MORTALITY, HUMAN.

We shall consider this very important, as well as curious subject, under two distinct heads; the first of which will treat of the History and Formation of Bills of Mortality; the second, of the Law of Mortality.

I. MORTALITY, BILLS OF.

Bills of Mortality are abstracts from parish registers, shewing, as their name imports, the numbers that have died in any parish or place during certain periods of time, as in each week, month, or year; and are, accordingly, denominated weekly, monthly, or yearly bills. They also include the numbers of the baptisms during the same periods, and generally those of the marriages.

The objects of the present article are these :—First, to give a brief history of the principal things that have been done in this way, which may suffice for such as are not disposed to go further into the subject, and may, at the same time, indicate the best sources of information to those who take more interest in it.

Asboth mortuary registers and enumerations of the people are much more valuable when combined than when separate, we shall also notice some of the principal enumerations, the results of which have been published. We shall then point out some of the principal defects in most of the published registers and enumerations; and, lastly, shall submit some forms, according to which, if enumerations be made, and registers kept, they will be easily convertible to useful purposes.

The ancients do not appear to have kept any exact mortuary registers, at least no account of any registers of that kind, with the ages of the deceased, have come down to us; and although, in the Roman Census, first established by Servius Tullius, both the ages and sexes of the people were distinguished, we have no exact account of these particulars in any one of their enumerations.

Indeed the principal object of the census among that warlike people, was the levying of men and money for the purposes of conquest; the duration of human life appears to have occupied very little of their attention, and their proficiency in the science of quantity was not sufficient either to shew them what the necessary data were, or to enable them to draw just inferences from them, had they been in their possession.

A g∞d account of what the ancient Romans did in this way, with references to the original authorities, may be found in the Italian translation of Μ. Demoivre’s Treatise of Annuities on Lives, by Gaeta and Fontana, which was published at Milan, in the year 1776, in 8vo. (Discorso Preliminare, parte 2).

The keeping of parish registers commenced in England in the year 1538, in consequence of an injunction issued in that year by Thomas Cromwell, who, after the abolition of the Pope’s authority in this kingdom, in the reign of Henry VIII., had been appointed the king’s vicegerent in ecclesiastical affairs.

Some parish registers in Germany appear to have commenced with the sixteenth century; and in the Göttliche Ordnung of Süssmilch (t. iii. s. 23), we are informed, that at the time of Lord Cromwell’s injunction, they had already old registers of that kind both at Augsburgh and Breslaw. However, the extracts there given from the Augsburgh registers do not go back further than the year 1501, nor those for Breslaw beyond 1555. About the beginning of the seventeenth century, such registers appear to have been established in most parts of Europe; but it was not until the year 1662 that they began to attract public notice, and to be considered as the sources of valuable and interesting information.

In that year, John Graunt, a citizen of London, (afterwards an officer in the trained bands of the city, and a Fellow of the Royal Society), published his Natural and Political Observations on the Bills of Mortality, principally those for London. The London bills, or accounts of baptisms and burials, appear to have been occasioned by the plague, and to have been begun in the year 1592, a time of great mortality. They were afterwards discontinued, but were resumed in 1603, after the great plague of that year. They have ever since been continued weekly, and an annual bill also has been regularly published. In 1629, the number of deaths by the different diseases and casualties, were first inserted in them, also the distinction of the sexes; and these have been continued ever since. But it is in the totals only of the baptisms and burials that the sexes are distinguished in these bills. They do not shew how many of each sex died of each disease, neither have they, since 1728, when the distinction of the ages of the dead was first introduced, shewn how many of each sex died in each interval of age, but only the total number of both sexes.

This book of Graunt’s, although the first, is also one of the best that have been published on the subject. It contains many judicious observations on the imperfections of the bills, on the proportions of the deaths from different diseases and casualties, and on their increase and decrease, with the probable causes of such fluctuations. He also observed, that “the more sickly the years are, the less fecund or fruitful of children also they be.”

Besides the London bills, he gave one for a country parish in Hampshire, in the first edition of his book; and, in an appendix to the later editions, two others, one for Tiverton, the other for Cranbrook in Kent, with a few observations on foreign bills. He almost always reasons justly from his data; but, as these were very imperfect, in his endeavours to draw more information from them than they could supply, he has sometimes fallen into error.

Even in this enlightened age, when a much greater proportion of the people devote a portion of their leisure to the acquisition of knowledge than in Graunt’s time, subjects of this kind have but few attractions for the generality even of reading men, who cannot endure the fatigue of thinking closely for any length of time. The author, accordingly, expected his readers to be rather select than numerous, and was ambitious of that distinction, as appears by the motto he prefixed to his work,

Non, me ut miretur turba, laboro, Contentus paucis lectoribus.

The book was, however, favourably received by the public, and went through five editions in fifteen years, the two first in 4to, the three others in 8vo; the last of them, published in 1676, two years after the author’s death, was edited by his friend Sir William Petty, who, in consequence of having sometimes spoken of this edition as his own, has by some writers been erroneously considered as the author.

Graunt’s observations, like all others of a similar kind, by shewing the usefulness of parish registers and bills of mortality, contributed to form a taste for these inquiries amongst thinking men; and, consequently, to improve both the registers and the bills derived from them; so that, from his time, the subject has been continually cultivated more and more. Parish registers, in most parts of Europe, have been kept with more care; and a succession of works of considerable merit have been published on the subject, containing an [7:15:514] important part of the natural and political history of our species, and affording valuable materials for the science of political economy.

The principal of these works we shall proceed to give a short account of, in the order of their publication.

As the ages at which the deaths took place were not inserted in the London bills till 1728, Captain Graunt could not avail himself of that important information, but made a fruitless attempt to determine the law of mortality without it.

The Breslau bills appear to have been the first wherein the ages at which the deaths took place were inserted, and the most important information which bills of mortality can afford was first drawn from them by Dr. Halley; who, in 1692, constructed a table of mortality for Breslau from these bills for the five preceding years, and inserted a paper on the subject in the Philosophical Transactions, (No. 196.)

In 1o99, Dr. Davenant, in An Essay upon the probable Methods of making a People Gainers in the Eallance of Trade, published some extracts from Natural and Political Observations and Conclusions upon the State and Condition of England, by permission of their author, Mr. Gregory King, Lancaster herald, who had completed them in 1696, though they still remained in manuscript; and the whole of this very curious production was published by Mr. Chalmers at the end of his Estimate in 1802. Mr. King derived his information from the poll-books; from actual observations in particular places; from the assessments on marriages, births, and burials; and from the parish registers. Many of his conclusions agree surprisingly well, considering the time he wrote, with those which are the results of a hundred years of further observations and inquiries. He had access to much better data than Graunt, and his conclusions are more accurate; but he does not explain so fully how he arrived at them.

From the publication of Davenant’s essay, above mentioned, nearly forty years had elapsed without any thing further being done in this way, when Μ. Kersseboom published an essay, in the Dutch language, on the probable number of people in Holland and West Friesland, which he deduced from the Bills of Mortality, Hague, 1738, 4to; and two others in 1740 and 1742. (See Law of Human Mortality.)

In 1742 was published the first edition of the celebrated work, entitled Die Göttliche Ordnung in den Veranderungen des menschlichen Geschlechts aus der Geburt, dem Tode und der Fortpflanzung desselben erwiesen von Johann Peter Süssmilch. The second edition appeared in 1761, enriched with the materials which had been laid before the public through various channels in the interim; the third in 1765, and in 1775 a fourth edition of the two volumes of Süssmilch was published by Christian Jacob Baumann, to which this editor himself added, in 1776, a third volume, consisting of additions to the other two, and remarks upon them, with many new tables, and a copious index. The last edition of this work was published in 1798, but it does not appear to have been augmented or improved since 1776. It contains long dissertations on every thing not mathematical connected with the subject, and, besides original information, includes the substance of all the other publications on it previous to 1776; with an immense collection of materials, which, when borrowed, are often better arranged and rendered more convenient for reference, than they will be found to be in the works they were extracted from; besides. the original sources of information are always referred to, and these advantages, with that of a full index, render it a valuable work for occasional reference. The three thick octavo volumes contain upwards of two thousand three hundred pages, closely printed with a small type, and the tables alone occupy three hundred and thirty pages.

In 1746 was published the Essai of Μ. Deparcieux, which has been already mentioned in the historical introduction to the article Annuities. Information much wanted on this subject, was there given in a very clear and popular manner, and the work no doubt contributed greatly to the advancement of the science. It probably had some influence in promoting the establishment of what is called the TabeU-varket in Sweden, which took place in 1749, and of which we shall have occasion to take further notice presently.

In 1750 appeared, in octavo, New Observations natural, moral, civil, political, and medical, on City, Town, and Country Bills of Mortality ; to which are added, large and clear Abstracts of the best Authors who have written on that subject ; with an Appendix of the Weather and Meteors, by Thomas Short, M.D. which he had “had on the anvil” for eighteen years, as he informs us in the preface to his History of Air, Weather, &c. This author, with incredible labour, collected extracts from the motuary and baptismal registers in a great many market-towns and country parishes in England, chiefly in the northern counties, in almost every variety of soil and situation, and reduced them into tables in various ways, so as to enable him to draw useful inferences from them.

He informs us that Lord Cromwell’s injunction in 1538 was but little regarded in many places till the year 1559, when another was issued for the same purpose by Queen Elizabeth; nevertheless, he had procured several exact country registers, commencing with 1538, and continued without one chasm, for more than two hundred years; and the registers before 1644, he considered to be much more valuable than afterwards, on account of the increase of dissenters from that time. He likewise procured both the numbers of families and of souls in seven of the market towns, and fifty-four of the country parishes, for which he had registers; and thus arrived at satisfactory information on several points, which, till then, had been very imperfectly understood. But the sexes were not distinguished in his enumerations; neither were the ages, in any of the enumerations or registers he has given accounts of, except in the London Bills of Mortality, and what he has taken from Dr. Halley, respecting those for Breslau.

Although Dr. Short took so much trouble in collecting materials, and has generally reasoned well upon them, he has shown but little skill, and does not appear to have taken much pains in communicating his information to his readers; so that it costs them considerable labour to find what they want, especially in his tables; and when found, to understand it.

In 1751 was first printed a tract by Corbyn Morris, entitled, Observations on the past growth and present state of the City of London, with the most convenient and instructive tables of the London bills that have been printed; they contained the annual baptisms and burials from the year 1603, the number of annual deaths by each disease from 1675, and of each age from 1728; all brought down to the year 1750. This tract was reprinted in 1758, with a continuation of the tables to the end of 1757; these also contain useful annual averages and proportions. Mr. Morris’s observations are generally very judicious, but he was one of those authors who appear to have laboured under much misconception with regard to the evils to be apprehended from the mortality of London, and what they considered to be its baneful effects in drawing recruits from the country. These writers did not perceive, or did not sufficiently consider, that the natural procreative power is much more than adequate to supply any waste of that kind, and that the real obstacle to the increase of the people, is the limited means of subsistence. This had been observed by Dr. Halley in his Further Considerations on the Breslau Bills of Mortality, (Phil. Trans. 1693,J though it there also appears, that he had not sufficiently considered the mode of its operation: this was first fully illustrated by Dr. Franklin in his excellent Observations on the Increase of Mankind, Ρeoρ- [7:15:515] ling of Countries, &c. written in Philadelphia in 1751, the same year in which Mr. Morris’s pamphlet was first published. The author also pointed out in that pamphlet, material defects in the Bills of Mortality, and proposed a better method of keeping them, not only in London, but throughout the kingdom. This gave occasion to a paper by Mr. James Dodson, which was inserted in the Philosophical Transactions for that year (1751,) wherein he showed the importance of their being so kept as to afford the means of valuing annuities on lives, and proposed other alterations which appeared to him calculated to fit them for the purpose.

Nicoaas Struyck of Amsterdam, who, in his Introduction to General Geography, published there in 1740, had inserted (Gissingen over den Staat van ’ t Menschelyh Geslagt,) Conjectures on the State of the Human Species ; published at the same place in 1753, a quarto volume, the first half of which is astronomical, the other (216 pages) is entitled (Nader Ontdehhingen noopens den Staat van het Menschelyk Geslagt,) Further Discoveries concerning the State of the Human Species. It contains statements of actual enumerations of the people in many Dutch villages, principally in North Holland, wherein the sexes are distinguished, and the numbers in childhood, celibacy, marriage, and widowhood; but with respect to their ages, it is only stated for each sex, how many were under ten years, and how many of the unmarried were above that age; except in two instances, wherein the number of each sex is given in each interval of five years of age, from birth to the extremity of life: they amount altogether to 2728, of whom not one was above the age of eighty-five, and only four above eighty.

He generally gives, for each place, the names and professions or occupations of the persons who made the enumeration, and the precise day on which it was made; or if it occupied the parties more days than one, those on which it was commenced and completed are given; a practice which shows a laudable solicitude about particulars, and a title to our confidence, the want of which we have great cause to lament in too many other writers.

Extracts from many parish registers are also given; in these, too, the ages are seldom noticed; but in a few cases they are given very minutely, especially in that of West-zaandam, for which, the numbers who died in each interval of five years of age, from birth to the extremity of life, are given; also the number in each year of age under fifteen, the number in each month of the first year of age, even the number that died in the first hour from birth, in the first twenty-four hours, and in each day of the first week of their age. During a term of nineteen years, the whole number of deaths thus registered was 3328; but the sexes were not distinguished under fifteen years of age, which Struyck himself lamented. The work also contains much information respecting the population and parish registers of Amsterdam, Haarlem, &c. with some accounts of other countries, and of other works on the subject.

In 1759 was published at London, in 4to, A Collection of the yearly Bills of Mortality, from 1657 to 1758 inclusive, together with several other Bills of an earlier date ; to which were subjoined Captain Graunt’s Observations ; Another Essay in Political Arithmetic, by Sir William Petty; the Observations of Corbyn Morris, Esq. ; and A Comparative View of the Diseases and Ages, with a Table of the Probabilities of Life for the last thirty years, by J. P. Esq. F. R. S∙ This is a valuable compilation, and has been generally attributed to Dr. Birch, the Secretary and Historian of the Royal Society; the preface is very judicious, and contains a good deal of information. For the following history of this publication, the author of the present article is indebted to the kindness of Dr. Heberden :—

“The bills were collected into a volume by his father, the late Dr. Heberden. He procured, likewise, observations from several of his friends, rectors of some large parishes, or others likely to give him information; particularly from Bishop Moss, Bishop Green, Bishop Squire, and Dr. Birch. These, together with some of his own remarks, were thrown into the form of a preface; and the whole was committed to the care of Dr. Birch. To make the calculations which appear at the end of the book, Dr. Heberden employed James Postlcthwayt, Esq. a very distinguished arithmetician.”

In the year 1766, this branch of knowledge was enriched with new materials, of more value than all that had previously been laid before the public. These were contained in three publications, of which we shall first notice the Recherches sur la Population des généralités dû Auvergne, de Lyon, de Rouen, et de quelques Provinces et Villes du Ro-yame. Par Μ. Messance, Receveur des Tailles de l’Election de Saint Etienne.

Most of the political writers in France, for some years previous to the date of this publication, had asserted confidently that the kingdom was depopulated, but without producing any proofs. The object of Μ. Messance was, to enable his readers to judge of the merit of such assertions, and to pronounce less vaguely on a subject in itself so interesting, the knowledge of which can only be obtained by a great number of facts and actual observations. The work, accordingly, is filled with tables, exhibiting the results of actual enumerations of the people, and of extracts from the parish registers. They show, for each sex, how many were under fourteen, or in celibacy above that age; those in the states of marriage and of widowhood; and the number of domestic servants. The numbers of families are also stated; and the enumerations of the ecclesiastics, properly classed, are given separately; but no other information respecting the ages of the living is given than that mentioned above. A great many statements are also inserted of the numbers that died in different parishes and more extensive districts, under five years of age, between five and ten, and in each interval of ten years, from thence to the age of one hundred; during different periods of from ten to forty years or more, generally ending about the year 1760; but in these the sexes are not distinguished.

In all cases, he has given the general results of his tables, and the proportions they afford, very distinctly stated; and among these results, the increase of the population during the preceding sixty years, to which his researches were generally limited, is clearly ascertained.

The work also contains many interesting tables, in which the rate of mortality and the produce of manufacturing labour, are compared with the contemporaneous prices of grain, in various places, generally for periods of twenty years each.

In the same year was published, at Yverdon, in octavo, the work entitled Mémoire sur l’Etat de la Population, dans le Pays de Vaud, qui a obtenu la prix propose par la Société Economique de Berne. Par Μ. Muret, premier Pasteur à Vevey, et Secretaire de la Société Economique de Vevey.

The Pays de Vaud contains 112 parishes, and the population at that time was about 113,000 souls. Μ. Muret wrote for information to all the clergymen in the country, who made him returns of the numbers of baptisms and burials in their respective parishes, for different periods, from ten to forty years, in many of which both the ages and sexes were distinguished; and from about two-thirds of them he obtained also the numbers of marriages and families actually subsisting; also the number of souls, “or at least of communicants,” in their parishes: but neither the ages nor sexes were distinguished in any of the enumerations of the living.

This performance does much credit both to the author’s industry and judgment, but it has also material defects. He gave upwards of fifty tables, by which he intended to show the probabilities and expectations of life till five years of age, and at every fifth year after that, in different parishes [7:15:516] and places, under various circumstances of soil and situation, and for people of different habits and occupations; also for the two sexes separately. These must have cost him a good deal of labour, and would have been extremely valuable had they been correct; but, unfortunately, he did not understand the construction of such tables, and they are not to be depended upon. He also took considerable pains to determine the rates of mortality among married and single women, considered separately, and thought he had proved that it was less among the married; but the proofs he adduced were not conclusive. Some of his observations on the state of the population, and the plans he recommended for encreasing it, also show, that he did not understand the principle on which its progress depends.

It is with much reluctance that we make, on so respectable an author, remarks which apply equally to almost all his predecessors in these inquiries; but this we consider to be rendered necessary, by the Memoir generally, and the Tables in particular, having been praised for their extreme accuracy, in a very good abridgment of them, inserted in the second volume of a book, entitled De Re Rustica, or the Repository, Lond. 1770, 8vo.

The disadvantages of her soil and climate necessarily keep Sweden thinly peopled in comparison with the countries which, in these respects, are more happily circumstanced; and since the year 1748, the state of the population has been an object of anxious solicitude with the government; which, in 1749, established what, in this country, would probably be called a Board of Population, but is there denominated Tabetl-Varket,Úí3Á,is, Table-Establishment, for reducing into convenient forms the extracts from the parish registers, and the returns from the magistrates of the numbers of the people, which the governors of the different provinces are required to state to the commissioners appointed for these purposes. The extracts from the registers are made and transmitted annually, but the enumerations only once in three years.

Printed forms, with proper blanks, distinguishing the ages and sexes, both of the living and the dead, with the diseases the deaths were occasioned by, are distributed throughout the country, to enable the people to make these returns correctly and uniformly; and the information thus acquired, respecting the state of population and mortality, is much more correct and satisfactory than what has been obtained in any other place of considerable extent; but from causes which we have not room to explain here, the results were not laid before the public until some years after the returns wore made.

Μ. Wargen tin who was one of the Royal Commissioners of the Tabell-Värket, inserted in the Transactions of the Royal Academy of Sciences at Stockholm for the years 1754 and 1755, six papers on the usefulness of annual registers of births and deaths in a country; which, like all his other productions, were written with much judgment and modesty; but, to illustrate the subject, he was generally under the necessity of borrowing materials from the writings of others; as, at that time, he was only in possession of the results of complete Swedish returns for the years 1749 and 1750. In the same Transactions for the year 1766, he inserted a paper on the mortality in Sweden, in which he gave Tables exhibiting the number of the Living of each six in each of the following intervals of age :—between birth and one year completed, between one and three, between three and five, and then in each consecutive period of five years of age till ninety, the last including all those above ninety years of age; at the three enumerations of the people which were made in the years 1757, 1760, and 1663; with the annual average number of still-born children and of those born alive, also the number of deaths that took place in each of those intervals of age, during each of the periods of three years, which ended at the times of these three enumerations, the sexes being always distinguished. These particulars he gave both for all Sweden and Finland, and for Stockholm separately; with other interesting results of the registers and enumerations, and many judicious observations on them. The ages of the living at the different enumerations, and those at which the deaths took place in all the subsequent publications of them, have been given for the intervals of age stated above.

This paper of Μ. Wargentin is more valuable than all that had previously been published on the subject; it is also to be found in the French abridgment of the Stockholm Transactions, in the eleventh volume of the Collection Académique (partie étrangère), which abridgment was also published separately in 4to at Paris, in 1772.

Condorcet in his Eloge of Μ. Wargentin states, that he had collected the results of his labours as Commissioner of the Tabell-Verket in a great work which he had not time to publish; but in that statement, there is probably some mistake. In the Stockholm Transactions for the first quarter of the year 1801, Μ. Nicander informs us, that Μ. Wargentin at his death, left in manuscript a continuation of the observations published in 1766, consisting of four statements similar to those just mentioned; the first for die years 1765, 1766, and 1767, the second for the two following years, the third for the year 1772 alone, and the fourth for 1774, 1775, and 1776; and having taken the mean of all the seven, he sent it a little before his death to Dr. Price, who published it in the fourth edition of his “ Observations on Reversionary Payments,” which appeared in 1783, the same year in which Wargentin died.

In 1767, Dr. Short published, in quarto, A Comparative History of the Increase and Decrease of Mankind, in which the tables are printed more intelligibly, and there is more information respecting foreign Bills of Mortality, than in his New Observations.

The first edition of Dr. Price’s Observations on Reversionary Payments appeared in 1771, and contained “Observations on the expectations of lives, the increase of mankind, the number of inhabitants in London, and the influence of great towns on health and population,” which had been published in the Philosophical Transactions for 1769, and added considerably to the information on those subjects which had been previously before the public; also observations on the proper methods of constructing tables of mortality.

In the Philosophical Transactions for the years 1774 and 1775, were inserted two excellent papers by Dr. Haygarth∣ of Chester, in which he gave the Bills of Mortality for that city, for the years 1772 and 1773 respectively, in a form calculated to exhibit, at one view, the most useful and interesting information such bills can afford without calculation, and presenting to the calculator data that are essential to the solution of the most important questions respecting the state of the population. Three papers by Dr. Percival (also of considerable merit) appeared in the same Transactions about this time, relating principally to the population of Manchester and its neighbourhood.

