | 90 | 7 | | 7 | 548 | 7 | 38 | 341 | 9 | 69 | 83 | 7 | | 8 | 541 | 6 | 39 | 332 | 10 | 70 | 76 | 6 | | 9 | 535 | 5 | 40 | 322 | 10 | 71 | 70 | 6 | | 10 | 530 | 4 | 41 | 312 | 10 | 72 | 64 | 6 | | 11 | 526 | 4 | 42 | 302 | 10 | 73 | 58 | 5 | | 12 | 522 | 4 | 43 | 292 | 10 | 74 | 53 | 5 | | 13 | 518 | 3 | 44 | 282 | 10 | 75 | 48 | 5 | | 14 | 515 | 3 | 45 | 272 | 10 | 76 | 43 | 5 | | 15 | 512 | 3 | 46 | 262 | 10 | 77 | 38 | 5 | | 16 | 509 | 3 | 47 | 252 | 10 | 78 | 33 | 4 | | 17 | 506 | 3 | 48 | 242 | 9 | 79 | 29 | 4 | | 18 | 503 | 4 | 49 | 233 | 9 | 80 | 25 | 3 | | 19 | 499 | 5 | 50 | 224 | 9 | 81 | 22 | 3 | | 20 | 494 | 7 | 51 | 215 | 9 | 82 | 19 | 3 | | 21 | 487 | 8 | 52 | 206 | 8 | 83 | 16 | 3 | | 22 | 479 | 8 | 53 | 198 | 8 | 84 | 13 | 2 | | 23 | 471 | 8 | 54 | 190 | 7 | 85 | 11 | 2 | | 24 | 463 | 8 | 55 | 183 | 7 | 86 | 9 | 2 | | 25 | 455 | 8 | 56 | 176 | 7 | 87 | 7 | 2 | | 26 | 447 | 8 | 57 | 169 | 7 | 88 | 5 | 1 | | 27 | 439 | 8 | 58 | 162 | 7 | 89 | 4 | 1 | | 28 | 431 | 9 | 59 | 155 | 8 | 90 | 3 | 1 | | 29 | 422 | 9 | 60 | 147 | 8 | | | | 30 | 413 | 9 | 61 | 139 | 7 | | |
### Table II
Showing the true probabilities of Life in London till the age of 19.
| Ages | Persons living | Decr. of Life | Ages | Persons living | Decr. of Life | Ages | Persons living | Decr. of Life | |------|---------------|--------------|------|---------------|--------------|------|---------------|--------------| | 0 | 750 | 240 | 9 | 285 | 5 | 18 | 253 | 4 | | 1 | 510 | 99 | 10 | 280 | 4 | 19 | 249 | | | 2 | 411 | 42 | 11 | 276 | 4 | 20 | 494 | | | 3 | 369 | 29 | 12 | 272 | 4 | 21 | 487 | | | 4 | 340 | 21 | 13 | 268 | 3 | &c. | &c. | | | 5 | 319 | 11 | 14 | 265 | 3 | | | | | 6 | 308 | 10 | 15 | 262 | 3 | | | | | 7 | 298 | 7 | 16 | 259 | 3 | | | | | 8 | 291 | 6 | 17 | 256 | 3 | | | |
The numbers in the second column to be continued as in the last table.
### Table III
Showing the true Probabilities of Life in London for all ages. Formed from the Bills for 10 years, from 1759 to 1768.