The second part of Dr. Moehsen’s “Collection of Observations for the better illustration of the great usefulness and value of Inoculation for the Small-pox,”^[1. Sammlung merkwürdiger Erfahrungen die den Werth und grossen Nutzen der Pocken-inoculation. Erstes Stuck, Lubeck 1774; Zweites und Drittes Stuck, Berlin und Leipzig 1775. The third part, however, appears never to have been published, though stated in the title, and no doubt intended to accompany the second. Indeed at the end of the second part he gave notice that his remarks on his third table would be continued, and explanations of the remaining ones would be given, in the following part; which, however, is wanting. ] was published in 1775; in which he gave a good historical account of [7:15:517] the first institution of Registers of Births, Marriages, and Deaths, and of their gradual progress and useful applications down to his time; also twenty-six tables derived from the Berlin Bills of Mortality for a period of seventeen years, commencing with 1758, and ending with 1774.

For each of the seventeen years he gave in the text what he calledaYcar Table, shewing for that year the number of deaths by small-pox, which took place during each month, in each of the first five years of age separately, and also in each interval of five years of age above that, with the number during the whole year in each of those intervals of age, the total number in each month of the year and also in the whole year; so far without distinction of sex or condition. But he added in each of those tables, the distribution of the number who died in the year by the small-pox into the civil and military population, shewing for each of these classes how many of each sex were children and how many adults, taking the age of fifteen years as the limit between them, without noticing the month or the interval of age in which the deaths took place. And in an 18th table he gave the same information for the first half of the year 1775. At page 152, he gave a table shewing the number of deaths in Berlin during each of those seventeen years, from all causes without distinction, but distinguishing the civil from the military population, and the sexes in each case. Amongst these deaths the still-born are included, which it is important to notice here, as he did not mention it. At the end he gave seven other which he called Principal Tables; the three first are summaries of his Year Tables; the first exhibiting at one view the number of deaths by small-pox in each month of each of the seventeen years, also those in each month during the whole term, with the whole number during each year, and the total during the whole term of seventeen years, without distinction of age, sex, or condition. The second shews the number of those deaths in each year, and the sum of them in all the years, distinguishing the sexes, the civil from the military population, and children from adults. The third shews the number of those deaths in each interval of age that took place in each year, and also during the whole term, without noticing the particulars given in the two first tables. In the fourth table he gave the numbers of male and female children separately which were born in each month of each of the seventeen years, with the total number in each year, and the total number born in each month during the whole term of seventeen years, but without mentioning whether the still-born were included in these statements or not; it seems probable that they were, as he included them in the deaths.

Taking the numbers of births and deaths, as stated by Dr. Moehsen, without attending to the still-born, it appears that
[table]

His fifth table shews how many children were still-born, and how many died during each of those seventeen years, also during the whole term, by each of thirteen different diseases which are the most prevalent amongst “children and others,” but without distinction of age, sex, or condition, and without including the small-pox, respecting which the same information was given both in his first and third tables; that makes fourteen, of which he has given this information. But two of them, Rittlen and Masern, appear to be only different forms or varieties of what we denominate measles, whilst of some other heads or denominations in the Berlin bills, probably each included several distinct diseases; as disease of the chest and consumption, both distinguished from phthisis (Swindsucht) which is given separately· But these Dr. Moehsen could only give as he found them in the Weckly Bills of Mortality, from which he states that he formed his Tables.

His sixth table shews the number of suicides that took place in each month of those seventeen years, and also during the whole term, in the five different divisions following, viz., by shooting, hanging, cutting the throat, drowning, and otherwise; also the number of deaths by accidents in forty-nine different ways, the whole number being 447; distinguishing the civil from the military population, males from females, and children from adults, but without stating the months in which the deaths took place. Amongst those causes of death, except drowning and sudden death, the numbers by which were ninety and one hundred and thirty-one respectively, the greatest number, thirty-nine, was of those who died by hunger and misery in the year 1772. Always excluding the still-born; the number of deaths in 1772 was 8314, whilst the annual average number of the remaining sixteen years was only 4339; so that in 1772 the mortality was nearly twice as great as on the average of the other sixteen years of the term, which shews how small a number of deaths is imputed in the bills to hunger and destitution in comparison with those which, although ascribed to other causes, were hastened and chiefly produced by want and misery.

The seventh table shews for the year 1774 alone, the number of the still-born, the number of deaths by unknown diseases, and the number of them produced by each of seventy-three different diseases and casualties according to the Berlin Weckly Bills, which took place in each month of that year and during the whole year, with distinction of the civil from the military population, males from females, and children from adults. The whole number of deaths, including the still-born in that year, was 4401; still-born 259, deaths by unknown diseases 276.

Dr. Moehsen states that the diseases were first introduced into the Bills of Mortality at Berlin in the year 1721. The sexton of every parish had some years before been ordered to leave at the senate-house, at the end of every week, a list of the names of all who had been baptized, married, or buried during that week; and in the case of the buried, the age at which, and the disease by which, each death took place, were also to be stated. But these orders were not properly attended to until 1733; from that year he made and preserved abridged extracts from them until 1753, when these were destroyed by fire. In 1757, he resumed his labours which we have here given an account of, more minute than in most other cases, but not more so than their value appears to entitle them to, whether for their useful applications or as examples worthy of being followed.

In 1778 was published at Paris, in octavo, the work entitled Recherches et Considerations sur la Population de la France, par Μ. Moheau. This book is agreeably written, in a way entirely popular, and will probably be perused with more pleasure by the generality of readers than most others on the subject of population. It contains a great number of tables, for many of which he was indebted to other writers, especially to Μ. Messance; but he has also given many that are original, derived from the Bills of Mortality and actual enumerations of the people, though without explaining in a satisfactory manner how he obtained his information, which, if it be correct, must have cost great labour. In his preface he says, “il est tel page de ce livre qui a coûté nécessairement deux mois de travail, et un volume de chiffres.” [7:15:518] The fourth edition of Dr. Price’s Observations on Reversionary Payments appeared in 1783, and contained much new and valuable information on these subjects, as has already been stated above, and in the historical introduction to the article Annuities.

In 1786 was published, at Petersburgh, in the Acts of the Academy of Sciences there, for the year 1782, an essay by Μ. Krafft, on the marriages, births, and burials, at St. Petersburgh, during a period of seventeen years, from 1764 to 1780, preceded by a general exposition of the uses such tables might be applied to, if the observations they record were extended over entire governments in Russia. This paper contains seventeen tables, which shew the number of deaths at each age, and by each of the principal diseases, together with the numbers of marriages and baptisms; the numbers in each case, being given for each of the seventeen years separately, as well as for the whole term; and the sexes are always distinguished; as are likewise foreigners from the native Russians.

These tables would have been rendered very valuable, had they been accompanied by statements of the numbers of the living of each sex in the different intervals of age; but for want of this information, it is difficult to apply them to any useful purpose, and many of the inferences Μ. Krafft has drawn from them are very uncertain.

During a period of nine years, commencing with 1779, and ending with 1787, Dr. Heysham of Carlisle kept accurate registers of the births, and of the deaths at all ages, in the two parishes which comprehend that city and its environs; also the diseases or casualties which the deaths at each age were occasioned by; and the sexes were in all cases distinguished. These excellent registers were kept with great care and skill on the plan of Dr. Haygarth above mentioned, and included all dissenters within the two parishes. Dr. Heysham published them from year to year as they were made, and accompanied them with valuable observations on the state of the weather and diseases in each year. Their value was greatly enhanced by two enumerations of the people within the two parishes, one made in January 1780, the other in December 1787, in both of which the ages were distinguished, but not the sexes of each age, though the totals of each sex were. These documents, printed in convenient forms, with further information respecting them, and many useful tables deduced from them, may be found in Mr. Milne’s Treatise on Annuities.

In the third volume of the Transactions of the American Philosophical Society, published in 1793, were inserted Observations on the probabilities of the duration of human life, and on the progress of population in the United States of America, contained in a letter from Mr. Barton, which had been read to the Society in March 1791; also a postscript to that letter, read in December following; the returns of an actual enumeration of the people of the United States having been made in the meantime. The information there given from the parish registers is of little value. In the enumerations the sexes were distinguished but not the ages, except the numbers of free white males under and above sixteen; but even that information with regard to the population of America is very interesting, whether we contrast the early with the more recently settled counties, or the whole of the United States with the population of Europe.

Μ. Wargentin having died in 1783, Μ. Henrich Nicander was in the following year appointed his successor as astronomer and secretary of the Royal Academy of Sciences at Stockholm; and in 1791 as one of the royal commissioners of the Tabell-Verket, and their secretary. Af ter the death of Μ. Wargentin, and perhaps for some time before, owing to his infirmities, the Tabell-Verket would appear not to have been duly attended to; no communications of the results having been made to the public for fifteen years after his decease. But other new commissioners were appointed at the same time as Μ. Nicander, and he commenced the performance of the duties of his office by forming a catalogue of the acts add tables in the archives of the commissioners, when he found so many deficiencies in the returns from different parts of the kingdom, and so little assistance was afforded him, that it was not until the year 1799 that he was enabled to commence the publication of the most important results for the term of twenty-three years ended with 1795, and he continued to insert papers on that subject in the same transactions for the remainder of his life; he died in 1815. The following statement will facilitate reference to those papers, eighteen in number.

The most valuable information contained in these papers is the mean number of persons living of each sex, in each interval of age during a certain number of years, and the annual average number of deaths of persons of each sex in the same intervals of age which took place during the same time; as these data are sufficient for determining the law of mortality for each sex separately, and also for the whole population« without distinction of sex. That information Μ. Nicander has given for all Sweden and Finland in his first paper in the transactions for 1801, both for the whole period of twenty years, 1776-1795, and for each of the four consecutive periods of five years contained in the same term; also derived from these, the proportion of the annual average number of deaths to the mean number of the living of each sex in each interval of age. And in the volume for 1809, (tab. B,) he gave the same information as to the population and mortality during the term of five years ending with 1805. In the volume for 1813, he gave the number of deaths of persons of each sex, which took place in each interval of age during every one of the five years, 1806-1810; also the number of living persons of each sex in each interval of age at the end of the year 1810. In the volume for 1814, he gave the number of deaths of persons of each sex in each interval of age which took place in each of the two years 1811 and 1812. And in all cases the numbers born alive and still-born of each sex were also given separately, but the still-born were never included among the deaths.

Sweden having lost Finland by the war with Russia m 1808, the observations recorded by Μ. Nicander in the volumes of the Stockholm Transactions for 1813 and 1814, were made in Sweden alone. The operations of the Tabell-Verket never extended to Swedish Pomerania, the Isle of Rugen, or the town of Wismar.

In the sixth and last paper of Μ. Wargentin, in the Stockholm Transactions for 1755, he gave a table shewing the proportion of the whole number of deaths produced by each of about thirty of the principal diseases; in all Sweden, in Stockholm alone, within the London bills of mortality, and in Berlin. But at that time complete returns from the whole of Sweden had only been received tor die two years 1749 and 1750; and from Stockholm fur the five years 1749-1753. Forty-six years from that time had elapsed without any thing further having been published on the mortality from different diseases in Sweden, when Μ.
[table]
[7:15:519]

Nicander resumed it in his second paper in the Stockholm Transactions for 1801, where, in table T, he gave for each of the twenty-one years 1775-1795, the number of deaths produced by each of thirty-seven different diseases, besides these four other causés, child-bearing, the infirmities of age, unknown diseases, accidents and other violent deaths; with the annual average number by each cause, and the proportionate number produced by each cause, out of a total number of 10,000 deaths.

In table U he gave for each diocese in the kingdom, for Stockholm and for Carlscrona, each separately, also for the whole of the kingdom, the annual average number of deaths during the same period of twenty-one years, produced by each of the causes above mentioned, without distinction of the sexes, except for the whole kingdom taken together; for which the average was given from each cause for males and females separately, and also for the whole population, without distinction of sex. Μ. Nicander continued his papers on the mortality produced by different diseases in Sweden, in the same Transactions for the years 1805,1809,1813, and 1814, which appears in the tabular statement of his papers given above, for the term of years there set against their respective dates of publication. But in these four papers, the mortality produced by several kindred diseases taken together was given, without distinguishing that which was produced by each disease separately. In his paper published in 1809, besides the number of deaths produced in each of the five years 1801-1805, by each disease or class of diseases, the annual average number produced by each, in every month during the same term, was given, so as to shew the effects of the seasons in increasing or diminishing the mortality from each.

Μ. Nicander’s papers contain much valuable information which, not coining within the scope of this article, it may suffice merely to mention here. Besides the statements above mentioned, of the births and deaths in the whole of the kingdom taken together, the numbers of them which took place in the city of Stockholm, and in each of the läns or governments the country is divided into, are given separately for the period between each two consecutive enumerations of the people, with the excess or defect of the births in each case, as compared with the deaths; and the difference is compared with the increase or decrease of the population in the same period, determined by actual enumerations at its extremities. The number of marriages contracted, and the number dissolved by death during given periods, are also stated; with'the number of pregnant women delivered in each interval of five years of age, from fifteen to fifty, and those above fifty; the number of those women who were married, and who were single; the numbers of double, triple, and quadruple births, distinguishing those born alive from the still-born, the legitimate from the illegitimate, and males from females. In the enumerations, the number of married persons of each sex, the numbers of widowers and widows, and the numbers unmarried above fifteen years of age, of each sex; also the number of children of each sex under that age, were given.

The numbers of the people, classed according to their ranks, conditions, and employments, were stated, with distinction of the sexes, and the number of children vaccinated in each year, from 1804. In the volume for 1813, the number of families in each of the four following classes was given :—1. the opulent; 2. other persons of property; 3. those subsisting by their labour; 4. the destitute poor; which consisted of two persons, from two to five, from five to ten, from ten to fifteen, and of more than fifteen persons; with the whole number of families of each of those five magnitudes, and also the whole number of families of each class or condition. In addition to these, tables were given for 1802, and the subsequent years, shewing how many Swedish tuns were sown of each kind of grain, also of pease, and of potatoes put into the ground, with the produce derived from each; the quantity of live stock of each kind; and the quantity of land under cultivation for each government of the kingdom separafely.

Some of the most valuable parts of these papers of Μ. Nicander, with deductions from them, will be found under the second section of this article.

After the death of Μ. Nicander, which took place in 1815, no reports on the state of the population and mortality were inserted in the Stockholm Transactions, where they had always appeared previously; and as books, or any information concerning them, can hardly ever be obtained from Sweden through the London booksellers, it was not till the summer of 1836 that the author of this article learnt from Professor Nilsson of Lund, who was then in London, in what way they had been published; and to that gentleman and Mr. Charles Tottie, consul-general in London for Sweden and Norway, he is indebted for a manuscript copy of the 1st, 2d, and 3d tables, at the end of this article, which give the most important information on the subject; their authenticity he considers to be sufficiently guaranteed, by his having received them through Mr. Tottie, from Μ. John Ad. Leyonmarck, the successor of Μ. Nicander, as the secretary to the Tabell-Verket, or Registry Commission; also by comparing them with the printed tables under mentioned.

The principal printed documents on the progress of population in Sweden, since the death of Μ. Nicander, which the author has yet succeeded in obtaining are the following:—

1. An oblong folio pamphlet, consisting of forty leaves, (each twenty-one inches by eighteen), and containing forty-two lithograph tables, most of the pages being very much crowded with small figures, shewing all the particulars above stated with respect to Μ. Nicander’s tables, not only for the whole of Sweden, but also for the city of Stockholm, and each of the läns or governments separately, which the kingdom is divided into, for the five years 1821-1825. The number in each of the usual divisions of age, at the enumeration. of 1825, is given, with distinction of the sexes, and of the country people from those residing in towns. The following were the numbers for the whole of the kingdom :—
[table]

The numbers of the people in that year, classified according to rank or condition, profession or occupation, are also given. And the number of deaths in each of the five years (1821-1825) by childbirth, also those of each sex separately, by eleven different diseases, including the principal of those prevailing among children, and those by seven different kinds of violent deaths or casualties, are stated for the city of Stockholm, and each län in the kingdom separately.

For that city, and each of those läns separately, the numbers of the people in 1805 and 1810, without distinction of age or sex; and the numbers in 1815, 1820, and 1825, both with and without that distinction are given; with the numbers of births and deaths during the two quinquennial periods 1816-1820, and 1821-1825. The divisions are indeed much more minute than these; the population of the city of Stockholm is given for nine different districts separately, and the births and deaths for twenty; this arises from the population being divided into those districts for the purposes of taxation, and the twenty others are the different congregations or places of worship, where the registers of births, deaths, and marriages, are kept. But every län in the kingdom being divided into several districts, and each district into its separate parishes; the particulars above mentioned, are [7:15:520] given for each parish separately, and also the sum of those in each district, which shows the same things for it.

This is a very imperfect statement of the contents of these valuable tables, but sufficient it is hoped, to show those who take interest in such subjects, that they are worth being consulted and studied. The title is as follows: The humble Report of the Royal Registry Commissioners to his Royal Majesty, on the Proportions of the Births and Deaths during the years 1821-1825, to the Population of the Kingdom in the last mentioned year ς also on the observed Increase of the population of the Kingdom, during the last elapsed compared with the next preceding Decennium. Dated the 10∕7z of May 1828. Printed by the gracious command of his Royal Majesty.^[2. Kongh. Tabell-Commissionens underdaniga Berattelse till Kongh. Maj : t. angaende Nativitetens och Mortalitetens forhallande Aren 1821 med 1825, Rikets Folkmangd sistberörde Ar, samt Folkmangdens vundna tillökning under det sistforflunta, jamnförelsevis emot det nastforutgangna decennium. Daterad den 10 Maji 1828. Pa Kongh. Maj: ts nadiga befallning till trycket befordrad. ]

2. A quarto of sixty pages, with the same title, containing an abstract of the above, printed with types in the usual way, and observations and remarks which were absent from the larger tables. In it, the results of the observations made in that quinquennium (1821-1825) are compared with those of the preceding, by placing the corresponding numbers on the same line; those of the next preceding quinquennium (1816-1820) on the left; and those of the present (1821— 1825) on the right of the page, with the explanation of their import between them.

These contain almost all the more important information in the larger tables, at least to persons residing out of Sweden, and are much more convenient to use. But this is defective in giving only the numbers of violent or sudden deaths, and those without distinction of sex, with hardly any information as to the numbers by different diseases, except stating in what parts of the country they produced the greatest mortality in different years.

3. A similar quarto of seventy-four pages for the quinquennium 1826-1830, with a similar title, was in 1833, handsomely printed with much larger and more beautiful types, especially the figures, which is important. The contents of the tables in possession of the Commissioners, twenty-five in number, are here stated, and then very satisfactory extracts from them are given. The number of deaths from childbirth and twelve different diseases are given; for the preceding quinquennium, the annual averages only; but for this, 1826-1830, they are stated for each year separately; but the annual average only for violent deaths, casualties, and unknown causes. As each of these gives the results of the preceding quinquennium, the two together give them for fifteen years, 1816—1830; and Μ. Nicander’s papers in the Stockholm Transactions, gave the observations to the end of 1812; those for the years 1811 and 1812 being contained in the volume for 1814. So that only the observations for the three years, 1813, 1814, and 1815, are wanting to complete the series; and the most important parts of these and others are contained in the tables above mentioned, which are given at the end of this article. Whether two other quartos similar to those above mentioned, were published, with the observations made in the two preceding quinquenniums, 1811-1815, and 1816-1820, the author had not been able to ascertain when this article was printing, (in February 1837 ;) nor whether any other large folio tables, similar to those above mentioned, have been published; but it is probable there have not; for in the German translation of the second edition of ForselΓs Statistics of Sweden, by the Rev. A. G. F. Freese, preacher to the royal court of Sweden, and rector of the German National Lyceum at Stockholm, (8vo, Lubeck 1835,) it is stated in a note at page sixty-seven, on entering upon the subject of the Swedish tables, that they are often quoted by foreign authors, and that the very large and instructive tables published in 1829, deserve much attention. There can be no doubt that these were the tables ordered by the king to be printed in 1828; although they might not have been published before 1829. Had there been any others of the kind, those probably would not have been so noticed, and as the translator must have had the best information on the subject, the obvious inference is, that no others existed in 1835.

4. A folio pamphlet of three sheets extracted from the Tabell-Verket, showing the number of persons carried off by epidemic cholera in Sweden in the year 1834.^[3. Utdrag af Tabell-Wercket öfver de i Cholera-Farsoten uti Swerige añedne personer Ar 1834. Stockholm 1836. ] It contains five tables, but we shall only notice the first and most important of them here; it shows the number of deaths which were produced by that disease in the year 1834,—in every län in the kingdom, and in every town and every subdeanery in each län, in each of the usual intervals of age till twenty-five, those between twenty-five and fifty, and the number above fifty years of age; also the number in each month, without distinction of age. The estimated number of the people in each place at the commencement of that year, and the proportion of them who died of the disease are also given, the sexes being distinguished throughout. This appears to be the first publication of the number of deaths in Sweden classed according to the ages of the deceased, as well as, and together with, the causes of death. For their assistance in procuring the last mentioned and other valuable books from Sweden, the author makes his grateful acknowledgments to Mr. George Warde Norman, and Mr. H. James Prescott; also to Mr. Norman, for a manuscript table showing the number of children of each sex born alive, and the number of the still-born, without distinction of sex; with the number of deaths of persons of each sex, which took place in each of the intervals of age there mentioned, in every one of the ten years 1824-1833, in the kingdom of Norway, the authenticity of which, that gentleman has no doubt of, and therefore, neither has the author of this. In the fourth table at the end of this article, the total of those numbers for the whole term of ten years are given.

It is gratifying to see this table from Norway, so similar to the excellent form of the Swedish. In every point in which they differ, the Swedish is entit!ed to preference; especially in the smaller intervals of age, in which the numbers of children are given in the Swedish; and it is to be regretted, that in giving the numbers of the still-born, the sexes were not kept distinct; as the great excess of stillborn males above still-born 'females, is an interesting subject of inquiry. It is much to be desired that these should be continued in Norway, and that periodical enumerations of the people on the Swedish plan should also be made regularly. But the author has not yet succeeded in his endeavours to ascertain whether those have been made, or are intended or not.

In the year 1800 was published, at Paris, in octavo, under the title of Essai de Statistique, a memoir by J. A. Mourgue, on the births, marriages, and deaths, that took place in Montpellier during a period of twenty-one years, ending with 1792, with the ages at which the deaths happened, the sexes are also distinguished, and the population of the place appears to have been nearly stationary. The tables and observations of Μ. Mourgue appear to be more valuable than any others relative to the pepulation of France, that had previously been published, except those of Μ. Deparcieux, which related only to select orders of the people. This memoir was read at a meeting of the French National Institute in 1795, and printed in the Mem. des Sαv. Εtr. an. 14.
[7:15:521]

An enumeration of the people in Spain was made by royal authority in the years 1768 and 1769, and again in 1787; a minute account of this last was printed at Madrid, showing for each province separately, the numbers of parishes, cities, towns, villages, &c. &c. with the number of people in each class according to their ranks, professions, occupations, &c. and the monastic orders of both sexes were particularly distinguished: to these was prefixed a summary of the census of 1768 and 1769- In these two enumerations, the ages of the people were not distinguished with sufficient minuteness; they only showed how many were under seven, between seven and sixteen, sixteen and twenty-five, twenty-five and forty, forty and fifty, and above fifty. In both enumerations, together with the ages, the distinction of the sexes was given; in the first, the married were only distinguished from the single; but that of 1787 showed how many of each sex, and in each interval of age, were in the states of celibacy, marriage, and widowhood.

A third enumeration of the people in Spain and the Spanish possessions in Europe and Africa, including the Canary Islands, was made in 1797; and a full account of it, occupying nearly fifty large tables, was printed at Madrid in 1801. The distinction of the ages in this enumeration was still not sufficiently minute; under forty it was the same as in the two preceding; but after that age, the number of the living in each interval of ten years to one hundred was given, and the number above one hundred.

No information from the parish registers in Spain was given in any of these cases; although satisfactory extracts from them all, distinguishing the ages and sexes of the deceased, or even from those only which could be most depended upon, during the ten years that intervened between the two last enumerations, would have rendered the results of these incomparably more valuable, provided that the population of the places for which correct registers were given, could be distinguished from the rest. Those to whom the superintendence of these measures were entrusted in Spain, seem to have been well aware of this, and to have actually entered upon the formation of these necessary supplements to the enumerations, as appears by the following passage extracted from the introduction to the printed statement of the last census:

u Interin que se forman las tablas necrológicas, las de nacidos y casados, en que entiende el ministerio de Estado, y que son mny utiles para valuar casi geométricamente el total de la poblacion del Reyno, debemos contentarnos con las noticias que nos proporcionen los censos executados por el método que el presente.” But these tables of births, deaths, and marriages, have not yet (in the year 1836,) been published, neither does it appear probable that they were ever formed.

Inl801 werepublished, in quarto, Observations on the Increase and decrease of Different Diseases, and particularly of the Plague, by William Heberden, junior, M.D. F.R.S., containing some tables, chiefly deduced from the London bills. In the advertisement prefixed to this valuable tract, we are informed that it had been intended to be subjoined to a new edition of the Bills of Mortality; which edition, however, was not published. We are also indebted to the same ingenious physician for other interesting observations on the mortality in London, inserted in the Philosophical Transactions of the Royal Society (for 1796,) and in those of the London College of Physicians, vol. iv.

In the same year (1801) was published another valuable work, entitled, Reports on the Diseases in London, particu larly during the years 1796, 1797, 1798, 1799, and 1800, in 12mo, by Robert Willan, M.D. F.A.S. part of which had been previously inserted in some periodical publications. The author’s observations were made both on the Bills of Mortality, and on the cases that occurred in his own practice.

Dr. Bateman commenced a series of similar observations and reports on the diseases of London with September 1804, which he continued till the end of August 1816. The subjects of those reports were, the cases that occurred at the Public Dispensary in London, in which he was a physician; they were first published quarterly in the Edinburgh Medical and Physical Journal, but the author collected them into a separate octavo volume, which he published in 1819, with an introduction, in which he gave a Historical Survey of the Diseases of London.

All of the three works last mentioned, are very interesting and instructive; but it would not be consistent with the objects of this article, to notice them further here.

By art. 1, sect. 2, of the constitution of the United States of America, it was provided that the representatives and direct taxes should be apportioned amongst the several states which should be included within the union according to their respective numbers. The first actual enumeration to be made within three years after the first meeting of the Congress of the states, and within every subsequent term of ten years, in such manner as they should by law direct.^[4. Dr. Seybert, in his Statistical Annals of the United States of America, published in 1818, (p. 17) makes the following statement: “The United States of America alone require an actual enumeration of the inhabitants to be made at regular intervals; as far as our knowledge extends, no other instance can be furnished from the history of mankind; our practice is worthy of being followed by other nations.” And a statement to the same effect is made in the American Almanac for the year 1832, (p. 106) by which it would appear, that the writers were not aware of Sweden having set a still better example of that kind more than thirty years before. ] In consequence of this, five enumerations of the inhabitants of the United States have been made, viz. in 1790, 1800,1810, 1820, and 1830; statements of the first four are given in the American Almanac for 1832, and of the last in the same Almanac for 1833. In the first, as was stated above, no attention was paid to the ages, except the distinction of the numbers of free white males under and above sixteen years of age. In the enumerations of 1800, 1810, and 1820, the numbers of free white persons of each sex in five different intervals of age were ascertained; but three of the intervals were much too long to admit of the enumerations being available for determining the law of mortality; the first of those long intervals being all under ten years of age; the second, those between twenty-six and forty-five years; and the third, all above that age. Of these three enumerations, it was in that of 1820 only, that the free coloured persons and the slaves were classified according to their ages and sexes; and the intervals of age into which they were distributed, were longer than those for the free whites.

In 1830, the numbers of free white persons of each sex, in thirteen different intervals of age were determined; the four divisions under twenty years of age being of five years each; the eight between twenty and a hundred, of ten years each; and the thirteenth division included those of a hundred years of age, and upwards. The numbers of each sex, of free coloured persons, and of slaves separately of each sex, in each of the following divisions of age, were ascertained. Between 0 and 10, 10 and 24, 24 and 36, 36 and 55, 55 and 100, and above 100. These particulars were given for each state and territory separately, and also the totals for the whole of the United States. Statements of all the five enumerations from that of 1790 to that of 1830, both inclusive, may be seen in the American Almanac for the year 1832. That of 1830, with the ages of the living for each state and territory will be found in the same Almanac for 1833. No general returns of the numbers of births, marriages, and deaths, appear to have been required or made throughout the United States; and previous to the [7:15:522] year 1820, but few births were registered there. Many marriages were till then, and probably still are, contracted before magistrates, whose records of them were seldom preserved.^[5. In consequence of the notice which was taken in the first edition of this article, published in the Supplement to the Encyclopaedia Britannica, in June 1817, of the enumerations of the people, and the published extracts from the parish registers in the United States, with some suggestions for improving the best of them, those of Philadelphia, and increasing their usefulness, John Vaughan, Esq·, the Librarian of the American Philosophical Society, had the goodness to communicate to the author in June 1818, most of the information given above, as to the state of things down to that time, both in the United States generally, and in Philadelphia in particular; with eight of the annual statements (all he could procure and part with,) of the Board of Health in Philadelphia, showing the number of deaths at every age by each disease or other cause, in that city and its liberties; and several American newspapers, showing the number of deaths in each of the same intervals of age, the number in each month of the year, and the number of deaths by each cause, without in this last case, stating at what ages they happened, in Baltimore, Boston, Charleston, New York, Philadelphia, Salem, and Washington ; for which the author feels it incumbent upon him to acknowledge his obligations, and express his gratitude in this place. ]

In the city and liberties of Philadelphia more attention appears to have been paid to these subjects than in almost any other part of the United States. In the first number of the American Journal of the Medical Sciences, published at Philadelphia in November 1827, in octavo, there is an excellent article (the 8th), entitled, Medical Statistics : being a series of Tables, showing the Mortality in Philadelphia, and its immediate causes, during a period of twenty years, by Gouverneur Emerson, ME. Dr. Emerson states, that the subject of the diseasesand mortality of Philadelphia, was first made one of regular record in the year 1807, through the influence and exertions of Professor James, and that “their authenticity may be régarded as resting on very solid grounds.” From authority vested in the Board of “Health, this municipal power makes it obligatory upon physicians to give certificates designating the name, age, and sex, of all who die under their care; and sextons are bound by still heavier penalties, not to permit the interment of any dead body, until such certificate is obtained, which he returns to the health office on the last day of every week, for publication. The accuracy with which the diseases are designated in these certificates, rests chiefly upon the general intelligence of the medical profession in that city, the members of which are very much in the practice of testing their pathological opinions by autop-sical examinations. For the purpose of ascertaining the number born, the various practitioners of midwifery are required to render an account at the health office of all births. With regard, however, to this department, there is some reason to suspect a deficiency in the returns, especially from the outskirts of the city and liberties. But the registry of the dead has, for the most part, been kept with a care and fidelity creditable to those who have had its superintendence.”

Dr. Emerson after making some general observations on the topography and climate of Philadelphia, proceeds with his observations on the eleven valuable tables which are inserted at the end of the article.

The first shows the results for each calendar month of thermometrical observations made at Philadelphia, during the term of ten years, which commenced with March 1811, and ended with February 1820. The second is an abstract of the census of the city and county of Philadelphia, taken by order of the general government in 1820.

All the observations on the Mortality were made within the period of twenty years, which commenced with 1807 and ended with 1826; the still-born being always, as they should be, given separately, and not included amongst the deaths; except in Table IV., which shows the number of deaths in each month of each of the twenty years; the Board of Health having found it impracticable to make an accurate monthly estimate of them for deduction.

In the number stated in the Philadelphia bills to be stillborn, the abortions are included. The fifth and eleventh of these tables are the most valuable. In the fifth are stated the numbers of deaths from the principal diseases during the whole period of twenty years in the following intervals of age, viz. between birth and one year completed, between one and two years, between two and five, between five and ten; then in each interval of ten years of age to a hundred and twenty; fifty-five deaths having happened between the ages of a hundred and a hundred and ten, and six between a hundred and ten and a hundred and twenty. After the columns set apart for those fifteen different intervals of age, in a sixteenth the number of deaths produced by each disease at ages not ascertained, is given; and in the seventeenth and last column, the total number of deaths produced by each of those diseases. The total number of diseases in the table is sixty-six, and the number of causes of death, old age being included, is sixty-seven.

A few cases of deaths occasioned by accidents and diseases of vague character, Dr. Emerson omitted, as tending rather to perplex than to elucidate the subject; and adopted the alphabetical arrangement in this table, as the most convenient.

The total number of deaths registered during the term of twenty years was 53,004, whilst the number included in this fifth table was 50,614; so that 2390 were excluded for the reason just stated.

Dr. Emerson’s other tables and his observations on the whole of them, will be found well worth the attention of those who take interest in the subject.

In Hazard’s Register of Pensylvania for July 30, 1831, (No. 5, vol. viij.) there is an elaborate paper entitled, Comparative Views of the population of the city and county of Philadelphia, from the time of the first census in 1790, till that of the last in 1830; in which the number of white persons of each sex in that city and county at the time of the census of 1830, in each of die thirteen intervals of age, stated above to have been adopted throughout the United States at that census, is given; and die same information is given as to the coloured population at that time, but distributed into the six intervals of age only, above stated to have been adopted for them. The number of whites was 173,345; of coloured persons, 15,595; total, 188,940.

A statement of the deaths which took place within the Bills of Mortality during the term of ten years 1821-1830, is also given for the whole population without distinction of colour or sex, and distributed into the following sixteen intervals of age in which they happened, viz. under one year, between one and two, between two and five, then in each of the three intervals of five year’s each to twenty, and the remaining ten intervals of ten years each between twenty and a hundred and twenty; thirty-two persons having died between a hundred and a hundred and ten years of age, and five between a hundred and ten and a hundred and twenty. The whole number of those deaths, which did not include the still-born, was 37,914.

The number of births of each sex in each of the ten years 1821-1830, is also given, including the still-born, but without distinction of colour; and the number of still-born for each year separately, but without distinction either of colour or sex.

The number of deaths in each of the ten years is stated separately, both with and without distinction of sex, but always without distinction of age; and it is only where the whole number of deaths of both sexes without distinction, in each of the ten years is stated, that the division of it into [7:15:523] the numbers of white and coloured persons is given; in these numbers of deaths without distinction of age, the stillborn are included. So that these documents do not enable us to determine out of how many persons of each sex, one died annually during the ten years 1821-1830.

Taking the limits of the Bills of Mortality from Dr. Emerson’s second table, where he stated the wards and districts from which the returns of interments were made, and the population of each at the census in 1820, amounting in all to 121,980; and assuming the limits of the bills to have been the same in 18.30, the population within them at the census of that year, was, according to Hazard’s Register, 171,212; and the mean number of the people during the intervening ten years, appears to have been 146,596.^[6. Including the township of Blockley in the limits of the bills according to Dr. Emerson, although in the register it is removed from them and placed in the rest of the county. If the interments in or from Blockley were not included in the bills, the annual average mortality must have been one of 37 - 9167. ] The number of deaths in the same time, exclusive of the stillborn, was, according to the statement with the ages, 37,914; according to that without the ages, 37,814; taking 37,864, the mean between these for the true number, we find that there died annually on an average of those ten years, one person for every (38*7165 or nearly) thirty-nine in the whole population. The number of persons in the city and county at the census of 1820 was 137,097, at that of 1830, 188,961, mean number during the intervening ten years, 163,029∙

The following statement of the progress of population in the city alone of Philadelphia, appears to be sufficiently interesting to deserve a place here.
[table]

The three first columns are taken from the article above mentioned in Hazard’s Register; but since the numbers in the third are proportional to the rarity of the population at the five enumerations, those in the fourth have been added, as they measure its density at the times of those enumerations.

The whole population of the city and county of Philadelphia, without distinction of age, sex, or colour, was distributed as follows, at the times of the enumerations in 1820 and 1830.
[table]

(Hazard’s Register, vol. viii. p∙ 65.)

Here the inhabitants of Blockley, amounting in 1820 to 2655, in 1830 to 3401, are included within the suburbs and bills of mortality. It is much to be regretted that in the census of 1830, the coloured population were not distributed into the same intervals of age as the whites; also that the colours and sexes of those who died within the bills of mortality during the ten years, 1821—1830, were not distinguished in the published statements, as well as the ages. Dr. Emerson was of opinion that the rate of mortality amongst the coloured population was much greater than amongst the whites.

It is equally to be regretted that, while the bills of mortality extended only to the city and suburbs, of which the mean population during the ten years, 1821-1830, was 146,596, the enumeration of that portion of the population of the city and county distributed into the different intervals of age, with distinction of the colours and sexes, was not given separately. For with such documents as are before us, even if the enumeration of 1820 had been made exactly in the same manner as that of 1830; in attempting to determine the rate of mortality in any interval of age, we should only have the means of comparing the annual average number of deaths which took place in that interval within the bills of mortality, with the mean number of the people in the same internal of age in the whole of the city and county. But the mean population within the bills of mortality was only 146,596

while that of the whole city and county was 163,029

that is 16,433

or about one-ninth greater.

The difficulty arising from this would not be great, if the population without the bills were known to be distributed into the different intervals of age in a manner similar to that within them; but there is no doubt of the distribution in the two cases being very dissimilar; for, excluding the stillborn both from the numbers of the births and of the deaths, during the ten years ended with 1830,

The total number born within the bills of mortality was 61,945

Total number of deaths in the same time...... 37,814

Increase of population, within the bills, by procreation 24,131

While the increase from all causes during these ten years, was 49,232

So that the increase by migration must have been 25,101

within the bills of mortality; that is, one twenty-fourth part greater than by procreation. The part of the county without the bills certainly could not have been increased in a like proportion in the same way; therefore the population without the bills must have been much more dense at early ages, and more rare at the advanced ones, in comparison with the population within them, than in proportion to the mean number of the people of all ages, without and within the bills respectively. Whence it is manifest that nothing but enumerations of the people in each interval of age, within the limits of the bills, at each extremity of the period for which the annual deaths at the different periods of life are given, can make either those enumerations or the registers of deaths, available for the most important purposes they can be applied to.

In pursuance of an act of Parliament (41 Geo. III. cap. 15), an enumeration of the people in Great Britain was made in 1801; also returns of the baptisms and burials in England and Wales, during the year 1700, and every tenth year after that till 1780, then for every year to 1800 inclusive, with the number of marriages in each year, from the commencement of 1754 to the end of 1800. Large and clear abstracts of the answers and returns to this act were printed [7:15:524] by order of the House of Commons in 1802, and occupy more than one thousand pages folio. In 1811, another act (51 Geo. III. cap.6),was passed, “for taking an account of the population of Great Britain, and the increase or diminution thereof ;” in consequence of which, returns were that year made to Parliament, of the number of persons in every part of Great Britain; also of the numbers of baptisms, burials, and marriages in England and Wales, during each of the preceding ten years; very satisfactory abstracts of these were also printed by order of the House of Commons, in 1812, with some preliminary observations, in which corrections of the preceding returns are given.

The sexes were distinguished both in these enumerations and extracts from the registers, but the ages in none of them; and the proportions of males to females among the living are not to be depended upon,, a number of males in the army and navy, which it is difficult to estimate, not being natives of Great Britain, nor usually resident there. The returns of baptisms and burials were also defective, but few registers of Dissenters having been included in them.

These abstracts are, however, with respect to the objects they extend to, more minute and satisfactory, than any other accounts of the same kind that had previously been published; and it was very desirable that such returns should have continued to be made, and abstracts of them to be printed at regular intervals; for nothing is so well calculated to shew the influence of different causes on the prosperity of a nation, as the comparison of the different states of the population, and the rate of its progress or declension, under different circumstances; besides, the value of the abstracts, once obtained, will be much enhanced by the publication of others of a similar kind thereafter.

It is much to be regretted, that no information as to the ages of the living, or those at which the deaths took place, was required by either of the acts above referred to, nor any encouragement or facility afforded to those who might be disposed to collect such information; and, consequently, that none was given in the returns.

Without better regulations for the keeping of mortuary registers than those heretofore in force, without such as should extend to dissenters of every denomination, it would probably be better not to require returns of the ages of the deceased from all parts of the kingdom; for defective or inaccurate returns would only mislead; and, not to mention the difficulty and expense of procuring returns of the ages of all the living, they would be comparatively of little use, where those of the dead were wanting.

But if government were to print forms for making returns both of the numbers of the living and of the annual deaths in proper intervals of age, throughout the extent of life; only sending these forms along with those now in use, to such as should apply for them; then persons who take an interest in such inquiries, and have the means of making correct returns, might do so with advantage. And a summary of all of that kind made from different parts of the kingdom, would convey much important information. Returns also, from such places only as were similarly circumstanced, might be collected into as many summaries as there were material varieties in the circumstances; and thus would afford the means of determining the different modifications of the law of mortality, which different circumstances produce. If the diseases that occasioned the deaths were also inserted, the greater prevalence of particular diseases in some circumstances than in others, would be apparent, with their effects, and the probable means of preventing them, or lessening their mortality.

But, the population enumerated must always be precisely that which produces the deaths registered; the grand desi deratum being, to determine the number of annual deaths at each age, which takes place among a given number of the living at the same. age.

Mr. Milne’s Treatise on Annuities and Assurances was published in 1815, and contains clear abstracts of the most important statements of this kind that had been published between Dr. Price’s time and the date of its publication; these will, we believe, be found to be much more valuable than any thing of the kind that was extant when that respectable author wrote, whose work had long been referred to for the best information on such subjects.

Since the first publication (in 1817^[7. In the Supplement to former editions of this work. ]) of what has been stated above respecting the two first enumerations of the people in Great Britain, and the extracts from the parish registers of England and Wales, two other enumerations have been made in 1821 and 1831; and abstracts of the answers and returns under the acts that required them, (1 Geo. IV. cap. 94, and 11 Geo. IV. cap. 30), have been printed by order of the House of Commons, (in 1822 and 1833 respectively.) The extracts from the parish registers, shewing in each case the numbers of births, marriages, and burials, returned for each of the ten years next preceding that of the enumeration. The principal difference between the queries put at the two enumerations of 1811 and 1821 was, that in 1811 no inquiry was made as to the ages of the people, while in 1821, after nearly the same questions had, according to the act, been put to the overseers in England, and to the schoolmasters in Scotland, the following instructions as to the ages of the people were given: “If you are of opinion that in making the preceding inquiries, (as to the number of families and persons), the ages of the several individuals can be obtained in a manner satisfactory to yourself, and not inconvenient to the parties, be pleased to state the number of those who are under five years of age,” &c. The thirteen intervals of age into which the persons of each sex separately were to be distributed, being these: 4 of 5 years each from birth to 20 years of age; then 8 of 10 years each to 100; the thirteenth including all those above 100 years of age. Thus it was left optional with the returning officer whether this important question should be put, and with the party interrogated, whether it should be answered or not; from which it would appear that this part of the inquiry was not intended to be made with much correctness, and those whose onerous duty it was to put the question in populous places, might easily lighten the burden; accordingly, from such places the ages of a considerable part of the population were not returned. None were obtained from Manchester, Newcastle-upon-Tyne, or Sunderland. The proportion of the ages which were not returned was, in Birmingham, about ½ğths, in Leeds, ½th, in Bristol, ½th of the returned population. In Middlesex, ∣th, York, east riding, ∣th, north riding, ½th, in Lancashire, ½th, in Warwickshire, ½d, evidently owing to the large manufacturing towns they contain, especially Birmingham, the population of which is more than a third of that of the county of Warwick. These deficiencies in the returns may reasonably be ascribed to the option which was offered to the overseers, who, however, performed the duty imposed upon them with great good will and attention, as appears by the complete return of ages where the obstacles were not too great.

That the people were not unwilling to state their age⅝ may be inferred from the complete returns of them from Hull, Liverpool, Portsmouth, Plymouth, and Great Yarmouth, as well as from every city in England, if we mistake not, except London, Canterbury, and Bristol. From the counties of Bedford, Chester, Rutland, and Leicester, nearly the whole were obtained; and from those of Lincoln, Norfolk, Suffolk, and Wilts, the deficiency was only on an aver [7:15:525] age about one-thirtieth, while from all Wales it was only a forty-second part of the whole.^[8. Those above mentioned are only a few cases, others may be easily found in the Population Abstract. The ages of the inhabitants of London within the walls were very nearly all returned; those of Canterbury were deficient byth part of the whole. ]

The following table may throw some light on the influence of large manufacturing towns, migration, and some other circumstances, in producing a more or less complete return of the ages of the people at that enumeration. It being borne in mind that from Glasgow the whole were returned.

Omitting the army, navy, marines, and seamen in registered vessels.
[table]

With regard to the extracts from the parish registers, the principal difference between the questions put in 1831 and at the three preceding decennial periods of enumeration, was, that in these no inquiry was made as to the ages at which the deaths happened, while in 1831 the officiating minister of every church or chapel was requested to state the ages of the individuals of each sex entered in his burial register, during each of the eighteen years 1813—1830, in consequence of which the ages of 3,938,496 persons buried during those eighteen years were returned, 1,996,195 males, and 1,942,301 females. The number of each sex separately, and of both sexes, who died in each year of age during every one of the eighteen years, in all England and Wales, according to the returns, were given in the preface to the Enumeration Abstract, (pp. 36-42); besides which, a similar table was also given for each county separately, and sometimes for its principal town, at the end of the returns from that county, in the Parish Register Abstract.