| Ages | Persons living | Decr. of Life | Ages | Persons living | Decr. of Life | Ages | Persons living | Decr. of Life | |------|---------------|--------------|------|---------------|--------------|------|---------------|--------------| | 0 | 1518 | 486 | 31 | 404 | 9 | 62 | 132 | 7 | | 1 | 1032 | 200 | 32 | 395 | 9 | 63 | 125 | 7 | | 2 | 832 | 85 | 33 | 386 | 9 | 64 | 118 | 7 | | 3 | 747 | 59 | 34 | 377 | 9 | 65 | 111 | 7 | | 4 | 688 | 42 | 35 | 368 | 9 | 66 | 104 | 7 | | 5 | 646 | 23 | 36 | 359 | 9 | 67 | 97 | 7 | | 6 | 623 | 20 | 37 | 350 | 9 | 68 | 90 | 7 | | 7 | 603 | 14 | 38 | 341 | 9 | 69 | 83 | 7 | | 8 | 589 | 12 | 39 | 332 | 10 | 70 | 76 | 6 | | 9 | 577 | 10 | 40 | 322 | 10 | 71 | 70 | 6 | | 10 | 567 | 9 | 41 | 312 | 10 | 72 | 64 | 6 | | 11 | 558 | 9 | 42 | 302 | 10 | 73 | 58 | 5 | | 12 | 549 | 8 | 43 | 292 | 10 | 74 | 53 | 5 | | 13 | 541 | 7 | 44 | 282 | 10 | 75 | 48 | 5 | | 14 | 534 | 6 | 45 | 272 | 10 | 76 | 43 | 5 | | 15 | 528 | 6 | 46 | 262 | 10 | 77 | 38 | 5 | | 16 | 522 | 7 | 47 | 252 | 10 | 78 | 33 | 4 | | 17 | 515 | 7 | 48 | 242 | 9 | 79 | 29 | 4 | | 18 | 508 | 7 | 49 | 233 | 9 | 80 | 25 | 3 | | 19 | 501 | 7 | 50 | 224 | 9 | 81 | 22 | 3 | | 20 | 494 | 7 | 51 | 215 | 9 | 82 | 19 | 3 | | 21 | 487 | 8 | 52 | 206 | 8 | 83 | 16 | 3 | | 22 | 479 | 8 | 53 | 198 | 8 | 84 | 13 | 2 | | 23 | 471 | 8 | 54 | 190 | 7 | 85 | 11 | 2 | | 24 | 463 | 8 | 55 | 183 | 7 | 86 | 9 | 2 | | 25 | 455 | 8 | 56 | 176 | 7 | 87 | 7 | 2 | | 26 | 447 | 8 | 57 | 169 | 7 | 88 | 5 | 1 | | 27 | 439 | 8 | 58 | 162 | 7 | 89 | 4 | 1 | | 28 | 431 | 9 | 59 | 155 | 8 | 90 | 3 | 1 | | 29 | 422 | 9 | 60 | 147 | 8 | | | | 30 | 413 | 9 | 61 | 139 | 7 | | |
All the bills, from which the following tables are formed, give the numbers dying under 1 as well as under 2 years; and in the numbers dying under 1 are included, in the country parish in Brandenburg and at Berlin, all the stillborns. All the bills also give the numbers dying in every period of five years. ### TABLE IV
Showing the Probabilities of Life in the District of Vaud, Switzerland, formed from the Registers of 43 Parishes, given by Mr Muret, in the First Part of the Bern Memoirs for the Year 1766.
| Age | Living | Decr. | |-----|--------|-------| | 0 | 1000 | 189 | | 1 | 811 | 46 | | 2 | 765 | 30 | | 3 | 735 | 20 | | 4 | 715 | 14 | | 5 | 701 | 13 | | 6 | 688 | 11 | | 7 | 677 | 10 | | 8 | 667 | 8 | | 9 | 659 | 6 | | 10 | 653 | 5 | | 11 | 648 | 5 | | 12 | 643 | 4 | | 13 | 639 | 4 | | 14 | 635 | 4 | | 15 | 631 | 5 | | 16 | 626 | 4 | | 17 | 622 | 4 | | 18 | 618 | 4 | | 19 | 614 | 4 | | 20 | 610 | 4 | | 21 | 606 | 4 | | 22 | 602 | 5 | | 23 | 597 | 5 | | 24 | 592 | 5 | | 25 | 587 | 5 | | 26 | 582 | 5 | | 27 | 577 | 5 | | 28 | 572 | 5 | | 29 | 567 | 4 | | 30 | 563 | 5 |
### TABLE V
Showing the Probabilities of Life in a Country Parish in Brandenburg, formed from the Bills for 50 Years, from 1710 to 1759, as given by Mr Sufmilch, in his Gottliche Ordnung.
| Age | Living | Decr. | |-----|--------|-------| | 0 | 1000 | 225 | | 1 | 775 | 57 | | 2 | 718 | 31 | | 3 | 687 | 23 | | 4 | 664 | 22 | | 5 | 642 | 20 | | 6 | 622 | 15 | | 7 | 607 | 12 | | 8 | 595 | 10 | | 9 | 585 | 8 | | 10 | 577 | 7 | | 11 | 570 | 6 | | 12 | 564 | 5 | | 13 | 559 | 5 | | 14 | 554 | 5 | | 15 | 549 | 5 | | 16 | 544 | 5 | | 17 | 539 | 4 | | 18 | 535 | 4 | | 19 | 531 | 4 | | 20 | 527 | 5 | | 21 | 522 | 5 | | 22 | 517 | 5 | | 23 | 512 | 5 | | 24 | 507 | 5 | | 25 | 502 | 4 | | 26 | 498 | 3 | | 27 | 495 | 3 | | 28 | 492 | 3 | | 29 | 489 | 3 | | 30 | 486 | 4 |
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**TABLE**
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Mortality. ### TABLE VI.