Omitting the army, &c., as above mentioned, the whole returned population in 1821 was 11,978,875 persons; but the ages of 10,530,671 only were obtained, the number of persons whose ages were not obtained havingbeen 1,448,204. As the ages withheld were generally those of residents in large manufacturing towns, whilst those returned were from the rest of the population, and a considerable proportion of the former class had migrated from the latter, many of them probably about the age of puberty; there are good reasons for believing that the ages returned and those omitted were not similarly distributed, as to their numbers, into the different periods of life; so that, although the total number omitted be given, they cannot be interpolated in their proper places by calculation or otherwise, among the ages returned.

In the returns of burials at different ages, there are also omissions, which can only be guessed at. Thus it appears that these documents, after all the pains and expense they have cost, do not afford the means of determining the law of mortality, although that undoubtedly is the most important purpose to which enumerations and registers of these kinds can be applied.

The act 6 and 7 Wm. IV., cap. 86, passed in August 1836, is likely to secure satisfactory records of marriages, births, and deaths, in England; but the abortive and stillborn should be distinguished from the children born alive, which does not appear to be provided for. They may, indeed, be entered as abortive or still-born, under the cause of death, in the register of burials; if that be done, they should be carefully excluded from the number of deaths, in making extracts or returns, and stated separately. And if, at the future decennial enumerations, the ages of the people be determined with corresponding accuracy, the values both of the enumerations and registers will be greatly enhanced, and the law of mortality, with much other important information, may be derived from them. The insertion of the cause of death, in the register of it, is of itself a great improvement.

As has already been Observed in the article Annuities, (p. 209, col. 2), it is much to be regretted that in the population returns of 1831, the people were not classed according to their ages, as in 1821; but without giving any option either to the party by whom or to whom the question on that subject was required to be put, as to putting or answering it. It appears highly probable that there would be no occasion to impose any penalty for refusing to answer that question, or for giving wilfully an incorrect answer; and in the few cases where it might be so given, or altogether withheld, if a memorandum were made of it, the desired information might afterwards be obtained nearly enough from other parties; if it came but within the right interval of age, that would be sufficient. It is true that in the present defective state of the returns of births and deaths, that would not have enabled us to determine the law of mortality in a satisfactory manner; but with the returns of 1821, and those of a similar kind to be made at the future enumerations, it would have been of great use. Indeed it must be obvious to all, that one of the greatest uses of such periodical inquiries into the state of the population, is to ascertain its progress, by comparing the returns at the several successive periods, which can only be done satisfactorily when the same method of proceeding is adhered to at each, or as nearly so as may be consistent with the introduction of improvements into it.

Dr. Robert Watt’s Inquiry into the Relative Mortality of the Principal Diseases of Children, and the numbers ινho died under ten years of age in Glasgow during the thirty years 1783-1812, forming the appendix to his Treatise on Chincough, was published with it, in 8vo. in 1813.

He states, (p. 336,) that, “on inquiring into the state of [7:15:526] the Registers of the City, he found something of that kind had existed from a very remote period; but that it was only from the commencement of the year 1783 that they had been kept in a regular manner.” The Bills extended to the suburbs as well as the city, and he stated that so early as the year 1798, more than half of the funerals were without the city. With the most laudable zeal and unwearied industry, he collected from the different registers of burials contained in fifteen folio volumes, for every one of those thirty years, the number of children under ten years of age who died in each month of that year, by each of eight different diseases, (counting fevers of all kinds as one disease only, designated by the term fever, according to the bills,) the number of the abortive and still-born, and the numbers of deaths under two years of age, between two and five, and between five and ten; and gave a separate table exhibiting those particulars for each of the thirty years; shewing also the total number of deaths during the whole of each year from each of the causes, and in each of the intervals of age above mentioned; with the whole number of deaths at all ages, and from all causes that took place in each year.

Then, dividing the whole term of thirty years into five periods of six years each, he gave a table (his 31st) shewing how many deaths took place in that period from each of the causes and in each of the intervals of age above mentioned, for every hundred in the whole numbers of deaths, including the abortive and still-born, which took place during the same period.

The following are four of the fifteen columns in that table.
[table]

Dr. Watt, in common with almost all others who have well considered the subject, was an advocate for vaccination; and if he overrated the degree in which the reduction of mortality effected by it was counteracted by the contemporaneous increase of mortality from other diseases; he has given abundant proof that it was neither from the want of an earnest desire to discover the truth, nor of persevering industry in the pursuit of it.

At the conclusion of his work he recommended scarlatina to be thenceforward carefully distinguished from other fevers in the bills, and expressed his opinion that it had been a very considerable cause of mortality among children for some years previous to the date of his publication.

Medical men in general, both in London and in Glasgow, dissent from the opinion of Dr. Watt, that the mortality from measles had materially increased since the introduction of vaccination; but it is supported by the Bills of Mortality both of London and Sweden, as well as those of Glasgow; the increase has also been observed both in Cornwall and at Plymouth, although the numbers there are small.^[9. Sketch of the Medical Topography of the Hundred of Penwith, Cornwall, by Dr. Forbes, partii, p. 138, in Trans, of Provincial Assoc. vol. ii; and Dr. Blackmore on the Rise and Decline of Particular Mortal Diseases, 8vo. Plymouth 1829, from Trans, of Plymouth Institution. ] Perhaps this increase of mortality may take place principally among the children of die poor, who, in such cases, seldom have proper medical assistance; and either from ignorance or necessity do not sufficiently protect the patients from cold whilst labouring under the disease.

The third edition of Dr. Cleland’s Statistical Tables relative to the City of Glasgow, was published there (in 8vo.) in 1823, containing a good account of the population and mortality both of the city and suburbs down to that time; he there gave the bills of mortality of the city and suburbs for the year 1822, which appears to have been the first published, and continued to prepare these bills during fourteen years, 1821-1834, with great care and attention, and to publish them in the Glasgow newspapers, with the approbation of die magistracy, who cheerfully defrayed the expense.

These bills were similar to those published by Dr. Haygarth at Chester, and by Dr. Heysham at Carlisle; except that the intervals of age the numbers of deaths were given in under five years, were much less minute, and that the causes of death were not stated in Dr. Cleland’s bills. That gentleman was also appointed to superintend the two enumerations of the people in the city and suburbs of Glasgow in 1821 and 1831; and having been appointed on this last occasion by the sheriff of Lanarkshire to superintend the enumeration of the county also, in a letter to the author of this article, dated February 15th 1831, he expressed his apprehensions that he should not be able to give a classification of the inhabitants of Glasgow and its suburbs according to their ages at that enumeration in the same manner as in 1821; but upon being informed, in reply, that in that case all the labour he had bestowed upon the parish registers during the ten years then elapsed would be fruitless, he answered, that, notwithstanding the extra trouble, he would prepare fresh schedules, and give the number of the people of each sex in each of the same intervals of age as in 1821, which he did accordingly; and that is the only instance, except the Carlisle enumerations in January 1780 and December 1787, of its having been done in this country.

In the year 1831, Dr. Cleland published, in a folio volume, his Enumeration of the Inhabitants of Glasgow and Lanarkshire, including all the details of his labours above mentioned, and, in 1832, a second edition of nearly twice the bulk; in the first, the bill of mortality for each year of the ten, 1821-1830, is given; but in the second, only those for the first and the last of them.

The following is an extract from the folio volume, (first edition, p. 11.) “From my official situation I am enabled to state, that the books of the church-yard wardens are kept with such perfect accuracy that every reliance may be placed on the number of burials in the city and suburbs.” ∙

Since the year 1834 the Glasgow bills of mortality have been prepared by Henry Paul, Esq. convener of the Committee of Churches and Church-yards, under the superintendence of a committee of the magistrates and town council, with some material improvements upon those of Dr. Cleland. The bill for 1835 contains six tables, besides General Remarks, the principal improvements are in the third and fourth tables, which were not given by Dr. Cleland, in both of them the sexes are always distinguished; in the third, the number of still-born children, and the number of deaths in each interval of age that took place in each month of the year is given separately; and the sum of the monthly numbers shews the same thing in each case for the whole year. But the fourth table, which is still more valuable, shews the number of deaths of each sex in each interval of age, by each of the causes most easily discriminated.

Part of these two bills have been published in the Glasgow newspapers; of that for 1836, in the Scottish Guar [7:15:527] dian of the 3d of February 1837; but only the contents of the first two of the tables above mentioned for that year had been published when this article was put to press, and the author acknowledges his obligations to Mr. Paul for the copies sent him by that gentleman of the papers already published. In these the intention of the council committee is announced, to improve as they proceed, the statements of the diseases by which the deaths were occasioned; also their intention to detail, in the future bills of mortality, the particular trades and professions of those who have died; and to give a table exhibiting the mortality among children from one month up to five years of age, with a statement of the various diseases which have proved fatal at those ages; all of which improvements are very desirable. .

It is much to be regretted that only about one half of the births in Glasgow and its suburbs are registered, also that certain registers in the Barony Parish burying-grounds contain no record of the cause of death. The act passed in 1836, for registering births, deaths, and marriages, extends to England only; and the committee of the city council express their opinion that these defects cannot well be supplied without some legislative enactment.

In the bills of mortality for London, Glasgow, and too many other places, the still-born have been included among the burials, as the numbers are obtained from the burial registers; although, as was observed before, p. 525, col. 1, they never should be, for in that case they are generally included among the deaths in calculating the rate of mortality, in consequence of which, that rate comes out greater than the truth in the ratio of the whole number of the re-gisterial burials to the number interred who had lived and breathed.

The Observations on the Mortality and Physical Management of Children, by Mr. Roberton of Manchester, were published (in 12mo.) in 1827; it is the first part only of that valuable work, namely, the observations on the mortality amongst children, which we have occasion to notice here; and we consider that no gentleman of the medical profession has treated it better, few, if any, so well. Mr. Roberten informs us that no bill of mortality is published in Manchester, and that, before the year 1812, the ages were not entered in the registers. He extracted, with great care, the numbers of deaths under ten years of age from the register of the collegiate church of Manchester, for the term of eight years, 1816-1823; and from the valuable register at the Rush-οlme Road cemetry there, for the term of four years, ended with April 1825. The results he has stated shortly, (p. 19.) with the proportion in each interval of age under ten, to the whole number of deaths in each register; and has given a valuable table, shewing, without distinction of sex, the number of children buried in the Rusholme Road cemetry during the four years 1821-1825, who died under one month old, between one and two, two and three, three and six, six and nine, and between nine and twelve months; also between one and two years, two and three, three and five, and between five and ten years old, with the total under ten; by each of forty-seven different diseases, and twelve other causes separately. The total number of deaths under ten having been 2056, and at all ages 3559∙

We have already stated in the article Annuities, (vol.iii. p. 203,) that Mr. Finlaison’s Report to the Lords of the Treasury, on the mortality among government annuitants in this country, was printed by order of the House of Commons in 1829∙ Government having raised money at different times by the sale of life annuities, either by way of tontines, with benefit of survivorship, or otherwise; a separate register of the nominees or annuitants on whose lives the annuities depended, was on each occasion kept; the name, and consequently the sex, also the age, satisfactorily certified, of each nominee at the time when the annuity commenced, with the day of death, and the age attained, were entered in the register. For each of these classes of nominees generally, but in some instances for two or three of the smaller ones combined, Mr. Finlaison has given a table, showing for each sex, 1. The number enrolled at each age last completed, during the observations; 2. The number alive of each age when the observations terminated; 3. The number who died at each age during the observations; and, 4. The number who passed on from that to the next greater age.

Mr. Finlaison calls each of his tables above mentioned an observation, although each records several thousands of observed facts or occurrences. Of these tables he has given twenty-one, but the recorded facts, which alone we have occasion to notice here, are contained in six only of them, the other fifteen being combinations of two or more of the six, or of selections from them.

These six are the following :—
[table]

In the article Annuities (pp. 202 and 203) we mentioned the desire of the members of the Equitable Assurance Society to ascertain the law of mortality which had obtained among them; and that the late Mr. Morgan, their then actuary, had been able to form a table which had induced him to alter his opinion on the subject; accordingly, in February 1834, the Society printed for the use of the members a folio pamphlet of “Tables showing the total number of persons assured in the Equitable Society, from its commencement in September 1762, to January 1,1829, distinguishing their ages at the time of admission into the Society, and exhibiting the number of years during which they have continued members of it, the periods of life at which their assurances have terminated, and the ages which the surviving membershad attained on the first of January 1829∙ To which are added, Tables of the Probabilities and Expectations of the duration ofhumanlife, deduced from these documents; a statement of disorders (as certified to the Court of Directors) of which 4095 persons assured have died, in thirty-two years, ending December 31, 1832; and a Supplement, showing the mortality of the Society for the years 1829, 1830, 1831, and 1832.” With an introduction by Mr. Arthur Morgan, who succeeded his father as actuary of the Society.

By these documents it appears that, of the persons whose lives were assured in the Society during the period of 66½ years from its commencement, till the end of the year 1828,.
[7:15:528]

The number then surviving and continuing insured, was 6930

The number who went out of the Society during their lives, the assurances on them having been discontinued 9324

Carry forward 16254

Brought forward 16’254

The number who continued assured till death... 5144

And that the total number of lives insured was 21,398

The most valuable of these data are contained in a table, marked A, of the following form, the ages stated being those last completed :—
[table]

The number in each column on the extreme right and left shows the age at which the lives in the horizontal line passing through it were insured; and each large column, with the age written over it, gives in its four subdivisions the information there expressed for each age of admission separately.

1.-The number of lives who attained that over-written age.

2. * How many of them were living of that age when the observations terminated.

3. How many went out of the Society alive, by discontinuance of insurance at that age, during the observations.

4. How many of them died insured during the same time.

And as none of the last three descriptions of lives could have entered into the next greater year of age during the observations, while all the rest of the lives of the first description must have done so; if the sum of the 2d, 3d, and 4th numbers be subtracted from the first, the remainder, being the number who entered on the next greater age, is inserted in the first division of the column for that greater age.

The numbers in each horizontal line of the table always begin with the number admitted during the observations at the age of admission standing on the same line in the marginal columns; and the number admitted is placed in the first division of the column with the same age at its head; from which it necessarily follows that the number of lives insured at any age, is always the last number in the first division of the column with that age written over it. Thus, the numbers admitted of the ages 29, 30, and 31, were 783, 762, and 785 respectively. 785, the number admitted at 31, that is, in the 32dyear of age, is greater than the number admitted at any other age, which shows that to be the time of life at which assurances were most frequently effected in the Equitable Society previous to the year 1829, and may be taken as a proof that they are most generally wanted at that age, although no such inference could be safely drawn from the records of that or any other office, during a period of twenty years or more, commencing with 1829, on account of the great diversity in the rates of premium required for life assurance by different offices, and in the advantages held out by them, since about 1825 or 1830. The numbers admitted at the four ages 29-32, vary but little. The three first are given in the above specimen of the table, that for the age 32 was 780; they decrease gradually on both sides of that interval of age, so that from the commencement of the 30th to the end of the 33d year of age, appears to be the period of life in which most life assurances are applied for; probably also that in which most first marriages of men are contracted in this country.

There are in the table 70 ages of admission, beginning with 7, and ending with 88; but only ten lives were admitted after completing their 67th year. As the greatest age attained by any life assured, and that by one only, was 94 years completed, there are 88 columns with the ages from 7 to 94 written over them, each divided into four.

Thus, it appears, that in this very valuable table, which had long been wanted before it appeared, and is one of the many important benefits derived by the public from the Equitable Assurance Society; the progress of all the 21,398 lives through the different ages from seven to ninety-four, so long as they respectively remained insured, the respective ages at which they entered the society, and at which they went out of it, whether by death or discontinuance of assurance, are distinctly shewn, and the means of determining the law of mortality amongst the lives are given, even for determining it amongst those separately which were admitted at any one age, so far as their limited numbers will allow. Immediately after this, two other tables, undistinguished for reference either by number or letter, are given; the first exhibiting for each of the four divisions of every column with the age set over it, that age standing in the margin of this table on the same line, the sum of the numbers in that division set against all the ages of admission. The numbers in the first column of this table we consider to be of very little importance in comparison with those in the three other columns; they shew the number of observations of each kind obtained in each year of age, and consequently the different degrees of confidence the rates of mortality derived from them at different ages are entitled to. It shews, that between twenty and seventy-four years of age, the number of observations, or of lives passing into, and in whole or in part through each year of age, was always above 1,000; that number increased from the age of seven where it was forty, to the age of forty-three, where it attained its maximum of 7,725, arid then decreased gradually to the age of ninety-four, where there was but one life left which did not reach ninety-five. But the same things were shewn, although not at one view, in table A, where the sum of the numbers in each column standing [7:15:529] against all ages of admission were given; therefore the numbers in that first column might well have been omitted, 'and the number of admissions at each age substituted for them; or if the first were retained, a column for the number admitted at each age should have been added, for then that table would have exhibited at one view, and in small compass, all the data necessary for determining the law of mortality.

The other small table merely gives the same information as the first, not for each year of age separately but for the interval between seven and ten, and then for every interval of five years of age between ten and ninety-five years.

A table marked B differs much from A both in its contents and value; it is stated to shew “the duration of the lives of those persons only who became members of the Equitable Society between September 1762 and January lst 1829, and who either continued their assurances to the latter date or died during the intervening period ;” all those lives the insurances on which were discontinued, having been omitted. But all of those omitted lives were, while insured in the society, subjected to the chances of mortality equally with the others which continued insured till they either survived the period in which the observations were made or became extinct. By the extract given above from table A, it appears that 783 lives were ad-mited at 29 years of age; but that table shews, that of these, 379 went out of the society during the observations by discontinuance of the assurances on them; the remaining 404 only are inserted in table B, as having been exposed to the chances of mortality in that year of age during the observations, and the three deaths which happened in the same year of age, are assumed to have taken place out of 404 instead of 783 persons admitted in the same year of age. The same number, 379 of those admitted at 29 years of age, also went out after the age of 30, which number being taken from 780, leaves 401; 334 of them went out after the age of 31, which, taken from 729, leaves 395; and in this manner table B has been formed from table A. The following extract from table B corresponds with that given above from table A.
[table]

Let us now consider those lives only which were twenty-nine years of age when admitted, and since the number of deaths among them at that and each of the greater ages was the same according to both tables, whilst the number attaining the age 29, 30, 31, was, according to table A, 783, 780, 729,

B, 404, 401, 395, it is manifest that the mortality, at each age according to table B, will be greater than according to table A, in the ratio of the number attaining that age according to table A, to the number attaining the same age according to table B;^[10. Here we omit the deduction shewn in the section on the Law of Mortality to be necessary for the number of lives entering the society remaining insured when the observations terminated, and leaving it by discontinuance of insurance at each age. To make and to explain it here might perplex some readers, and the false views of the subject table B is calculated to give, are here, we trust, sufficiently exposed without it. ] that is, at these three ages nearly in the ratio of two to one. But the younger the lives are at admission the greater is the proportion of them who leave the society by discontinuance of insurance; and after the lapse of eight or ten years from the age of admission, the number of lives which leave the society in that way diminishes rapidly as the age increases, so that the two tables (A and B) approximate closer and closer as old age comes on, and differ but little after sixty.

It is also to be borne in mind that the numbers attaining the age of thirty, and dying of that age, are obtained by taking the sum of all the numbers in the first and last divisions respectively of the column in table A with 30 at its head, from seven, the least age of admission, to the age thirty, the mortality in which is the object of inquiry; and the higher in the column any number is, or the less the age of admission, the longer have the lives then thirty years of age been insured, both in table A and B. Hence it is evident that the error in excess of the mortality according to table B in any year of age (thirty for instance) will not be so great as among those lives only which were admitted at that age. And all that is shewn here, with regard to lives admitted at thirty years of age, and attaining that age, applies equally to those admitted at and attaining to any other age.

Those marked C and D are tables of mortality derived from A and B respectively; and two other tables, marked E and F, shew the expectation of life at every age from ten to ninety-seven years according to tables C and D.

After these a valuable table is given, shewing the number of deaths which took place amongst the persons insured in the society during the term of thirty-two years, 1801— 1832, in each interval of ten years of age from ten to eighty and those above eighty, by each of forty-three different causes, as certified to the Court of Directors. The whole number of deaths during that term was 4,095, of which there were occasioned

By thirty-seven different diseases....3,449 Natural decay of age 566

Childbirth 4

Accidents 40

Suicide 29

Murder 3

Being slain in war 4

4,095

This table shows the comparative numbers of deaths by each disease at different ages, and from different diseases in the same interval of age; but not the rate of mortality from each disease in each interval of age; for this purpose, the annual average number of insured lives existing in the society in such interval of age during that term of thirty-two years is necessary, but unfortunately wanting. Lastly, as a supplement to Table A, a small table is given, showing for the intervals of age between 7 and 10, 90 and 97, and in each interval of 10 years between 10 and 90, the numbers living and dying in each of those intervals of age during each of the four years. Upon comparing the numbers living in the same intervals of age at the end of the year 1828 given in Table A, with those in this supplemental table, we infer that it was at the end of the year placed at the head of the column in this table that the numbers stated in that column were living in those intervals of age. But the only information given on the subject, is the word “Living” placed at the head of the column of numbers.

In the year 1832 was published a compilation in 4to, by Mr. Marshall, entitled, Mortality of the Metropolis, containing the London Bills of Mortality to the year 1830 inclusive[7:15:530]; with various statistical details taken from the enumeration and parish register abstracts of this country, with a few short notices of a similar kind relating to Spain and Portugal, Prussia, the Netherlands and Sweden, but without any distinction of ages, except for Sweden, and even for that population, only the numbers of deaths in the single year 1820, under one year of age, between one and fifteen, and those above fifteen.

Dr. Forbes’s very valuable Sketch of the Medical Topography of the Hundred of Pennith, comprising the district of the Landsend in Cσrnrvall, already quoted in this article, was published in the second and fourth volumes of the “Transactions of the Provincial Medical and Surgical Association,” in the years 1834 and 1836. It is divided into two parts; and it is only the first chapter of the second part, which is contained in the volume of the Transactions published in 1834, that we have occasion to notice here. The progress of the population is first treated of, and the information on that subject is taken from the population abstracts at the four decennial enumerations of 1801-1831; but keeping the mining parishes separate from the agricultural. There are twenty-five small tables; in the first seven, the numbers of marriages, births, and deaths, are given, and compared with those of all England, and with particular parts of it, without noticing the ages of the deceased; but in the eighteen others the number of deaths in each decade of age from birth to a hundred years, and those above a hundred are given. On these Dr. Forbes makes the following observation: “Abstracts of all the registers in the hundred were made by myself, with the utmost attention to accuracy.”

The publication of bills of mortality in Paris commenced during the administration of Colbert, an epoch rendered memorable by so many useful establishments. That great minister proposed to the king to issue an order, that a bill for that city should be printed and published at the end of each month, containing in addition to what is usual elsewhere, the numbers admitted into the hospitals; there were also added short remarks on the character of the seasons, and the principal diseases which had prevailed; with the prices and weights of different kinds of bread, and some other objects of general consumption. The motive of this ordinance was thus expressed: “Estant important au public, pour la santé et pour la subsistance des habitans, d’en con-noistre l’estât en tout tems, et d’observer soigneusement les causes qui augment ou diminue le peuple en chacqun des quartiers de Paris, il sera fait, tous les seconds jours du mois, one feuille qui contiendra le nombre des baptesmes, des mariages et des mortuaires du mois précédent et de chacune des paroisses en particulier.”

This ordinance was attended to for fifteen years, 1670— 1684, but after the death of Colbert, which happened in 1683, it was neglected during twenty-four years, 1685-1708;^[11. As were also those for the three last months of the year 1684; and the bills for 1676 and 1677 are wanting; so that, altogether, there were twenty-seven years from the first publication of the bills, in which their publication was either interrupted or neglected, unless the two missing bills were lost, which is probable. ] the publication of the bills was resumed in 1709, and has been continued ever since, improvements having also been introduced into them from time to time.

This information is taken from a “Mémoire sur la Popu-tion de la ville de Paris depuis la fin du 17 e siècle,” in the second volume of a great and important work printed by the French Government, but not for sale, entitled, Recherches Statistiques sur la ville de Paris et le Département de la Seine; Recueil de Tableaux dressés et réunis dé après les ordres de Monsieur le Comte de Chabrol, conseiller dé état, préfit du département.

The first volume was published in 1821, in small octavo, and contains sixty-three tables; it is stated in the introduction, that lithography was made use of by the administration in the publication of the tables in that volume, to multiply the applications, and to encourage the exercise of that new art; probably this gave occasion to its being used as above mentioned in the large Swedish tables published in 1829∙ Three other volumes of this work have been published in quarto, with all the tables printed by types in the usual way; the use of tables for digesting and presenting the information collected is continued throughout the work, which, as is justly observed, admits of an'immense number of results being brought together, excludes superfluous dissertations, and facilitates all comparisons. Topography, population, institutions, agriculture, manufactures, commerce, and finances; are all minutely detailed in so many separate chapters; but we have only occasion in this article to attend to the population; and on that subject shall notice principally those parts of the work, where the numbers of annual births, and the numbers both of the people and of the annual deaths, with the ages of the living and those at which the deaths took place, are stated.

An enumeration of the inhabitants of Paris was made in February 1817, and in the first volume, where the results of that enumeration are given; there is also given an extract from a report made to the minister of the interior, by the Count de Chabrol, dated the 3d of July 1818, explaining the manner in which it was effected. He states, that attempts had been made on several previous occasions to ascertain the population of Paris by an effectual enumeration; but that different circumstances had contributed to render the results very inaccurate. He gives reasons for which he considers it indispensable to obtain, not only for each house, but for each separate location, a distinct list with the Christian and surname of each person of whatever age, the sex, (shown by the Christian name), the state of celibacy, marriage or widowhood, and the condition, profession, or occupation of each; he explains minutely the measures that were taken to carry this into effect, and the checks used to ensure a great degree of precision. To avoid including the same person twice in the enumeration, the place of residence chosen for that of inscription was the habitation during the night, which rule was always strictly adhered to; to prevent the effects of changes it was desirable to complete the work as quickly as well might be; and in one month and ten days the enumeration of 657,172 persons was made at their places of residence in the manner stated above. This is called nominative enumeration.

But a part of the population from their continual change of place, could not be enumerated so correctly. These were foreigners, or native French subjects then resident in the capital, but without any fixed habitation, travellers, the inmates of twenty-seven hospitals,^[12. Under which term we here include les Hospices et les Hôpiteaux. ] civil and military, of ten prisons, of forty-three military establishments, of six hundred and ninety-two furnished hotels, of divers other establishments, and the persons with regard to whom the information obtained was insufficient; all of these persons are said to be numbered collectively, and no distinction is made either of their ages or sexes.

Of the persons enumerated nominatively, the number of each sex separately in each quinquennial interval of age from birth to thirty years completed, then in each decennial interval to a hundred, and of those above a hundred years of age was given. The whole numbers of them of all ages were these:
[7:15:531]
[table]

the whole population of Paris on the first of March 1817. An attempt was made to class according to their ages the persons who were only enumerated collectively, the ways in which the different estimates were made, are explained, and a table (No. 7.) of their results is given; but we consider them to be so uncertain, that we are not aware of any useful purpose they can be applied to, and therefore take no farther notice of them here.

It is also observed that the number of the living under five years of age, even in the nominative census, was much less than it should have been in consequence of the very great number of children which are sent to be nursed in the neighbouring villages, both by their parents and by public establishments, neither the mean number of them, nor the mean duration of their absence from Paris, could be ascertained, and any estimates that could be made on the subject were so uncertain that it would have been useless to state them.

The nominative census was also deficient in numbers after fifty years of age, on account of the number of aged poor who die in the civil hospitals. The approximations to the ages in these appear to be entitled to more confidence than in the rest of the collective census, and for those within the walls of Paris they are given in column sixth, whilst the numbers of the nominative census at the same ages are given in column seventh of table seven; and by them we find that the numbers were
[table]

From what has been stated above, it will be evident to those who understand the subject, or who read the next article, that this enumeration, although performed with great skill and labour, does not afford the means of determining the law of mortality in Paris, even if we had the most satisfactory accounts of the numbers of births and of the deaths that took place at all ages.

Paris being for municipal purposes divided into twelve districts called arrondissements, distinguished by so many numbers from one to twelve, and each of these into four quarters, Table III. shows for each arrondissement and for each quarter of it (giving also the names of the quarters), the numbers of houses, of families,^[13. The French word is Ménage, and to render family synonymous, we have, we believe, only to extend its meaning to the case of a single person residing and conducting all his or her domestic affairs alone; whether occupying the whole of a house or only a part of it. ] and of persons, that were ascertained by the nominative census to be in it on the first of March 1817; also for each of the six descriptions of persons separately, mentioned above as those who were numbered collectively, how many persons were so numbered in each arrondissement and in each quarter of it. And in the last two columns of that table, the total number of persons in each arrondissement and in each quarter of it on the first of March 1817, is given; but there is no distinction of age or sex in this table.

Table IV. exhibits the number of the living ascertained by the nominative census to be then in each of the fourteen intervals of age above mentioned, with the distinction of sex and condition as to celibacy, marriage, or widowhood; the totals of which, omitting the ages, we have stated above.

Table V. shows for every 10,000 persons in each of the twelve arrondissements, how many were in each of the same intervals of age, but without distinction of sex or condition. The following tables to the tenth inclusive, relating to the numbers and proportions of the people, we do not think necessary to notice here particularly; the whole number of the tables relating to the population and extent of Paris is twelve, numbered from three to twelve, and including two as first and second supplements to table ten.

We now proceed to those parts of the work which exhibit what the French denominate the mouvement, but we call the progress ^[14. î The movement or motion of the population would be the better term if it were admissible in English, as it applies equally whether the number of the people is increasing or decreasing. ] of the population; which is shown by statements of the numbers of annual marriages, births, and deaths, during a series of years, with the ages at which the deaths happened.

The volumes these documents are contained in, and the years in which the events recorded took place, are as follow:
[table]

There are able introductions and memoirs prefixed to all the volumes, which it would not be consistent with the objects of this article to notice further here; except the memoir already mentioned on the progress of the population of Paris during the 17th, 18th, and 19th centuries; which we now resume.

Before 1710 the numbers of foundling infants were, or at least can only now be found, recorded, for the years 1670, 1680, 1690, and 1700; but the publication of the bills of mortality having been resumed in 1709, the number of foundlings was stated in them for 1710, and every following year. The sexes were not distinguished either in the numbers of births, deaths, or foundlings, till the year 1745; after which it was always preserved; it was only from the year 1795 that the numbers of still-born children were recorded separately, and we are not informed whether they were previously included among the births or deaths, or both or neither of them. 1806 was the first year in which the illegitimate children were distinguished from the legitimate; they had previously been put together without distinction. This information is taken from the table in the second volume numbered 53, (and the notes that ac [7:15:532] company it) showing the numbers from the year 1670 to 1821, with the exception of twenty-six years above mentioned necessarily left blank, and another which was defective.

The progress of the population of Paris during each of the ten years 1817—1826, as exhibited in the four volumes above mentioned, is contained in ten tables. In the first six there is no distinction of ages.

The first shows the numbers of births, marriages, and deaths, that took place in each month of the year, without reference to place; and then those which took place in each of the twelve arrondissements of Paris, without reference to the months of the year which they happened in; the sexes being distinguished both in the births and deaths.

The second shows the same things in greater detail; the columns of the first table being subdivided in this, so as to show how many both of the births and deaths took place at home, and how many in the hospitals; also, of each of these two descriptions of births, how many of the children were legitimate and how many illegitimate.

The third is confined to natural children; and with regard to them, the same information is given as to the sexes, and the months and arrondissements in which they were born; but in addition to this, it is shown how many of them were acknowledged at their birth, and how many were not; also how many were acknowledged by celebration of marriage, and how many after birth, before a magistrate.

The fourth shows the number of still-born children of each sex, during each month, and in each arrondissement.

The κ ∕z∕ZΛ shows the number of marriages in each month and in each arrondissement, which were given without further particulars in the first table; but here, the number of marriages in each horizontal line of that table, is shown to consist of four different numbers of so many different kinds of marriages. Thus:
[table]

Hitherto for the sake of perspicuity, we have taken no notice of the rural arrondissements of Saint Denis and Sceaux; but we add them here, to show the way in which the numbers for them are introduced in all the first six tables, after the totals for the city of Paris are obtained; and by adding them to the totals for the city, the grand or general total is also obtained for the whole of the capital, or department of the Seine. The last four of the ten tables relate to the city of Paris only.

The sixth shows the deaths in each month and arrondissement, the same as the first; but each column in the first table is so divided in this, as to show how many of each sex died at home, also how many in the civil, how many in the military hospitals, and how many in prisons. In this and the first table of deaths, the dead bodies deposited at the Morgue within the year, are added to the sum of the deaths both in the different months of the year, and in the different arrondissements within the walls of Paris, to obtain the total number of deaths in the city.

The seventh table we consider as being the most valuable of the ten. It shows, for the city of Paris only, the numbers of deaths in the first and second quarters of the first year of age, also in the last half, consequently in the whole of that year; then in every following year of age separately, to that often years completed; and after that in every interval of five years of age to a hundred, and those above a hundred; always distinguishing the sexes, and showing the numbers who, in each interval of age, died unmarried, married, widowers or widows.

Were it not for the salutary practice of sending children born in Paris into the neighbouring villages to be nursed; as the numbers of births of both sexes are given, and also the numbers of deaths of both sexes separately in minute intervals of age under ten years; the law of mortality among them might be determined, even independent of enumerations of the living. But under the actual circumstances, that very desirable object cannot be attained.

The eighth shows the numbers of violent and accidental deaths, voluntary and involuntary, in each of various ways, which took place in the city of Paris in each month of the year, and in the whole year; the sexes being distinguished in each of the numbers for the whole year, but not for each month.

The ninth shows the number of suicides attempted during the year, in the department of the Seine; the number of those attempted which were effectuated, and the number of them which were prevented; with the means of destruction employed, and the presumed motives of suicide. The sexes are also distinguished, and the married from the unmarried.

The tenth shows the number of deaths from small-pox in each month of the year, and in each arrondissement in the city of Paris, without distinction of age; also the number of them that took place in each of the intervals of age employed in the seventh table, without distinction of months or arrondissements; the sexes being in all these cases distinguished. Then the number of gratuitous vaccinations during the year, in each arrondissement, is shown. The sexes of the vaccinated were distinguished for the years 1817 and 1818, but not afterwards. Each of the two tables here numbered 9 and 10, was, for the years 1817 and 1818, divided into two; so that the number showing the progress of the population in those two years, was twelve instead of ten.

In addition to these, a table numbered 37, in the first volume, is too curious and interesting to be passed unnoticed here. It was formed from extracts made by M Benoiston dè Châteauneuf from the statements of deaths prepared in the mayoralties of the different arrondissements; which statements were founded on the declarations made by the physicians and surgeons who certified the deaths.

The table shows, for each of the four years, 1816—1819, the number of deaths produced in the city of Paris, by each of the following pulmonary diseases: Asthmas, catarrhs, defluxions on the chest (fluxions d e poitrine), and consumptions (phthysies) ; in the spring, summer, autumn, and winter of each year, without distinction of age; but also in each interval of ten years of age from birth to seventy years, between seventy and ninety, and between ninety and a hundred; without distinction of seasons. The total by each of these diseases in each of the four years is also [7:15:533] stated, with the total number of deaths in Paris from all causes during the same year; and the proportion of the mortality from each of those pulmonary diseases to the whole mortality; the sexes being distinguished throughout. No table of that kind, nor of the deaths by other diseases than the small-pox, was inserted in any of the other three volumes. Statements of the annual average progress of the population in each of the arrondissements of Paris during the five years 1817-1821 are given in the third volume, tables 42—50; and for the next following quinquennial period 1822-1826 in the fourth volume, tables 54-62. Table 102 of the second volume shows the comparative riches of the different arrondissements in the city of Paris; it was constructed from the register of personal taxes imposed in the year 1820; that table with the others above mentioned in the first three volumes, were the principal dataon which Μ. Villermé founded his very valuable Mémoire sur la Mortalité en France dans la classe aisée et dans la classe indigente, in the first volume of the Mémoires de f Académie Royale de Médécine, tome i. 1828.

In the introduction to the fourth volume of the Recherches Statistiques it is stated, that a fifth would terminate the work; and a short account is there given of its intended contents; but in May 1837, when this article was printed, that volume had not appeared.

Statements of the progress of population in Paris and in every department of France, are regularly published in the Annuaire du Bureau des Longitudes, also of the population of the different departments, and of their arrondissements and chief towns, but without any notice of the ages. The numbers of deaths in the city of Paris of each sex by the small-pox at the different ages, have also been inserted in the same work, for 1817 and every subsequent year; but not the numbers gratuitously vaccinated.

The ages at which the deaths happened are not given in any of the statements in the Annuaire, except those for the city of Paris.

ín February 1835 was published at Troyes, the capital of the department of the Aube in France, Recueil des principaux travaux des Conseils de Salubrité du département de l’Aube, containing the same kind of information, given in the same manner, but rather more fully respecting the progress of population in Troyes, as is given in the Recherches Statistiques for the city of Paris; except that there is no mention made of still-born children, or of the deaths from small-pox, or of the numbers gratuitously vaccinated.

The statements of the deaths in all the intervals of age, are given not only for each year, but for each month of each of the ten years 1821-1830; also in one table, those in each month during the whole term.

These documents were derived from the bills of mortality by Dr. Patin, president of the council for the arrondissement of Troyes.

The population of the place at the commencement of the term was 25,076, at the end of it 23,749, of whom 10,626 were males, and 13,123 females. The ages of the people do not appear to have been distinguished at either of the two enumerations made at the commencement and at the end of the term; neither are the total numbers of the two sexes who were living at its commencement given separately. So that the law of mortality cannot be determined from the data obtained.

The three following tracts relating to the Netherlands, were all published at Brussels in 8vo:

1. In the year 1827 a Memoir on National Statistics, entitled, Développement des trente et un Tableaux publiés parla Commission de Statistique, et relatifs aux mouvemens de la Population dans lesPays-bas, depuis la création du Royaume jusqu a 1824 inclus; par Edouard Smits, Sécrétaire de la Commission, &c. &c.

The tables shew the numbers of persons on the first of' January 1815, and on the thirty-first of December 1824, residing in the towns, and in the rural communes separately, for each of the nineteen provinces in the kingdom; with the numbers of them for the whole kingdom of the Netherlands taken together. They also show what the number of the people with the same distinction of town and country residence, was on the first of January in each of those ten years; with their mean number during the first and second halves of that period, and during the whole of the same period; but in these numbers of the people there is no distinction made either of age or sex; the number at the end of 1814 is stated (p. 2) to be estimated, and that at the end of each year after it, was found by adding the excess of the births above the deaths in the same year, to the population at the end of the preceding; so that the numbers of the people there stated, are not entitled to much confidence.

The progress of the population is also shewn by statements of the numbers of births, marriages, divorces, and deaths, and the differences between the numbers of births and deaths during each of the ten years for the whole of the kingdom; and for each province during the whole of the ten years, the inhabitants of towns being distinguished from those of the country, and males from females, in all that relates to the numbers of births and deaths. The proportion between the sexes in the numbers both of births and of deaths, and that of the annual births as well as of the annual deaths, and of the difference between them to the whole population, in the towns and the rural communes jointly and separately are given, for the whole term of ten years, the two periods of five years each, and for each year of the whole term.

2. In the same year (1827) Recherches sur la Population les Naissances, les Décès, les Prisons, les Dépôts de Mendicité, éfc. dans le royaume des Pays-Bas, par Μ. A. Quetelet, sécrétaire de la commission de statistique du Brabant-méridional, tye. Μ. Quetelet (p. 2)states the population on the 1st of January 1825, to have been estimated at 5,992,666, which falls short of 6,013,478, stated by Μ. Smits, by 20,812; and that this estimate was founded on two partial enumerations of the people made previously, one under the imperial government, the other about the commencement of the then (in 1827) actual government; and that from these, and the numbers of annual births, the estimate was made in the manner proposed by Laplace.^[15. Théorie Analytique des Probabilités, p. 391, and Essai Philosophique sur les Probabilités, p. 45. It was first adopted by the French government in 1802. ] He states that the data they then (in 1827) had, could only be considered as provisional and wanting rectification. There is little more in this tract that we can properly notice here, as it is chiefly on subjects not within the scope of this article; but the note A at the end, by Μ. Le Baron de Keverberg, contains some good observations on enumerations of the people,

3. In 1832, Recherches sur la reproduction et la mortalité de VHomme aux differens ages, et sur la Population de la Belgique, par MM. A. Quetelet et Ed. Smits, (premier recueil officieD. An enumeration of the people in Belgium was made in November and December of the year 1829, but owing to the partial occupation of the provinces of Limburgand Luxemburg, the information obtained respecting them, especially the latter, was incomplete. The whole number of the people on the 1st of January 1830 was found to be 4,064,209, of whom 998,118 were resident in towns, and 3,066,091 in the rural communes. The people were throughout classed according to their residence in town or country, their sexes, and their state of celibacy, marriage or widowhood.

The authors state (p. 13) that in the tables of enumeration[7:15:534] the ages of the inhabitants were carefully specified; but although we consider this to be of much more importance than any other part of the inquiry, the information they have given on this subject is far from being satisfactory. In every other place of any considerable magnitude where this important and laborious operation has been performed; in Sweden, Spain, Carlisle, Paris, Great Britain, Glasgow, and Philadelphia, a distinct statement of the absolute number of persons found to be in each interval of age at the time of the enumeration has been published; and in some cases, as in those of Carlisle, Paris, and Glasgow, the manner of proceeding and the checks employed to ensure a considerable degree of accuracy have been explained. But in the case of Belgium, all information of this kind has been withheld, and the authors have only given us (p. 16) a table shewing the relative numbers of the people in the different intervals of age. For every million of them it shews for each sex separately, and for each of forty-seven ages from birth to one hundred years inclusive; how many were above that age, and also how many of these were in a state of celibacy, marriage, or widowhood.

Although the professed object of the authors was to treat of the mortality at the different ages of human life, they have given their readers no information whatever as to the ages at which the deaths took place; nothing in the form of bills of mortality, nor any abstracts from them; they merely state that the data from which they formed the table of mortality they have given (p. 36), were carefully collected during three years from the civil registers of the kingdom.

A very valuable memoir, the result of more than two years’ labour, entitled Recherches Historiques et Statistiques sur la Population de Génève, son mouvement annuel et sa longévité, depuis le 16 me siècle jusqu’à nos jours (1549— 1833), by Μ. Edouard Mallet, was read to the Société de Physique et d’Histoire Naturelle of that city on the 18th of November 1834. It is divided into three parts; the first contains all that is known of the population of Geneva, and the successive enumerations of its inhabitants from the sixteenth century to the present time, with some details respecting the extent of the place, its habitations, its climate, and the industry of its inhabitants. The second exhibits the progress of the population from the commencement of the registers in Geneva, in December 1549, to the restoration of the republic at the end of December 1833, a period of 164 years, especially the meritorious but hitherto unpublished labours of Drs. Cramer and Joly; the progress of the population is given year by year, viz. for the deaths from 1549, for the marriages and births from 1693; and some theoretical inferences are drawn respecting the different elements of this population, the continual increase of its longevity and decrease of its fecundity. The third part presents the detailed results of the progress of population in Geneva during the twenty years 1814-1833, from the restoration to the end of the latter year. The necessary length of this memoir prevented the whole of it being published in the second part of the seventh volume of those above mentioned; he therefore gave in that place the third part of it only, but not even that without omitting an explanation of the steps he took in making, himself, extracts from the registers, to render them available for useful purposes. This third part being the result of his own labour, and containing new facts and discussions relative to the progress of the population during that term of twenty years, 1814-1833.

The above is nearly a literal translation of the short preface to that part; although read to the society in November 1834, it was not published till the end of the year 1836; and the whole of the memoir, including what was omitted in the first publication of the third part was inserted in the Annales d ’ Hygiène Publique, No. 33, (being tome xvii. prem. partie^) which appeared in January 1837-

M. Mallet shews, that at a remote period the legislature of Geneva considered an exact knowledge of the population of the city a matter of importance, and he has given it at nine different periods of enumeration; the first in the year 1589, when it was 13,000, the last in 1834, when it was 27,177, of whom 12,573 were males and 14,604 females; at the same time the population of the suburbs was 9052. In these enumerations the administration took no account of the numbers of locations or of families, nor of the proportions of the people in the states of celibacy, marriage or widowhood; neither do they appear to have taken any account of the ages of the people at any of the enumerations, which is much to be regretted, as that information would have greatly enhanced the value both of the enumerations and of the extracts from the registers of births, deaths and marriages; it would have enabled us to determine the law of mortality in Geneva, which has not yet been done, although repeatedly attempted and thought to have been effected satisfactorily.

The deaths are certified by a visiting surgeon, who gives an account of them every week to the hospital where the civil registers are kept; and it is from his statements that the general mortuary registers are formed. The births, marriages and deaths that take place in the suburbs are entered in the registers with those of the city till 1791 for the marriages and births, and till 1805 for the deaths. Since 1799 for the marriages, and since 1806 for the births and deaths, those only for the population of Geneva within the walls are stated. The population of the suburbs has seldom been ascertained or stated with that of the city. In the registers of births and deaths the sexes are always distinguished; the abortive and still-born are stated separately; but before the year 1814, at which period Μ. Mallet took up the bills twenty years afterwards, as in too many other bills of mortality, they were also added to the number of deaths, properly so called, which took place among the living, and were therefore likely to be included among them by incautious or unskilful persons in calculating the rate of mortality.