Showing the Probabilities of Life at Vienna, formed from the Bills for eight Years, as given by Mr Sufmilch, in his Gottliche Ordnung, page 32, Tables.
| Age | Living | Decr | Age | Living | Decr | Age | Living | Decr | |-----|--------|------|-----|--------|------|-----|--------|------| | 0 | 1495 | 682 | 32 | 358 | 5 | 64 | 116 | 7 | | 1 | 813 | 107 | 33 | 353 | 6 | 65 | 109 | 8 | | 2 | 766 | 61 | 34 | 347 | 7 | 66 | 101 | 8 | | 3 | 645 | 46 | 35 | 340 | 8 | 67 | 93 | 8 | | 4 | 599 | 33 | 36 | 332 | 8 | 68 | 85 | 7 | | 5 | 566 | 30 | 37 | 324 | 9 | 69 | 78 | 7 | | 6 | 536 | 20 | 38 | 316 | 9 | 70 | 71 | 6 | | 7 | 516 | 11 | 39 | 307 | 9 | 71 | 65 | 5 | | 8 | 505 | 9 | 40 | 298 | 8 | 72 | 60 | 5 | | 9 | 496 | 7 | 41 | 290 | 7 | 73 | 55 | 5 | | 10 | 489 | 6 | 42 | 283 | 6 | 74 | 51 | 4 | | 11 | 483 | 5 | 43 | 277 | 6 | 75 | 47 | 5 | | 12 | 478 | 5 | 44 | 271 | 7 | 76 | 42 | 5 | | 13 | 473 | 6 | 45 | 264 | 8 | 77 | 37 | 5 | | 14 | 467 | 6 | 46 | 256 | 9 | 78 | 32 | 5 | | 15 | 461 | 6 | 47 | 247 | 9 | 79 | 27 | 4 | | 16 | 455 | 7 | 48 | 238 | 9 | 80 | 23 | 3 | | 17 | 448 | 6 | 49 | 229 | 9 | 81 | 20 | 2 | | 18 | 442 | 6 | 50 | 220 | 8 | 82 | 19 | 2 | | 19 | 436 | 6 | 51 | 212 | 7 | 83 | 16 | 2 | | 20 | 432 | 5 | 52 | 205 | 7 | 84 | 14 | 2 | | 21 | 425 | 5 | 53 | 198 | 7 | 85 | 12 | 2 | | 22 | 420 | 5 | 54 | 191 | 7 | 86 | 10 | 2 | | 23 | 415 | 6 | 55 | 184 | 8 | 87 | 8 | 2 | | 24 | 409 | 6 | 56 | 176 | 8 | 88 | 6 | 2 | | 25 | 403 | 6 | 57 | 168 | 9 | 89 | 4 | 1 | | 26 | 397 | 6 | 58 | 159 | 8 | 90 | 3 | 1 | | 27 | 391 | 7 | 59 | 151 | 8 | 91 | 2 | 1 | | 28 | 381 | 7 | 60 | 143 | 7 | 92 | 1 | 1 | | 29 | 377 | 7 | 61 | 136 | 7 | 93 | 1 | 1 | | 30 | 370 | 6 | 62 | 129 | 6 | 94 | 1 | 1 | | 31 | 364 | 6 | 63 | 123 | 7 | 95 | 1 | 1 |
### TABLE VII.
Showing the Probabilities of Life at Berlin, formed from the Bills for Four Years, from 1752 to 1755, given by Mr Sufmilch in his Gottliche Ordnung, vol. ii. p. 37, Tables.