The mortuary registers of Geneva, as Μ. Mallet remarks, have been the object of a great and laborious work, which the celebrated economist Μ. D’Ivernois has lately discovered by chance.^[16. The author of this article happened accidentally to contribute to this. In his letter of the 20th March 1834, to Sir Francis D’Ivernois, he requested information respecting the extracts from the mortuary registers of Geneva made by the late Dr. Cramer, which Μ. Duvillard, in his work on small-pox and vaccination, stated were communicated to him by Dr. Butini; also respecting the labours and publications of Dr. Odier, and others there mentioned, p. 105. In answer, Μ. D’Ivernois was so obliging as to favour him with three letters dated respectively the 2d and 16th of April, and the 17th of May of that year, with satisfactory information as to where the publications of Dr. Odier on the subject are to be found. In the first is the following passage: “Quant aux ouvrages, ou plutôt aux notes du Dr. Cramer ce n’étaient que des notes manuscrites qu’il laissa à sa mort à son ami le Dr. Butini lequel les communiqua dans le temps à Μ. Duvillard·” In the second; “J’en profite aussi pour vous remercie d’une découverte bien précieuse que vous m’avez fait faire en me demandant les ouvrages du Dr. Cramer, son petit neveu le C. Cramer, vient de découvrir dans les papiers de famille un manuscrit qui est sûrement sans parallèle nulle part, rien moins que près de 200 tables de mortalité tenues année par année, et avec une exactitude remarquable pour Génève ville depuis l’origine denos registers jusqu’ en 1768.” The third was accompanied by a printed half-sheet, in 8vo, being Proposition de Μ. D’Ivernois, lu au Counseil Représentatif dans la séance du lundi 12 Mai 1834, in which he mentions the results of Dr. Cramer’s labours as “consigné dans un manuscrit qu’un heureux hazard m’a fait découvrir depuis quelques semaines sculment.” That third letter commences thus; “Voici un discours dont je vous dois Thommage car le première idée m’en est venue à la suite des renseignmens que vous m’aviez demandés sur le Dr. Cramer, et qui m’ont fait découvrir dans la poussière d’une grenier le recueil non interrompu de 200 tables de mortalité pour Génève. Il m’a paru mériter d’être mis en evidence. Mais voilà tout ce que je puis vous envoyer des oeuvres de ce modeste ecrivain.” We perfectly agree with Μ. Mallet in the opinion expressed by him in a note supporting it, from which the following is extracted: “Le travail de Μ. Cramer a été attribué à Μ. Odier par divers auteurs, MM. Prévost, Serre, D’Ivernois, Lombard. Pour rendre à chacun ce qui lui est dû, je dois dire qu’il est démontré à mes yeux, que le relevé mortuaire de 1560 à 1760, appartient en propre a Μ. Cramer. Le beau manuscrit qui le renferme est tout entier de la main de Μ. Cramer, comme je m’en suis assuré en le comparant à la signature du docteur, dans la registre de la faculté de médécine de Génève. A l’epoque où s’arrête les tables de recapitulation de Μ. Cramer en 1760, Μ. Odier n’avoit encore que 12 ans.” ] This work, the fruit of immense researches in the old registers, for a period reaching so far back as the [7:15:535] year 1549, and which,'from 1560, when their representation of the progress of the population became regular, to the year 1760, contains no less than 115,777 deaths classed according to the ages at which they happened, was performed by Dr. Jean-Antoine Cramer. Periodical recapitulations and general tables give the results to the year 1760; Dr. Cramer continued the bills of mortality from that year till his death in 1775, and left then a continuation of them to the year 1770 inclusive. It was only from the year 1560 that the ages of the deceased were stated in the registers, and they were omitted during the twelve years 1568-1579, as were also those of 1648 individuals who died of the plague in 1615 and 1616.

Dr. Abraliam Joly continued the inquiries of Dr. Cramer in the same manner during forty-one years, 1771-1811, and died himself in 1812.

Dr. Louis Odier published, in the Journal de Geneve, for 9th July 1791, and in the Bibliothèque Britannique, for 1797, a General view of the Mortality at Geneva, which is nothing more than an abridged reproduction of Dr. Cramer’s tables, but unfortunately left it to be inferred that they were the results of his own labours, and that was the impression produced.

But the most important work of Μ. Odier was a continuation of the labours of Μ. Cramer for the last forty years, 1761-1800, of the last century, and the first thirteen (1801- 1813) of the present.

The other authors who have laboured in the same field of research, besides Μ. Mallet himself, are MM. De Candolle-Boissier, Serre, Dr. H. Lombard, Μ. Heyer.

Among many other useful and interesting tables, Μ. Mallet gives one which shews the progress of the population by giving the number of births, marriages, and deaths for each year, from 1549 to 1813, both inclusive, in the second part of his work; those for the next following period of twenty years in the third part.

We have here given a very imperfect account of this able memoir, which we consider highly creditable to the author’s judgment and taste; almost all we have taken from it here is nearly literal translation, as we felt that we could hardly do otherwise without doing worse. Those who take interest in the subject will no doubt refer to the original, which, by being printed in the Annales de Hygiene, is easily accessible. We had gotten together the materials for a more lengthened notice of the labours of Μ. Odier, gathered from the Bibliothèque Britannique, but the opportune appearance of Μ. Mallet’s memoir induces us rather to refer to it

In Μ. Mallet’s account of his own inquiries into the state of the population and mortality during the twenty years 1814-1833, we have the fullest information on every point, in the same manner and to the same extent for Geneva, as it has been given for Paris, in the Recherches Statistiques; but whilst these are generally confined to mere tabular statements of numbers and their proportions, with as few observations on them as can well be avoided; Μ. Mallet accompanies his tables with observations, reasonings, references to other authors, and the results of calculations very clearly stated, that greatly increase their value. As instances of the way in which he shows the uses of his tables, and assists his readers in drawing inferences from them, which will become much more interesting and instructive by being compared with those drawn in the same way from other tables of a similar kind; we give the two following statements: after a table showing the numbers of births of males and females separately, in each of the twenty years, and for the whole term; also distinguishing the legitimate from the illegitimate, he gives the following Proportion of the sexes.
[table]

Μ. Mallet justly observes, that the proportion of boys to girls in the births at Geneva, is high in comparison with other places, and higher there in the present than in the last century, when Μ. Cramer estimated it to be 18: 17; whilst in France since the restoration, it has been 17: 16. He also states, that “Μ. Poisson a fait remarquer qu’il y a dans la proportion des sexes une différence notable entre les enfans légitimes et les naturels: chez ceux-ci, les naissances des filles se rapprochent plus de celles des garçons que chez ceux-la. Μ. le Professor Prévost a même donné one explication, si non tout-à-fait satisfaisante, du moins très-ingénieuse de ce phénomène. La plus grande proportion des mâles dans les naissances légitimes n’est nulle part plus frappante qu’ à Génève. En effet, on trouve:
[table]

Μ. Mourgue, however, had stated the numbers, of births of both sexes separately, with distinction of the legitimate from the illegitimate, in the first part of his valuable memoir on the progress of population in Montpellier, published in the Mem. de la Soe. Roy. de Médecine, ann 1780 et 1781; and the whole of the memoir was read at a meeting of the French National Institute as above mentioned in 1795; but he made no remark on the difference in the proportion of the sexes between the legitimate and illegitimate births. Mr. Milne in his Treatise on Annuities, published in 1815, (article 789) has stated the proportion or the sexes at birth for several places at different times and under various circumstances; with distinction of the legitimate from the illegitimate in Sweden and Finland, and in Montpellier; he also there expressed his opinion, confirmed by subsequent observations, that the difference depends principally upon the age of the parents; the younger the parents, the nearer the proportion of the numbers of their male and female children at birth approaching to equality. What the connexion is, between the cause and effect, is a curious and interesting problem, which has not yet been solved that we are aware of.

In Wales the pressure of the population upon the means of subsistence in a way suited to the wants and habits o. the people, is such as, notwithstanding their great disparity in civilization and refinement, to produce great similarity [7:15:536] between the inhabitants of the principality and those of Geneve intra muros, in the proportion of the annual marriages to the population, and of the sexes at birth; which Μ. Mallet appears not to have been aware of. Whence we infer a similar resemblance in the advanced age of marriage, and the small average number of children to a marriage (in Geneva during these 20 years 2∣); the very defective state of the British registers of births rendering them of no use in this inquiry, except in determining the proportion of the sexes at birth, for which they may be used, as, however defective these registers may be, there is no reason to suppose they are more so for one sex than the other.
[table]

Dr. Casper’s Contribution to Medical Statistics, ^[17. Beitrage sur medecinischen Statistik und staatsarzncikunde∙ ] was published at Berlin in 8vo in 1825; it is divided into three parts: the first treats of suicide and its increase in our time; the second, of the poor and of the sick poor in Paris; the third, of the mortality among children in Berlin. The' last part contains a variety of tables shewing the numbers of births in different years, distinguishing the legitimate from the illegitimate, and of the deaths that took place among them under fifteen years of age. The numbers of deaths by small pox, and a few other diseases of children, (but not each of those others separately,) both before and after the introduction of vaccination, are given; but no mention is made of their ages, and we need not notice them farther here.

A second volume by the same author was published at Berlin in 8vo in 1835 with two title pages, one being the same as that of the work above mentioned, published ten years before, with the addition of “vol. ii. ;” the other, An Inquiry into the probable Duration of Human Life amongst different classes of the people. ^[18. Die wahrscheinliche Lebensdauer des Menschen, in den verschiedenen bürgerlichen und geselligen verhaltnissen, nach ihren bedingun-gen und hemmnissen untersucht vom Dr. J. L. Casper. ]

The second volume contains a great many tables in the text, and seventeen at the end; most of them copied from other works, but some that appear to be original; of which, those most material to notice here, are, 1st. The number of deaths in every year of age, from birth to 104 years completed, of males and females separately, which took place in Berlin during the twelve years 1818-1829, amounting to 36,895 males, and 32,467 females, of both sexes 69,362; these are given in his table of mortality for Berlin at the end of the work, numbered II. 2d. A table given in the text, (p. 106), showing the number of deaths that took place in Hamburg during the seven years 1819-1825, without distinction of sex, in the first and second years of age separately, then those between 2 and 5 and between 5 and 10; after that in every decade of age from 10 to 90, and those above 90 years of age. But the numbers of the people in the different intervals of age not being given in either of those cases, any tables of mortality constructed from the numbers of deaths alone, at the different ages, can be of no value.

In vol. i. part 1, of The Transactions of the Statistical Society of London, recently published, there is A statistical view of the births and deaths in the Prussian States, during the fifteen years 1820-1834, translated from the German of Μ. Hoffman, Director of the Statistical Bureau in Berlin, the numbers of births and deaths, with distinction of the sexes, and the mean number of the people without that distinction during that term of fifteen years are given; also the number of deaths during the same term, with distinction of the sexes, between birth and one year of age completed, between 1 and 3, 3 and 5, 5 and 7, 7 and 10, and then in each quinquennial interval of age to 90, and those above 90. But the intervals of age into which the people were distributed in the Prussian enumerations appear never to have been sufficiently minute to admit of their being available for determining the law of mortality. There is a good deal of interesting information in this paper; but the above is all we can with propriety notice here; especially as the translation must be easily accessible to most of our readers; and throughout this article it has been our object to give the most minute accounts of such interesting publications as, to many readers, may be difficult of access; that those who take interest in them may see whether it may be worth their while to procure the perusal of them; and also to assist others in perfecting similar labours which they may be engaged in.

. In the first volume (which is statisticaD of the work of the Baron of Sedlitz, On the power of the Prussian Monarchy under Frederic William III. ^[19. Die Staatskrafte der Preussischen Monarchie under Friedrich Wilhelm III. l ster band. Berlin, 8vo, 1828. ] there is given (p. 284) for each of the seven years 1816-1822, including the military but excluding the inhabitants of Neufchatel, the number of inhabitants of the kingdom, the number of marriages, the whole number of births, and the number of illegitimate births separately, also the number of deaths; but without distinction of age or sex. He also gives the number of inhabitants for two of these years under 14 years of age, between 14 and 60, and above 60, which, how ever, are included in the statistical view of Μ. Hoffman.

One of the best bills of mortality we have seen, is prepared by the Board of Health at Hamburg, and published under the name of a Table of Mortality, covering all the four sides of a large folio sheet; and consist in fact of five tables regularly numbered.

I. The first shows the total number of interments and the daily average number, also the total number that took place at each of fifteen different burying places, during each month of the year separately, and during the whole year; without distinction of age or sex.

II. The second shows the same during each month for the abortive and still-born separately; then the deaths properly so called, which took place amongst the living, during each of the four quarters of the first year of age, in the second year, between the ages of 2 and 5, and of 5 and 10 years, then in each decade of age to 100, and those above 100; with the total for each month and for the whole year, of each sex separately, and for both sexes without distinction. There is also a column set apart for those whose ages were not known.

III. The third table consists of two parts, both of which are abstracts from the second; the first showing for each month the number of the abortive and still-born, and also of the deaths under and above ten years of age. The second, [7:15:537] besides the number of abortive and still-born, shows the number of deaths in each of the above-mentioned intervals of age. The sexes are distinguished throughout.

IV. The fourth table, besides the abortive and still-born, shows the number of deaths of each sex, and of both without distinction, that took place within the year, both under and above ten years of age, by about eighty different causes, besides those by suicide in various ways, and other violent deaths.

V. The fifth table shows the number of children born in each month of the year, and during the whole year, both alive and dead at birth, with distinction of the sexes of those born alive, but not of the others; that, however, is given for them both in the 2d and 3d tables; the'number of twin and triple births are also stated in separate columns.

The only fault we see in this bill of mortality, which, in in other respects, may well serve as a pattern for others, is the most improper practice of including the abortive and still-born children in the totals both of the births and the deaths; they should always be stated, but kept separate, both from those born alive, and from the deaths that took place among the living. The distinction of the legitimate from the illegitimate births with that of their sexes, would also be an improvement, if it could well be made; but we consider it to be much more curious than useful. The author is only in possession of one of these Hamburgh bills, which is for the year 1836. The totals were as follow:
[table]

No attentive reader can fail to be struck with the difference (so ill understood) in the proportion of the sexes among the three kinds of births; those born alive, the stillborn, and the abortions. This bill is but for a single year, but the same kind of difference prevails generally; and can hardly be contemplated by a philosophical mind without exciting curiosity and the desire of further information as to the difference between the sexes, first, in the difficulty of fully entèring upon life, and afterwards in retaining it, more strongly marked, as we approach nearer to the period of conception.

In October 1836 appeared, in the 32d number of Annales d ’ Hygiene (tome xvi. part 2), Considérations Statistiques sur le Royaume de Naples, addressed to the Roval Institute of France by Dr. Salvatore de Renzi, in which he shews why the population of the kingdom, and consequently the rate of mortality among the people, could not be determined previous to the year 1818. He gives four tables. The first shews for each of the sixteen years 1818-1833, the number of the people, and the numbers of births and deaths which took place among them, in each of the fifteen provinces of the kingdom separately, without distinction of the sexes, and without including Sicily, being able, he states, to assure his readers of their exactness and precision during that period being incontestible.

The number of inhabitants in 1818 was 4,990,380, and at the end of 1833 it was 5,883,273. In his second table, he gives for each of the provinces, and for the whole of the kingdom, the proportions of the annual average numbers of births and of deaths to the number of the people. The following are a few of them :—
[table]

Μ. set against a number denotes that the mortality or fecundity is there a maximum, and m. that it is a minimum, not of those above mentioned only, but of all the provinces in the kingdom. The third table shews in what proportions 1000 inhabitants, and the fourth in what proportions 1000 deaths were, in each province separately, and in the whole kingdom taken together, distributed into the following intervals of age :—between birth and one year completed, between 1 and 8, 8 and 19, 19 and 26, 26 and 41, and those above 41 years of age.

A bill of mortality is published annually for the city of Naples, which contains most of the information contained in other bills of that kind; but is defective in one important point, the statement of the ages at which the deaths took place, those of the inhabitants are not even mentioned, which indeed is too common elsewhere. It states the number of the people at the end of the year it reports upon, and also at the end of the preceding year. The sexes are always distinguished in the enumerations of the people, as well as in the births and deaths; the legitimate are also distinguished from the illegitimate births; the number of twin births, with the sexes, are stated, and how many of them were pairs of boys, how many of girls, also how many of the pairs were children of different sexes; as was also done by Μ. Mallet and Μ. Hoffman, in their statements for Geneva and the Prussian states respectively.

The numbers of immigrants into and emigrants from the city, are stated, distinguishing native Neapolitan subjects from those of foreign states; the number of marriages contracted is given, but without any information as to the ages or previous conditions of the contracting parties. The number of deaths at home, and those in the hospitals and other public establishments are stated separately. The proportions also are always stated: as of the births, deaths, and marriages to the population, and of the annual births to the contemporaneous annual marriages, but not minutely; they are expressed in vulgar fractions, instead of decimals, haring always the same denominator, as 100 or 1000, which is a great fault. No information is given as to the ages of the people, and the deaths are only stated in the following intervals of age :—between birth and 1 year completed, between 1 and 11, between Hand 18, 18 and 26, 26 and 41, and those above 41. The only bill for the city of Naples in the author’s possession is for the year 1822; it was inserted in the Giornale del Regno dclle due Sieilie, of the 8th of February 1823. The population at the end of 1822 was 344,716, of whom 163,059 were males, and 181,657 females; at the end of 1821 the number of inhabitants was 341,143. The total number of births in 1822 was 14,233; of deaths, 12,195. The number of deaths in 1822 at ages above 100 years, was 17, and of the deceased 6 were males, and 11 females; the names, residences, and ages of them all are stated; they were all citizens of Naples but three, who came respectively from Procida, Salerno, and Venice, which last, Rosa Romanzo, was the oldest of all, having attained[7:15:538] the age of 107; three other ladies attained each to the age of 104.

In the same Journal, for the 23d of April 1823, a bill of mortality for the city of Palermo during the year 1822, compiled by Dr. Francesco Calcagni, is given. The number of inhabitants at the end of 1821 is stated to have been 160,051, and at the end of 1822, 161,735; but this last was derived from the first number, only by adding to it the excess of the births above the deaths during the year 1822. No useful information is given as to the ages of the deceased, and this bill is in other respects inferior to that for Naples; it differs from that, and all others we have seen, in tracing persons born out of wedlock to their graves, whatever age they may attain, and distinguishing the legitimate from the illegitimate in the numbers of deaths as well as of births. In 1822 the number of deaths of the legitimate was 4476, of whom 2294 were males, and 2182 females; that of the bastards, as they are called, was 418, of whom 151 were males, and 267 females. Of the illegitimate children born in that particular year, 256 were boys, and 307 girls. Out of the 4894 deaths, 16 of the deceased are stated to have attained ages from 97 to 105 years; but no information is given as to the distribution of those 16 persons into or among those last nine years of age.

For these two Italian bills of mortality, the author is indebted to Mr. W. R. Hamilton, who was so good as to send them to him from Naples, when they were published; and he is happy to avail himself of this opportunity to acknowledge his obligations to that gentleman, for the facilities he has afforded him of procuring information from abroad on other occasions.

Of all the statements derived from bills of mortality and enumerations of the people, which we have mentioned, only those for Sweden and Finland, Dr. Heysham’s for Carlisle, and Dr. Cleland’s for Glasgow, have been given in the proper form, and with sufficient correctness to afford the information, which is the most important object of them all, viz., that which is necessary for determining the law of mortality.

To effect this, it is only necessary to know the mean number of the living and of the annual deaths, in sufficiently small intervals of age, throughout the extent of life, for a period of time sufficient to allow of the accidental fluctuations arising from more or less fruitful years, and other causes, compensating each other: such periods, probably, should not be less than eight or ten years; but the necessary length will depend upon the climate, the number of the people, their general modes of life, and their political circumstances.

These data being obtained, it is not difficult to determine the proportion of the annual deaths to the number of the living in each year of age. Then, assuming any number of births, as 1000 or 10,000, it is easy to show how many would die in each year of their age; and, consequently, how many would survive that year; which numbers of survivors and of annual deaths, when arranged in the order of the ages, constitute the desired table of mortality, by which all the most important questions respecting the duration of human life may be easily resolved.

For want of understanding the principles upon which the proper construction of such tables depends, most of the writers on this subject, many of them men of great merit and industry, have taken much pains to little purpose, and after excessive labour, have arrived at false conclusions. Hardly any of them appear to have been aware of the necessity of obtaining the number of the living, as well as of the annual deaths in each interval of age, or that that would greatly enhance the value of Bills of Mortality, by extending their useful applications.

Dr. Price’s Essays on the proper Method of constructing Tables of Mortality, already mentioned in this article, was intended to show how such tables might be constructed from registers of the deaths only at all ages; but the hypotheses he proceeded upon can hardly obtain in any real case; and even if they did, his method would only determine the number of the living in the place, at every age; therefore, if it could be put in practice (which it never can), it would only supersede the necessity of actual enumerations; and, with the numbers so obtained, we should have to proceed as above.

That Essay of Dr. Price was an amplification of what Mr. Simpson had previously advanced on the subject, with his accustomed accuracy, and contains many just observations on the defects of the tables of mortality that had previously been published; but so far as it contributed to induce a belief that the determination of the number of the living in every interval of age, by actual enumeration, was not necessary to the construction of accurate tables, it must have done harm.

What is here stated will be found demonstrated in the third chapter of Mr. Milne’s Treatise on Annuities.

It is desirable that a bill should be published for each year separately, to show how the rates both of mortality and fecundity, vary with the circumstances of the people in different years; and, from these yearly bills, nothing is more easy than to derive others for longer periods.

According to the form A, the births of both sexes in each year will be distinguished, and the born alive from the stillborn; the number of marriages will also be given.

In this, and all other cases where those who undertake the formation of such bills are either unable or unwilling to distinguish all the particulars indicated, the reasons for the omissions should be inserted-in the spaces set apart for the numbers omitted. The number of still-born children should always be stated separately, and should never be included in the number either of the births or deaths with those who had lived and breathed.

The numbers of deaths of the two sexes in each interval of age, during any year, may, as they are collected from the registers, be conveniently disposed according to the form B; the intervals between five years of age and an hundred, being each five years; and the number dying at each age above an hundred should be particularly specified.

But some persons, who would not take the trouble of forming bills of mortality in which the ages are to be so minutely distinguished, might yet be willing to furnish them with the requisite care, according to the form ♭, which might ⅞till be very useful; and, indeed, from twenty to sixty years of age, intervals of ten years each might do very well.

The value of Bills of Mortality would be greatly enhanced, by inserting in them the contemporaneous wages of labourers in agriculture, and of the workmen employed in the more common kinds of trade and manufacture carried on among the people they relate to; also the prices of the necessaries of life which persons of these descriptions consume the most of; together with any thing uncommon in the seasons or the crops, and every material change in the circumstances of the people.

Enumerations.

The number of the people in the several intervals of age, which we have stated above to be of so much importance, may be disposed in tables exactly similar to B or ♭, recommended for the deaths; but it is not necessary that the duration of life should be divided into the same intervals for the living as the dead. It is always desirable that the intervals should, in both cases, be small; but yet not so small, as, by the increase of labour, to occasion the numbers being determined with less exactness, or to deter many from engaging in the work. Such intervals should not, however, exceed ten years.

When the bills are given for a certain period, if there be [7:15:539] but one enumeration of the people, it should be made at the middle of the period; if two, at its extremities; and if more than two, it is desirable that they should be made at equal intervals of time throughout the period.

We give no forms here of Bills of Mortality and Fecundity, designed to distinguish legitimate from illegitimate children, or the mortality or fecundity of each month of the year, nor the number of women delivered annually at the different periods of life, nor the diseases the deaths were occasioned by. Neither are the forms here recommended for enumerations of the people, calculated to distinguish the numbers in the different states of childhood, celibacy, marriage, or widowhood; nor the ranks, or professions, or occupations of the people. All these things are curious, and of some use, although, if we except the diseases which the deaths of each sex at the different ages were occasioned by, they are of little value in comparison with the information the forms here given are calculated to convey. And it is of so much importance that that information should be given correctly, that we would willingly forego these minor objects, to avoid dividing and fatiguing the attention of those who undertake the more important part of the task, which is of itself sufficiently laborious.

And those who may be disposed to keep registers, and form bills and enumerations, on a scale so much extended as to include all these particulars, or most of them, and have also the requisite qualifications, will find no great difficulty in preparing the most convenient forms of tables for the purpose. Several forms of that description, with references toothers, will be found in Mr. Milne’s Treatise on Annuities, and in many other works referred to in this article.

A.
[table]

B.
[table]

b.
[table]

The first, second, and fourth of the following tables are good examples of that kind; but for insertion of the deaths of children, we prefer the intervals of age between one and two, and between two and five, to those used in the Swedish tables, viz. between one and three, and between three and five; because the greatest mortality prevails at the earliest ages; and that from small-pox is greatest in the first year of age, while the mortality from measles is greatest in the second year. It is, therefore, desirable to have the means of comparing the rates of mortality in the first and second year of age in registers kept both before and after the prevalence of vaccination.

Information on the diseases and mortality of children is highly desirable; and as their ages at death can generally be stated correctly, if accurate registers were kept of the numbers born alive, and of the numbers of annual deaths at all ages, with the causes of them, the rate of mortality amongst children at every age might thence be determined, and even that produced by each of the principal diseases at each age. It will be seen by our account of the Parisian Recherches Statistiques, or by the Annuaire du Bureau des Longitudes, that the numbers of deaths of children are given for Paris in much more minute intervals of age than is usual in this country; and by the Jaarboekje of Μ. R. Lobatto, published at the Hague, that for Amsterdam, and also by the Annuaire de l’ Observatoire de Bruxelles, by Μ. A. Quetelet, that for that city, they are given in intervals of age still more minute than for Paris. This indeed is the case for more advanced ages, but we consider it as being there of less importance.

The expression we have adopted of the interval of age in which any lives were prolonged, or in which any deaths took place, we consider as at once the most simple and free from ambiguity; yet it has been stated to be ambiguous, an opinion which we conceive can only be held by those who do not clearly comprehend the exact import of the expression. We therefore trust we shall be excused for giving an explanation here, of what we thought could have required none.

The age of every individual being the time that has elapsed since the moment of birth, is at that moment nothing; we therefore express it by 0; and whatever portion we assume for the unit of time, whether an hour, a day, week, month, or year, the age at the expiration of that time from birth will be exactly one such portion; and all individuals of a less age than that, may be properly stated to be between the ages of 0 and 1. Except in infancy, one year is generally taken for the unit of age; a man at the moment of the 25th anniversary of his birth, is precisely 25 years of age, and until the 26th anniversary, he is between the ages of 25 and 26, or, in other words, in his 26th year; although, it being sufficient for common purposes, he is usually stated to be 25 years of age till he attains 26. At the 30th anniversary of the moment of birth, he will be precisely 30 years of age, but cannot continue of that or any other age during any assignable portion of time, however small. So that at the moment a man is enumerated amongst the living, or dies, the probability of his being precisely of any one age that can be expressed by a whole number of years, is infinitely small; and he may always with the greatest strictness and propriety be stated to be between two such ages. Thus, in the case last mentioned, of a man who has attained the 25th anniversary of his birth but not the 30th, he may be properly stated to be between the ages of 25 and 30.
[7:15:540]

TABLE I.

Showing the number of the people in Sweden who were in each of the under mentioned intervals of age, at the end of each of the four years, 1805, 1810, 1820, and 1830.
[table]
[table]
[7:15:541]

TABLE II.

Shewing the annual average number of deaths that took place in each of the undermentioned intervals of age in Sweden during each of the f lve quinquennial periods undermentioned.
[table]

Μ. Leyonmarck observes that “the mortality during the five years, 1806—1810, was greater than it is stated in this table, owing to the lists of those who died in the service during the war, not having been so accurately made out as they ought to have been.

In the table sent to the author, from which the above has been copied, the average number of each sex in each interval of age was given in years and tenth parts of a year; and that given here in each case is the nearest whole number, whether greater or less; the difference is obviously of no importance.
[7:15:542]

TABLE III.

Shewing the number of Deaths that took place in Sweden from each of the causes, and in each of the years under mentioned.
[table]
[7:15:543]
[table]

In the copy received by the writer of this article, the deaths from ardent spirits were put between the drowned and the other casualties; and the diseases were not arranged in the order in which they stand here.
[7:15:544]

TABLE IV.

Shewing the number of Persons who died in the Kingdom of Norway in each of the undermentioned intervals of age during the term of Nine years which commenced with 1824, and ended with 1833.
[table]

II.—MORTALITY, LAW OF.

The Law of Human Mortality is that which determines the proportion of the number of persons who die in any assigned period of life, or interval of age, out of a given number of persons who enter upon the same interval; and, consequently, the proportion of them who survive that interval.

Tables showing how many out of a great number of children, as 10,000, or 100,000, born alive, die in each year of their age; and, consequently, how many complete each year; exhibit this law through the whole extent of life, and are called Tables of Mortality.

This section is divided into three parts. In the first, we deliver the history of this branch of knowledge, with as much brevity as appears to be consistent with the chief object, which is that of conveying correct and useful information.

In the second part, we demonstrate the whole theory by common arithmetic.

In the third part, a new table of mortality is given, constructed on the principles previously explained; some observations are made on the comparative merits of the different tables that have been published; which were purposely omitted in the historical part, when the tables they relate to were mentioned, to avoid discouraging such readers as might not be previously acquainted with the theory; and the faults are explained, which render most of those tables really of no use, since others, more correct, have been constructed.

Part I.— History.

The first table of mortality was constructed by Dr. Halley, from the Mortuary Registers of Breslau, for five years ending with 1691; and was inserted in his paper on the subject in the Philosophical Transactions for the year 1693, with many judicious observations on the useful purposes to which such tables may be applied.

No further information of this kind was communicated to the public, until William Kersseboom of the Hague published there three tracts on the subject (in 4to.) The first, dated March 1, 1738, was entitled, Eerste Verhandeling tot cen Proeve om to weeten de probable menigte des volks in de provintie van Hollandt en Westvrieslandt. The second, dated May 15, 1742, Tweede Verhandeling befestigende de Proeve om to weeten de probable menigte des volks in de provintie van Hollandt en Westvrieslandt ; and the third, dated August 31, 1742, Derde Verhandeling aver de probable meenigte des volks in de provintie van Hollandt en Westvrieslandt.

A good account of the first of these tracts has been given by Mr. Eames, in the Philosophical Transactions for 1738; and rather 'a meagre one of the other two, by Mr. Van Rixtel, in the same Transactions for 1743. It is therefore unnecessary to repeat here, any thing contained in those accounts; but as they give no satisfactory information concerning the construction of Mr. Kersseboom’s table of mortality (which he called a Table of Vitality), it will be pro per to supply so material a defect in this place.

In his first tract, the author informs us that he constructed his table from registers of many thousand life-annuitants, in Holland and West Friesland, which had been kept there from 125 to 130 years previous to the date of his publication; and showed how many of the nominees, or lives the annuities depended upon, were, at the time of their nomination, under one year old, between one and two, between two and three, and so on for all ages.
[7:15:545]

An exact account was also kept of the age at which each life of every class failed; whence it clearly appeared, what degree of mortality prevailed at every age above one year. But because very few children were nominated at or near their birth, he could not, from these registers, determine the mortality under one year of age. He therefore had recourse to mortuary registers and other observations; from exact accounts of which he found, with sufficient certainty, as he says, that out of 28,000 born alive, 5500 died under one year. He also informs us, that, for this purpose, he made use of the observations of divers learned men in England and elsewhere, especially Major John Graunt’s, upon the number of the people and the rate of mortality; and upon taking an average of the whole, he found it to differ but little from that just stated.

And this appears to be the only ground for the assertion made by most writer * on this subject (probably copying from each other without having seen the original work), that Kersseboom’s Table of Mortality was constructed from observations made upon annuitants in England as well as in Holland; also, that it was formed partly from observations made upon the inhabitants of some Dutch villages.

He first published his Table of Mortality in his second Tract, and in his third, he gave abstracts of the registers from which it was constructed. These were contained in twenty-nine tables, twenty-two of which were for the two sexes separately; in the rest the sexes were not distinguished; and the ages at which the lives failed were generally given to the exactness of half a year.

The numbers of lives, whose current year of age at the time of their nomination was given precisely in these tables, were,
[table]

And none of these nominees were above twelve years of age at the time of their nomination.

These, however, are only specimens of Μ. Kersseboom’s labours. He says there were so many lives in the registers, that he had not the courage to undertake extracting the necessary particulars for more than 50,000 of them; and in that, he was greatly assisted by his friend Thomas von Schaak. Of all the lives, not more than 1 of 120 was past 55 years of age at the time of nomination.

Nicholas Struyck, in his Aanhangsel op de Gissengen over den Staat van het Menschelyk Geslagt, en de Uitree-kening der Lyfrenten, published at Amsterdam in 1740, at the end of the quarto volume, commencing with his Inleid-ing tot de Algemeene Geographie, gave, from registers kept at Amsterdam for about thirty-five years, two tables of observations made upon the duration of the lives of 794 males, and 876 female annuitants separately; and two tables of mortality he had constructed from them for the two sexes; both beginning with fjpe years of age. These two, taken together, differ but little from that of Dr. Halley; they represent the mortality to be considerably greater than Kersseboom’s: having been constructed from so few observations, they are not entitled to much confidence, and appear to have been very little known or attended to.

This work of Struyck gave occasion to the publication, in the same year, of a small tract in quarto, by Kersseboom, entitled, Eenige Anmerkingen op de Gissengen over den staαt van het Menschelyk Geslagt, &c. wherein he accused Struyck of plagiarism, with but too much appearance of justice.

Neither Kersseboom nor Struyck gave any information as to the manner in which they formed their tables of mortality from the observations on which they were grounded. Μ. Kersseboom informs us, that he submitted his table to Professor S’Gravesande, some years previous to its publication, and obtained his approbation of it for calculating the values of annuities on lives.

In the year 1742, Mr. Thomas Simpson, in his Doctrine of Annuities, (see the article Annuities) gave a table of mortality for London, being the same that had previously been constructed by Mr. Smart, at twenty-five and all the greater ages, but corrected at all ages under twenty-five years, on account of the greater number of strangers who settle in London under that age, which occasioned, till the commencement of the present century, a constant excess of the burials above the births. This correction Mr. Simpson made by comparing together the numbers of christenings and burials; and observing, by means of Dr. Halley’s table, the proportion between the mortality in London and Breslaw above twenty-five years of age.

In 1746, Μ. Deparcieux published (at Paris in 4to,) his Essai sur les Probabilités de la duree de la Vie Humaine, in which he gave six new and valuable tables of mortality; one of them constructed from the lists of the nominees in the French Tontines, principally those of the years 1689 and 1696, and the rest from the mortuary registers of different religious houses; four of these showing the mortality that prevailed amongst the monks of different orders, and the fifth, that which obtained amongst the nuns in different convents of Paris. Those for the monks and nuns, with the exception of the tables of Struyck, mentioned above, were the first ever constructed for the two sexes separately.

The Essay of Μ. Deparcieux is written popularly, and with great perspicuity; he has given the most satisfactory accounts both of the data his tables were constructed from, and the manner of their construction.

In his thirteenth table, he included with the five tables of mortality of his own construction; that of Mr. Smart for London, as corrected by Mr. Simpson, Dr. Halley’s, and Μ. Kersseboom’s, together with the expectation of life at, or its average duration after each age, both according to his own and Μ. Kersseboom’s table for annuitants, and for every fifth year of age according to each of the other tables; the fractional parts of a year being always expressed in months, and not in decimals.

Dr. Halley first, and Struyck after him, had given the probable duration of life after several ages, according to their respective tables, that is, the term at the expiration of which, the persons now living at any proposed age, will be reduced by death to one-half their present number.

But Deparcieux appears to have first given the average duration of life after any age, and showed how to calculate it correctly from tables of mortality. On account of the scarcity and value of Μ. Deparcieux’s Tables of Mortality, Mr. Milne has reprinted them, with the expectations of life just mentioned, in his Treatise on Annuities, with a short account of their construction; it is therefore unnecessary to pursue the subject further here.

In 1760 Μ. Deparcieux published (at Paris in 4to) his Addition a l’ Essai sur les Probabilités de la durée de la Vie Humaine, with five tables; three of them relating to life annuities deferred on a peculiar plan, we consider to be of no interest or value at this time: the two others are tables of mortality constructed from statements of the numbers of deaths that took place at different ages, without knowing the numbers of the living at the same periods of life. He obtained the data for the first of them from a clergyman on the frontiers of Normandy and Perche, whose accuracy in all he undertook, he could rely upon; and who gave him the names of the parishes from the registers of which he had extracted the information; but strictly enjoined him not to disclose his name in the event of his making use of [7:15:546] the documents. In these the sexes were not distinguished.

The other table of mortality Μ. Deparcieux constructed from statements sent to him by Μ. Wargen tin of the numbers of deaths of males and females separately, which took place in the different intervals of age in Sweden and Finland, during the three years 1754, 1755 and 1756. Those two tables have the same faults as others constructed from similarly defective data; and we consider them to be of no value.

Μ. Deparcieux states, (p. 28) that in 1744, he suggested to Μ. Aubert, the commissary who at that time prepared the Bills of Mortality for Paris, the expediency of distinguishing the sexes in the columns of births and deaths, which had not been done previously, but was in consequence of this commenced with the year 1745, and has been continued ever since, as we have already observed in our account of the Parisian Pecherches Statistiques.

Μ. de Buffon, at the end of the second volume of his Histoire Naturelle, published in 1749, inserted a table of mortality that had been constructed by Μ. Dupre de Saint Maur, from the registers of twelve country parishes in France, and three parishes of Paris; which Μ. de Buffon informs his readers that he inserted in his work the more willingly, since these were the only kind of documents, or combinations of them, from which the probabilities of life among mankind in general, could be determined with any certainty. Yet this was a very faulty table, and the numbers of annual deaths were so injudiciously distributed, according to the ages, that it often represented the mortality in one year of age to be three or four times as great, and in some cases, six times as great, as in the next year. Some remarks of Μ. Kersseboom on this table may be seen in the Philosophical Transactions for 1753. Μ. de Saint Cyran corrected some of its most obvious errors, and inserted both the original and his corrected copy in his Calcul des Rentes Viagères. (Paris, 1779, in 4 to.)

Mr. Simpson, in the Supplement to his Doctrine of Annuities, published in 1752, gave some further explanations of the corrections he had made in Mr. Smart’s table of mortality for London; and made some very judicious observations on the difficulties that attend the construction of tables of mortality from the mortuary registers only, of large towns.

In the Nouveaux Mem. de l’Acad, Ray. de Perlin for the year 1760, there is a paper by the celebrated Euler, entitled Recherches générales sur la Mortalité, et la Multiplication du Genre Humain, wherein the subject is treated algebraically. He assumes that the population is not affected by migration, and that the annual births and deaths are always as the contemporaneous population; consequently, that the number of the people increases or decreases in geometrical progression. Then he gives several theorems exhibiting the relations that would obtain between the annual births and deaths and the population, and determines the law of mortality upon these hypotheses, but does not shew how it may be deduced from actual observations independent of hypotheses; neither does he undertake the construction of any table of mortality, but, by way of example, gives that of Μ. Kersseboom, with the changes of the numbers which become necessary, in consequence of his altering the radix from 1400 annual births to 1000.

Süssmilch took great pains in collecting the numbers of annual deaths in the different intervals of age, which he published in his Göttliche Ordnung ; and four tables of mortality formed from these data are to be found in the same work; that in the second volume (§ 461), which has many imperfections, was formed by himself; the three others, being the 21st, 22d, and 23d, at the end of the third volume, were constructed by his commentator Baumann, according to the more correct method of Lambert.

The first edition of Dr. Price’s Observations on Rever sionary Payments, appeared in 1771, containing his observations on the proper method of constructing tables of mortality from bills which shew the numbers dying annually at all ages, and three new tables of mortality constructed from the London, Norwich, and Northampton bills.

The second edition of the same work was published in 1772, and contained, in the Supplement, much interesting and valuable information which did not appear in the first, together with five new tables, intended to exhibit the law of mortality that obtained, 1st, in the district of Vaud, in Switzerland; 2d, in a country parish in Brandenburg; 3d, in the parish of Holy Cross, near Shrewsbury; 4th, at Vienna; 5th, at Berlin. The first formed from bills of mortality given in the Mémoire of Μ. Muret; and the 2d, 4th, and 5th, from those given by Süssmilch in his Göttliche Ordnung', the 3d was from the parish register only of Holy Cross. But we consider none of those tables as now of any value, on account of the defects in the data from which they were constructed.

At the end of the first volume of the work of J. H. Lambert, entitled, Beitrage zum Gebrauche der Mathematik uni deren Amvendung, published at Berlin in 1765, 8vo, he gave a chapter on the certainty of inferences* deduced from observations and experiments; and the example with which he concluded the illustration of his theory, was the deduction of the law of mortality in London from the bills of mortality there; by means of a curve, of which the absciss being proportional to the age, the corresponding ordinate was proportional to the number of survivors of the same age.

In the third volume of the same work, published in 1772, the ingenious author treated the subject at much greater length: x being the age, and y the corresponding ordinate to the curve of mortality for London, proportional to the number of survivors of that age out of a given number (10,000) born alive, he gave this equation to the curve,

(e being the number of which unit is the hyperbolic logarithm), which determined the numbers in the table of mortality very near the truth, until 96 years of age, beyond which it was not intended to be used.

Μ. Lambert also constructed a table by which he intended to exhibit the law of mortality that prevails among mankind in general, from the 23d and 24th tables in the second volume of Süssmilch’s Göttliche Ordnung, which gave the numbers of deaths, in the different intervals of age, in seventeen country parishes in the mark of Brandenburgh, and from the London bills for thirty years; supposing, with Süssmilch, (Gott. Ord. t. i. § 34), that the country people are double the number of those residing in towns.

By an extract of a letter from Μ. Lambert to Gaeta and Fontana, given in their Italian translation of Demoivre’s Treatise on Life Annuities, (Discorso Pr eliminare, part iii.), it appears, that all his attempts to find à posteriori an equation which should determine the relation between the age and the number of survivors in this last table, proved fruitless; the formulae he arrived at having been either too long and intricate, or too incorrect. This is the less to be regretted, since there is no doubt that Μ. Lambert’s table did not represent the true law of mortality, as he made no allowance for the effect of the increase of the people by procreation; and it is singular he did not see that that law might be correctly determined from the numbers of the living, and the annual deaths at all ages in Sweden and Finland, given in Μ. Wargentin’s paper in the Stockholm Transactions for 1766, which paper he himself quotes.

Lambert appears to have first demonstrated clearly the principal properties of tables of mortality, in doing which he made use of the differential and integral calculus; but [7:15:547] as he could not determine the equation to the curve of mortality, that resource did not avail him much.

Flourencourt treated this subject algebraically in the third chapter of his Political Arithmetic, ^[21. Abhandlungen aus der Juristischen und Politischen Rechenkunst, von Carl Chassot de Florencourt. Altenburg, 1781, 4to∙ ] where he gave a perspicuous view of it, as it had been previously treated by Euler and Lambert; but added nothing himself that was original, except three new tables of mortality; one for males, another for females, and a third for both sexes without distinction; deriving his data in each case from the Göttliche Ordnung of Süssmilch. He also gave a new copy of the table of mortality Μ. Deparcieux had constructed from the registers of the nominees in the French tontines; assuming 10,000 for the radix, and inserting the numbers under three years of age, nearly according to Μ. Kersseboom’s table; this, however, does not differ materially from the original table of Deparcieux.

The fourth edition of Dr. Price’s Observations on Reversionary Payments was published in the year 1783, and contained new tables of mortality for Warrington and Chester, also for all Sweden and Finland, and for Stockholm separately, in which the sexes were di stinguished. Those for the whole kingdom were constructed from enumerations of the living, and registers of the annual deaths, in each interval of age, during twenty-one years; those for Stockholm during nine years. The tables for Sweden and Stockholm were the first ever constructed from the data that are requisite to determine the law of mortality among the bulk of the people, and were sufficiently accurate representations of that law, for the times and places in which the observations were made.

In a paper of Μ. Henrich Nicander, inserted in the Transactions of the Royal Academy of Sciences at Stockholm, for the first quarter of the year 1801, he gave two tables of mortality for all Sweden and Finland, in which the sexes were distinguished, but they were not properly constructed; and the mean duration of life which he gave in them at each age, was very erroneous, especially in early life. In that paper he asserted, without offering any demonstration or proof, that, in what we have called the curve of mortality above, if an ordinate be drawn through the centre of gravity of the portion of the area cut off by the ordinate at any assigned age, on the side of the more advanced ages, the part of the base, or of the axe of the abscisses, intercepted between these two ordinates, will measure the mean duration of life after such assigned age. And the mean duration of life after each age, which he has given, was determined in this manner.