| Age | Living | Decr | Age | Living | Decr | Age | Living | Decr | |-----|--------|------|-----|--------|------|-----|--------|------| | 0 | 1427 | 524 | 32 | 368 | 7 | 64 | 118 | 6 | | 1 | 903 | 151 | 33 | 361 | 7 | 65 | 112 | 6 | | 2 | 752 | 61 | 34 | 354 | 7 | 66 | 106 | 7 | | 3 | 601 | 73 | 35 | 347 | 8 | 67 | 99 | 6 | | 4 | 618 | 45 | 36 | 339 | 8 | 68 | 92 | 6 | | 5 | 573 | 21 | 37 | 330 | 10 | 69 | 86 | 6 | | 6 | 552 | 15 | 38 | 320 | 10 | 70 | 80 | 6 | | 7 | 536 | 13 | 39 | 310 | 10 | 71 | 74 | 6 | | 8 | 523 | 9 | 40 | 300 | 10 | 72 | 68 | 6 | | 9 | 514 | 7 | 41 | 290 | 9 | 73 | 62 | 5 | | 10 | 507 | 5 | 42 | 281 | 8 | 74 | 57 | 5 | | 11 | 502 | 4 | 43 | 274 | 7 | 75 | 52 | 5 | | 12 | 498 | 4 | 44 | 266 | 7 | 76 | 47 | 5 | | 13 | 494 | 4 | 45 | 259 | 7 | 77 | 42 | 5 | | 14 | 490 | 4 | 46 | 252 | 7 | 78 | 37 | 5 | | 15 | 486 | 4 | 47 | 245 | 7 | 79 | 32 | 4 | | 16 | 482 | 5 | 48 | 238 | 7 | 80 | 28 | 4 | | 17 | 477 | 5 | 49 | 231 | 7 | 81 | 24 | 3 | | 18 | 472 | 5 | 50 | 224 | 7 | 82 | 21 | 2 | | 19 | 467 | 6 | 51 | 217 | 7 | 83 | 19 | 2 | | 20 | 461 | 6 | 52 | 210 | 7 | 84 | 17 | 2 | | 21 | 455 | 6 | 53 | 203 | 8 | 85 | 15 | 2 | | 22 | 449 | 6 | 54 | 195 | 8 | 86 | 13 | 2 | | 23 | 443 | 7 | 55 | 187 | 8 | 87 | 11 | 2 | | 24 | 436 | 8 | 56 | 179 | 8 | 88 | 9 | 2 | | 25 | 428 | 9 | 57 | 171 | 8 | 89 | 7 | 1 | | 26 | 421 | 9 | 58 | 163 | 9 | 90 | 6 | 1 | | 27 | 412 | 9 | 59 | 154 | 9 | 91 | 5 | 1 | | 28 | 403 | 9 | 60 | 145 | 8 | 92 | 4 | 1 | | 29 | 394 | 9 | 61 | 137 | 7 | 93 | 3 | 1 | | 30 | 385 | 9 | 62 | 130 | 6 | 94 | 2 | 1 | | 31 | 376 | 8 | 63 | 124 | 6 | 95 | 1 | 1 |
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**Brief of Mortancestry**, in Scots Law; anciently the ground of an action at the instance of an heir, in the special case where he had been excluded from the possession of his ancestor's estate by the superior, or other person pretending right.
**Mortar**, a preparation of lime and sand mixed with water, which serves as a cement, and is used by masons and bricklayers in building walls of stone and brick. See Lime, Chemistry Index.
**Mortar**, a chemical utensil, very useful for the division of bodies, partly by percussion and partly by grinding. Mortars have the form of an inverted bell. The matter intended to be pounded is to be put into them, and there it is to be struck and bruised by a long instrument called a pestle. The motion given to the pestle ought to vary according to the nature of the substances to be pounded. Those which are easily broken, or which are apt to fly out of the mortar, or which are hardened by the stroke of the pestle, require that this instrument should be moved circularly, rather by grinding or bruising than by striking. Those substances which are softened by the heat occasioned by rubbing... Mortar rubbing and percussion, require to be pounded very slowly. Lastly, those which are very hard, and which are not capable of being softened, are easily pounded by repeated strokes of the pestle. They require no bruising but when they are brought to a certain degree of fineness. But these things are better learned by habit and practice than by any directions.
As mortars are instruments which are constantly used in chemistry, they ought to be kept of all sizes and materials; as of marble, copper, glass, iron, gritstone, and agate. The nature of the substance to be pounded determines the choice of the kind of mortar. The hardness and dissolving power of that substance are particularly to be attended to. As copper is a metal, which is soluble by almost all menstrua, and hurtful to health, this metal is rarely or never employed for the purpose of making mortars.
One of the principal inconveniences of pulverization in a mortar proceeds from the fine powder which rises abundantly from some substances during the operation. If these substances be precious, the loss will be considerable; and if they be injurious to health, they may hurt the operator. These inconveniences may be remedied, either by covering the mortar with a skin, in the middle of which is a hole, through which the pestle passes; or by moistening the matter with a little water when this addition does not injure it; or, lastly, by covering the mouth and nose of the operator with a fine cloth, to exclude this powder. Some substances, as corrosive sublimate, arsenic, calces of lead, cantharides, euphorbium, &c., are so noxious, that all these precautions ought to be used, particularly when a large quantity is pounded.
Large mortars ought to be fixed upon a block of wood, so high, that the mortar shall be level with the middle of the operator. When the pestle is large and heavy, it ought to be suspended by a cord or chain fixed to a moveable pole placed horizontally above the mortar: this pole considerably relieves the operator, because its elasticity assists the raising of the pestle.
**Mortar-Piece**, in the military art, a short piece of ordnance, thick and wide, proper for throwing bombs, carafes, shells, stones, bags filled with grape-shot, &c. See **Gunnery**, No. 50.
**Land Mortars**, are those used in sieges, and of late in battles, mounted on beds made of solid timber, consisting generally of four pieces, those of the royal and cohorn excepted, which are but one single block; and both mortar and bed are transported on block-carriages. There is likewise a kind of land mortars, mounted on travelling carriages, invented by Count Buckeburg, which may be elevated to any degree; whereas ours are fixed to an angle of 45 degrees, and firmly lashed with ropes. The following table shows the weight of land mortars and shells; together with the quantity of powder the chambers hold when full; the weight of the shells, and powder for loading them.
| Diameter of mortars | 13-inch. | 10-inch. | 8-inch. | 5-8-inch. royal. | 4-6-inch. cohorn. | |---------------------|----------|----------|---------|----------------|------------------| | Mortar's weight | c. qr. lb. | c. qr. lb. | c. qr. lb. | c. qr. lb. | c. qr. lb. | | | 25 0 | 10 2 | 18 4 | 20 1 | 3 0 | | Shell's weight | 1 2 15 | 0 2 25 | 0 1 15 | 0 12 | 7 | | Shell's cont. of powder | 9 4 8 | 4 14 12 | 2 3 8 | 1 8 | 8 | | Chamber's cont. of powder | 9 1 8 | 4 0 2 | 10 1 | 8 | |
**Sea Mortars**, are those which are fixed in bomb vessels for bombarding places by sea: and as they are generally fired at a much greater distance than that which is required by land, they are made somewhat longer and much heavier than the land mortars. The following table exhibits the weight of the sea mortars and shells, and also of their full charges.
| Nature of the mortar | Powder contained in the chamber when full. | Weight of the mortar. | Weight of the shell when fixed | Weight of powder contained in the shell. | |----------------------|------------------------------------------|-----------------------|-------------------------------|----------------------------------------| | 10-inch howitzer | lb. oz. | c. qr. lb. | lb. | lb. oz. | | 13-inch mortar | 12 0 | 31 2 | 26 | | | 10-inch mortar | 30 0 | 81 2 | 1 | 198 | | | 12 0 | 34 2 | 11 | 93 |
To Charge or Load a Mortar, the proper quantity of gunpowder is put into the chamber, and if there be any vacant space they fill it up with hay; some choose a wooden plug: over this they lay a turf, some a wood or tompon fitted to the bore of the piece; and lastly the bomb; taking care that the fuse be in the axis thereof, and the orifice be turned from the muzzle of the piece: what space remains is to be filled up with hay, straw, turf, &c., so as the load may not be exploded without the utmost violence. The quantity of gunpowder to be used is found by dividing the weight of the bomb by 30; though this rule is not always to be strictly observed.
When the proper quantity of powder necessary to charge a sea mortar is put into the chamber, it is covered with a wad well beat down with the rammer. After this the fixed shell is placed upon the wad, as near the middle of the mortar as possible, with the fuse hole uppermost, and another wad pressed down close upon it, so as to keep the shell firm in its position. The officer then points the mortar according to the proposed inclination.—When the mortar is thus fixed, the fuse is opened; the priming iron is also thrust into the touch-hole of the mortar to clear it, after which it is primed with the finest powder. This done, two of the mattocks or failors, taking each one of the matches, the first lights the fuse, and the other fires the mortar. The bomb, thrown out by the explosion of the powder, is carried to the place intended; and the fuse, which ought to be exhausted at the instant of the shell's falling, inflames the powder contained in it, and bursts the shell in splinters; which, flying off circularly, occasion incredible mischief wherever they reach.
If the service of mortars should render it necessary to use pound shots, 200 of them with a wooden bottom are to be put into the 13 inch mortar, and a quantity of powder not exceeding 5 pounds; and 100 of the above shot with 2½ pounds of powder, for the 10 inch mortar, or three pounds at most.
To Elevate the Mortar so as its axis may make any given angle with the horizon, they apply the artillery level or gunner's quadrant. An elevation of 70 or 80 degrees is what is commonly chosen for rendering mortars most serviceable in casting shells into towns, forts, &c., though the greatest range be at 45 degrees.
All the English mortars are fixed to an angle of 45 degrees, and lashed strongly with ropes at that elevation. Although in a siege there is only one case in which shells should be thrown with an angle of 45 degrees; that is, when the battery is so far off that they cannot otherwise reach the works; for when shells are thrown out of the trenches into the works of a fortification, or from the town into the trenches, they should have as little elevation as possible, in order to roll along, and not bury themselves; whereby the damage they do, and the terror they occasion, are much greater than if they sink into the ground. On the contrary, when shells are thrown upon magazines or any other buildings, with an intention to destroy them, the mortars should be elevated as high as possible, that the shells may acquire a greater force in their fall, and consequently do greater execution.
If all mortar pieces were, as they ought to be, exactly similar, and their requisites of powder as the cubes of the diameters of their several bores, and if their shells, bombs, carcasses, &c., were also similar; then, comparing like with like, their ranges on the plane of the horizon, under the same degree of elevation, would be equal; and consequently one piece being well proved, i.e., the range of the grenado, bomb, carcass, &c., being found to any degree of elevation, the whole work of the mortar piece would become very easy and exact.
But since mortars are not thus similar, it is required,
| Degrees | Degrees | Range | Degrees | Degrees | Ranges | |---------|---------|-------|---------|---------|-------| | 90 | 0 | 0 | 66 | 24 | 7431 | | 89 | 1 | 349 | 65 | 25 | 7660 | | 88 | 2 | 608 | 64 | 26 | 7880 | | 87 | 3 | 1045 | 63 | 27 | 8100 | | 86 | 4 | 1392 | 62 | 28 | 8320 | | 85 | 5 | 1736 | 61 | 29 | 8540 | | 84 | 6 | 2709 | 60 | 30 | 8760 | | 83 | 7 | 2419 | 59 | 31 | 8980 | | 82 | 8 | 2556 | 58 | 32 | 9200 | | 81 | 9 | 3090 | 57 | 33 | 9420 | | 80 | 10 | 3420 | 56 | 34 | 9640 | | 79 | 11 | 3746 | 55 | 35 | 9860 | | 78 | 12 | 4067 | 54 | 36 | 10080 | | 77 | 13 | 4384 | 53 | 37 | 10300 | | 76 | 14 | 4695 | 52 | 38 | 10520 | | 75 | 15 | 5000 | 51 | 39 | 10740 | | 74 | 16 | 5299 | 50 | 40 | 10960 | | 73 | 17 | 5592 | 49 | 41 | 11180 | | 72 | 18 | 5870 | 48 | 42 | 11400 | | 71 | 19 | 6157 | 47 | 43 | 11620 | | 70 | 20 | 6428 | 46 | 44 | 11840 | | 69 | 21 | 6691 | 45 | 45 | 12060 | | 68 | 22 | 6947 | 44 | 46 | 12280 | | 67 | 23 | 7193 | 43 | 47 | 12500 |
Vol. XIV. Part II. The use of the table is obvious. Suppose, for instance, it be known by experiment, that a mortar elevated 15°, charged with three pounds of powder, will throw a bomb to the distance of 350 fathoms; and it be required, with the same charge, to throw a bomb 100 fathoms farther; seek in the table the number answering to 15 degrees, and you will find it 5000. Then as 350 is to 450, so is 5000 to a fourth number, which is 6428. Find this number, or the nearest to it, in the table, and against it you will find 20° or 70°; the proper angles of elevation.