Mr. Milne’s Treatise on Annuities and Assurances was published in the year 1815; and, in the third chapter of that work, the construction and properties of tables of mortality are fully treated of.

In the second volume of the same work, three new tables of mortality are given; one constructed from very accurate observations made at Carlisle, by Dr. Heysham, who preserved the bills of mortality of the two parishes, which include that city and its environs, and supplied their déficiences with great care, together with correct accounts of two enumerations of the inhabitants, in which their ages were taken; and a table showing the diseases by which the deaths at all ages were occasioned, is also given.

The fourth and fifth tables in Mr. Milne’s work, exhibit the law of mortality which prevailed in all Sweden and Finland, both with and without distinction of the sexes, deduced from the registers kept and the enumerations made there, during the twenty years ended with 1795; which term was subsequent to that wherein the observations were made, from which Dr. Price’s tables were constructed.

The seventh table in the same work exhibits the law of mortality at Montpellier for males and females separately, and was constructed from the bills of mortality of that place for twenty-one years, ending with 1792.

The second table at the end of this article, was published in the first edition of it in 1822; the tables of mortality for the lives insured in the Equitable Office, which were constructed by Mr. Babbage and Mr. Davies, were published in 1826; and we have given some account of them as well as of those formed by Mr Finlaison, from observations on Government Annuities in this country, and published in 1829, in the article Annuities in this work.

MM. Quetelet and Edouard Smits, in their Recherches sur la Reproduction et la Mortalité de VHomme, in 1832, gave a table of mortality for the towns and the rural districts in Belgium separately, distinguishing males from females, and also for the whole population, without distinguishing the sexes, or the inhabitants of towns from those of the country.

Mr. Morgan, in the above mentioned publication of the Equitable Assurance Society, in 1834, gave a table of mortality for the lives insured in it, (marked C, p. 28), derived from table A of that work; another (D) derived from table B, is not worth a place there.

The second of the tables at the end of Dr. Casper’s work on the Probabilities of Human Life, published in 1835, was intended to exhibit the law of mortality in Berlin, with distinction of the sexes; it was constructed from 69,362 deaths at different ages; 36,895 of males, and 32,467 of females, which took place there during the twelve years 1818-1829∙ And Μ. Mallet at the end of his valuable Mémoire, published in 1836, has given one for Geneva, in which the sexes are distinguished: it contains both the mean and the probable duration of life after every age, and was formed from the bills of mortality there for the eighteen years 1814-1833. For males, females, and the two sexes without distinction, Μ. Mallet took so high a radix as 100,000 births; the number of deaths were, of males 5219, females 5688, of both sexes 10,907; and in the column of deaths, on the same line for any age, as the survivors of that age, the author has put the number of deaths in the registers in the next following year, instead of the decrement of life, or excess of the number attaining that above the number attaining the next greater age, which will probably puzzle many readers.

Part II— On the Construction and Properties of Tables of Mortality.

1. Suppose 10,000 children to have been all born alive at the same instant of time, more than 100 years since; and that the numbers of them who completed and who died in each year of age, were correctly entered in the following table:
[table]
[7:15:548]

which, then, would evidently be a table of mortality; and this mode of constructing one, were it practicable, would be the simplest possible.

2. But of 10,000 children taken indiscriminately at birth, it is manifest that the number who complete or survive any year of age, will be just the same, whether they be all born at the same time or not; and, therefore, this table might as well have been constructed by noting the times of the births of 10,000 children taken indiscriminately, and registering the time or the age at which each died; for then, after the whole were extinct, it would only be necessary to collect the sum of those who died in each year of their age, and insert it in the third column of the above table (1) against the proper age. The numbers in the second column would then be obtained by beginningwith the 10,000 births, and merely subtracting the number in the third from the number in the second column, and placing the remainder in the next line below, in that second column, throughout the table.

3. It is evident that the number against any age in the second column of such a table, is equal to the sum of those in the third column against that, and all the greater ages; that is to say, that the number who complete any year of age is equal to the sum of those who die at all the greater ages.

4. Now let us suppose the population of a place to have remained invariable for one or two hundred years past, during which period 10,000 children have been born alive, at 10,000 equal intervals of time in each year. Also that, there having been no migration, and the law of mortality having been always the same, both the number of the living and that of the annual deaths in each year of age, have remained constant, the whole amount of the annual deaths at all ages, as well as the number of annual births, having been 10,000.

5. Then, if the law of mortality exhibited in the above table (1) be that which obtains in the place just mentioned, that table will represent the stream of life which flows through it, and fills the vacancies left by those who advance in age, or are carried off by death, their successors incessantly following and being followed in the same course.

6. Thus: 10,000 children being born annually at so many equal intervals of time, 7096 will annually complete their fifth year, also at equal intervals; and of these, 112 will die annually in the sixth year of their age.

7. And it is manifest that the number who annually complete any year of their age in such a place, is equal to the sum of the annual deaths at all the greater ages.

8. Let us next suppose, that the constant number of deaths which happen annually in any one year of age, take place at equal intervals of age in that year. For instance, that the four deaths which happen annually, in the ninetyfifth year of age, always takes place at the ages of
[table]

and 95 years; or rather, that the last individual dies at the moment before completing the 95th year.

9. Then the number constantly living in any year of age may be determined as follows:

Let us take, for example, the ninety-fourth year, which 14 persons annually enter upon, and 5 die in. Now, if no deaths happened in that year, it is obvious that the 14 persons who annually enter upon it at so many equal intervals (4 and 6), would be all constantly living at 14 equal intervals of age in that year; and if that year of age were divided into five equal intervals, there would be

14

constancy living in each interval — persons; or, in a place 5 similarly circumstanced, but five times more populous, 14 persons.

But when five deaths take place at so many equal intervals in the ninety-fourth year of age, (the fifth part of a year being 73 days,) the case is altered. Thus,
[table]

Or rather, the oldest life that fails in the 94th year, must be considered to expire the moment before completing that year, as only 9 survive 94.

But the numerators of these fractions being in arithmetical progression, their sum is equal to half the sum of the first and last terms multiplied by the number of terms; or —Φ~ × 5; which sum being divided by the common denominator, 5, we have the number of the living in the 94th year of age=—⅛--; an arithmetical mean proportional between the numbers who enter upon the first and last of the intervals which that year of age was divided into.

10. Now, the number, 9, who survive their 94th year, is less only by unit than the number 10, who enter upon the last of the intervals that year was divided into; so that if, ; p 14+10 1 14 + 9

instead of —½—, we take —-—, or an arithmetical mean 2 2

proportional between the numbers who annually enter upon, and annually survive their 94th year, for the number constantly living in that year, it will only be less by half a life than what has just been demonstrated to be the true number, according to the hypotheses; and the difference would still have been but half a life, although the radix of the table had been 10,000,000 instead of 10,000; the number of the living would, in that case, according to these two methods, have been 1200 and 1199½. And the number of the living in any one year of age, even according to the above table, is generally several thousands, so that this difference, which remains always the same, is quite immaterial.

Besides, it is obvious that the above hypotheses can never coincide exactly with the facts. And the above reasoning is evidently applicable to any other year of age.

11. We are therefore authorised to conclude, that in a place, circumstanced as above stated, the number of the living in any year of their age is an arithmetical mean proportional between the numbers who annually enter upon, and who annually complete that year.

12. Thus it appears that
[table]

But it is to be observed, that the same numbers occur in [7:15:549] the first of these two series as in the second, except the first term of the first, and the last of the second, which are 14 and 0 respectively. Therefore the sum of the second of these two series falls short of the sum of the first by 14, the number who annually complete their 93d year; so that the series of half sums falls short of the sum of the first series by 7, the half of 14. And this reasoning will apply equally to any other age than that of 93 years.

13. Whence it follows, that in a place circumstanced as we have supposed, the number of persons constantly living at any assigned age and upwards, is less than the sum of those who annually complete that and all the greater ages, by half the number who annually complete that year of their age.

14. From the supposition that the number of persons who die annually in any one and the same year of age, expire at so many equal intervals of age in that year (8), it follows, that for each of these lives which fails before the middle of that year of age, there will be another which will fail just so much after it, and, consequently, that the average quantity of existence during any year of age, for the lives that fail in it, is just half a year.

15. But in taking, for any one year of age, the sum of the numbers in the second column of the table (1) at all the greater ages, each life is counted once for every complete year it survives, after the age first mentioned; and if, to the sum of these, we add half the number in the same second column against that first mentioned age, this half number being the sum of the fractional parts of a year, by which the whole of these lives survive the last year of age they complete (14); the sum total thus obtained will evidently be the whole^duration of life after the age first mentioned, enjoyed by all the lives that survive that age in any one year.

16. Therefore, if this last sum total be divided by the number who annually survive that first mentioned age, the quotient will be the mean duration of life after that age which is also called the expectation of life at the same age, being the portion of future existence which an individual at that age may reasonably expect to enjoy.

17. But, by No. 13, it appears, that the last mentioned sum total is also the number constantly living in the place, at and above the age first mentioned (15).

18. Whence, and from No. 16, it follows, that if the number of the living in the place at any age and upwards, be divided by the number who annually complete that age, the quotient will be the mean duration of life after the same age.

19∙ And, consequently, if the number constantly living at all ages, be divided by the number of annual births, the quotient will be the mean duration of life from birth, or the expectation of life of a child just born.

20. Hence also it appears, that the number of years in the expectation of life at any age, is the same as the number of living persons at that age and upwards, out of which one dies annually.

21. Thus, for example, the expectation of life at 40 years of age being 25∙495 years, the proportion of the living in the place aged 40 years and upwards who die annually, is one of 25*495, or, which is the same, 1000 out of 25,495.

22. The numbers represented by a table of mortality to die in any intervals of age, are called the decrements of life in those intervals.

23. And the interval between any age and the utmost extent of life, according to any table of mortality, is called the complement of life at that age, according to the same table.

24. If the decrements of life be supposed to be equal and uniform through its whole extent, and the interval between birth and the utmost extremity of life be divided into as many equal parts as there are annual births, then, one of the individuals born will die at the expiration of each of these equal intervals of age; and the numbers who survive the several intervals, from birth to the extremity of life, will form an arithmetical progression.

25. Whence it will be found (11), that the number of the living at any assigned age and upwards, will be equal to the number who annually complete that age, multiplied by half the number of years in the complement of life at the same age-

26. And if this last product be divided by the number who annually complete that age, the quotient, that is, half the complement of life, will be the expectation of life at that age (18).

27. The mean numbers of annual deaths at all ages, or, which in this case is the same, the number of deaths in each year of age, that take place during any one year, in a place circumstanced as we have supposed, being given, a table may be constructed as follows, which will answer all the most interesting questions that can be put respecting the population and mortality of the place.

28. Let there be five columns, in the first of which insert the ages 0, 1, 2, 3, 4 96, 97, 98, 99, and against every age, insert in the fifth column, the given number that died in the year between that and the next greater age; then begin at the greatest age, and proceed towards the least, as follows :—

L∕, To the number against any age in the fourth column, add that against the next less age in the fifth, and insert the sum against that next less age in the fourth (7).

2d , To the sum of the numbers in the third and fourth columns against any age, add half the number in the fifth column against the next less age, and insert this last sum against that next less age in the third column (11).

3d , Divide the number against any age in the third column, by the number against the same age in the fourth, the quotient will be the expectation of life at that age, to be inserted in the second column (16).
[table]

A complete table of this kind for the two sexes separately, formed from observations made in all Sweden and Finland, during twenty years ending with 1795, will be found in Mr. Milne’s Treatise on Annuities and Assurances, being the fourth in that work.

29∙ Hitherto we have supposed the state of the population to continue invariable for 100 years at the least, on account of the facility with which tables of mortality might be [7:15:550] formed from accurate mortuary registers in such circumstances.

But whether the population be stationary, or increasing, or decreasing, and from whatever causes these changes proceed, provided that they be produced gradually, and not by sudden starts during the time of the observations, the law of mortality may be determined from actual enumerations of the people, and the bills of mortality. Thus,

30. Let the number of persons in each year of their age, that are resident in a place at any one time, be taken, and let an accurate register be kept of the number that die annually in each year of their age, during a term of eight or ten years at the least, whereof the first half may precede, and the second follow the time of the enumeration.

Then, if the number of the inhabitants of every age either increase or decrease uniformly during that term, the mean number of annual deaths in each year of age thus registered, will be the same as if the population of the place had continued throughout that term what ,it was when the enumeration was made.

31. But if, to the number of the living in any year of age, we add half the number who annually die in the same year, the sum will be the number who annually enter upon that year of their age ♯ 1.)

And thus, from the enumerations and registers above mentioned, may be derived the ratio of the number who annually enter upon any year of their age, to the number who annually die in it.

32. But all the observations which have been made with sufficient minuteness, on the mortality during the first year from birth, concur in showing, that many more deaths take place in the first few weeks from birth, than in equal periods of time during the remainder of the first year; and that the nearer to birth, the greater is the mortality among infants. So that the number of the living in successive equal intervals in the first year of age, cannot be correctly assumed to be in arithmetical progression.

33. On this account it is desirable that the annual numbers, both of the children born alive, and the deaths under one year of age, should be correctly registered, as in Sweden.

34. Then, as the number annually born alive, is to the number of annual deaths under one year of age, according to the registers, so is the radix of the table of mortality, to the number dying under one year of age according to that table, which, being subtracted from the radix, the remainder is the number who complete their first and enter on their second year. Whence the numbers, both of survivors and annual deaths, at all the greater ages, may be determined in the order of their succession by No. 31.

35. If, instead of the number of the living in each year of age being taken only once, according to No. 30, that operation be performed several times during the term for which the mean number of annual deaths in each year of age is given ;—then, the mean number of the living in each year of age throughout that term, must be deduced from the given numbers; and, being substituted for the number at the middle of the term according to No. 30, the law of mortality may be determined with more certainty, than when the people are only numbered once.

36. Both in enumerations of the people, and in bills of mortality, the numbers are, however, almost always given only for intervals of age of several years each. For the manner of interpolating the numbers in each particular year of age, the reader is referred to Mr. Milne’s Treatise on Annuities and Assurances, arts. 180 and 181.

37. Hitherto we have only considered the determination of the law of mortality amongst the whole of the inhabitants of a place, of all ages, ranks, and conditions; and until within the last eight years, no statements of facts relating to particular classes of the people had been published, except those of Μ. Deparcieux, in his valuable Essai, sufficiently numerous and correct to be available for the purpose. But the inquiries made by order, and with the aid of government in this country, into the mortality amongst various classes of nominees, on whose lives annuities depended, published in Mr. Finlaison’s report to the Lords of the treasury in 1829, and already noticed in the article Annuities in this work; with the publication in 1834, of the still more interesting, important, and distinctly detailed observations on the mortality that has taken place among the lives insured in the Equitable Assurance Society, form most valuable accessions to our knowledge of the subject; we therefore proceed to show how the law of mortality among those classes of persons may be deduced from these documents. We shall have compassed that object, when we have determined out of a considerable number of persons who entered upon each year of age, how many died in that year, and, consequently, how many survived it; and the Equitable Assurance documents are so disposed, as to afford great facility in effecting this. The following table is extracted from them, with the addition of the column marked B.
[table]

38. According to the common mode of expressing the ages, which is adopted both in the government documents [7:15:551] and in those of the Assurance Society, the year of age stated is always that which was last completed; but where-ever that is the case, it should be distinctly stated, and kept steadily in view. We confine ourselves in this table to the 31st year of age, and mark it 30+ to avoid ambiguity; for the same reason ( + ) is put over the ages in column A, to show that each number in it denotes the age last completed.

39∙ Column B has been added for the sake of illustration; it shows at what earlier ages the different lives entered the society, which afterwards completed the 30th year of their age in it, and entered their 31st: thus, out of 40 insured in the 8th year of age during the period of the observations, only 5 entered their 31st while insured in the society, the rest having passed out of it either by death or otherwise, at earlier ages, as the preceding columns of the original table fully show; and of the 373 persons who were insured in their 22d year, 124 remained insured till they entered their 31.

40. This table shows that of 4692 persons who entered on their 31st year of age in the society, 265 went out of it alive in the same year of their age during the observations, 51 were still living and insured at the termination of the observations, and 762 came into the society in that year of their age; the individuals of those three classes amount together to 1078 persons. But of the 265 who went out of the society alive during that year of age, it may reasonably be assumed, that whatever number of them at the time of their exit exceeded 30½ years of age by any interval of time, as many would fall short of that middle age by the same interval, when they went out; and, therefore, that the whole of them on an average may properly be considered to have been exposed to the action of the Law of Mortality during one half of that year of age; so that the mortality among them must have been the same as it would have been among half the number of exactly similar lives, in passing through the whole of that year.

In the same manner it appears, that of the 762 persons who were insured at various periods of the 31st year of age, and of the 51 persons who remained alive and insured in the society at various periods of that year of age when the observations terminated; may, each of them on an average, be properly assumed to have been exposed to the action of the law of mortality in the society during one half of the 3lstyear of age; and we are therefore entitled to conclude that the mortality among them was the same as it would have been among half the number of exactly similar lives in passing through the whole of the 31st year of age.

But 4692, the total of the numbers in column C includes all those 1078 lives, the same as if they had all entered upon their 31st year of age in the society, and had all passed through it except those which were carried off by death. It is, therefore, manifest, that 539, the half of their number, must be substracted from 4692, and the remainder, 4153 must be taken as the number of persons entering on the 31st year of their age, and continuing exposed to the law of mortality in the society during the whole of that year, among whom thirty-two deaths take place in the same year of age.

This, when the principle is clearly understood, is certainly a very simple operation and easily performed; and its application to every other age in the original table of data is exactly the same as to the 31st year.

41. In constructing the table of mortality, supposing that in proceeding from the earliest age we have arrived at the completion of the 30th year, or the entrance on the 31st, and have determined the number of survivors at that limit to be 4305; since

4153: 32 :: 4305: 33∙1712, we find 33 to be the number of deaths which will take place in the 31st year of age out of 4305 persons who enter on it; and, consequently, that 4272 enter on their 32d year, according to the table we are constructing; the method of completing it is obviously the same throughout, and can be attended with no difficulty after the valuable documents requisite for the purpose have been obtained.

42. What has been shown here respecting the determination of the law of mortality amongst insured lives, applies also, and with rather more facility to the nominees on whose lives annuities depend. The life annuities sold by government in this country not being redeemable, are always continued during the whole of the lives they depend upon; therefore, with regard to them, column E in the above table is left blank; and in the case of the old English Tontine, which commenced in 1693 and ended in 1783 with the life of the last survivor, column D will also be quite blank.

Part III.— On the Law of Mortality as deduced by the preceding methods from actual observations ; and on the comparative merits of the different Tables of Mortality that have been published.

43. When the uniformity of anatomical structure in different individuals of the human species is considered, and the great power possessed by the human body, of so adapting itself to the circumstances it is placed in, as to avoid injury from changes in those circumstances, it appears natural to expect a priori, that, where the circumstances of the people are not greatly different, the law of mortality will be nearly the same. And, from a comparison of the best tables of mortality yet constructed, we are induced to believe that this expectation will be realized, whenever a sufficient number of good observations shall have been made, under circumstances sufficiently varied.

44. We know of no observations that have hitherto been made and published, from which the law of mortality may be correctly determined, except the following:

1. Those of Μ. Deparcieux in France.

2. The Swedish.

3. Dr. Heysham’s at Carlisle.

4. Dr. Cleland’s at Glasgow.

5. Mr. Finlaison’s on the nominees of life annuities granted by government in this country.

6. Mr. Morgan’s on the lives insured in the Equitable Assurance Society.

Those of Deparcieux, Finlaison and Morgan, were made only on select classes of the people; the Swedish are incomparably the most numerous and extensive; and whilst Dr. Cleland’s exhibit the mortality in a large manufacturing town, Dr. Heysham’s will, we believe, be found to be best authenticated, and most correct.

45. The climate of Sweden is so unfavourable to the products of agriculture, and the number of the people is so great in proportion to the quantity of food produced, that unfavourable seasons there, are generally followed by distressing dearths, and the destructive epidemical diseases constantly attendant upon famine, which raise the mortality, when they occur, much above what it would otherwise be; and both in that way, and by weakening the constitutions of those who survive them, they materially increase the average mortality deduced from observations made during any considerable number of years. Of this the reader will find ample proofs drawn from authentic sources, in the 10th, 12th, and 13th chapters of Mr. Milne’s Treatise on Annuities.

46. For these reasons, the mortality in Sweden deduced from many years’ observations, will be found to be higher than in the more temperate and fruitful parts of Europe. And we shall probably make the nearest approach to the general law of human mortality in the temperate climates, that can be made from the Swedish observations, by selecting a period in which no remarkable epidemics prevailed. Such a period was that of five years, 1801-1805; during [7:15:552] which, according to a statement of Μ. Nicander, in the Transactions of the Royal Academy of Sciences at Stockholm for the year 1809, the population and mortality were as stated in Table I. at the end of this article.

47. From these data, the second table at the end of this article has been formed. The numbers in the columns for males and females separately, having been determined according to Nos. 36 and 31-35; assuming that, of 20,000 children born alive, 10,219 are males, and 9,781 females, in the ratio of 275,599 to 263,812.

The numbers against each age in the columns for the whole population without distinction of sex, are arithmetical mean proportionals between the corresponding numbers in the columns for males and females separately, against the same age.

48. From the table last mentioned, Table III. has been deduced by No. 16, exhibiting the expectation of life at every fifth year of age; or its mean duration after that age.

49∙ Vaccination commenced throughout Sweden and Finland in 1804, during which year, the number vaccinated was 38,255; and, in the year following, 42,839∙

The number of deaths by small-pox there, during the year

1801, was 6,458

1802, — 2,679

1803, — 8,610 1804, — 3,764 1805, — 1,887

Sum, 23,398

Annual average number, 4,680

Whilst the annual average of the ten years ending with 1803, was 6962. (Vet. Ac. Handl. 1809, and Mr. Milne’s Treatise on Annuities, art. 698.)

50. Therefore if we assume that, had vaccination not been practised in the years 1804 and 1805, the annual average number of deaths during the five years ending with that last mentioned, would have been greater by 2,282 than it actually was, and that these 2,282 additional deaths would have all taken place under five years of age, both assumptions will be near the truth; and it will follow that the annual mortality under five years of age, which actually was but one of 13∙534, would have been one of 12∙629, had vaccination not been introduced. Its introduction cannot have affected the first three tables above five years of age; and under that age, not quite so much as has just been stated.

51. Of all ages, and both sexes, there actually died annually, during these five years, one of 40 ’ 901; had vaccination not been practised at all, the annual average mortality would not have been so great as one of 39*759∙

52. Table IV. exhibits the mean duration of life after every fifth year of age, according to twelve different tables of mortality; the first six, A, B, C, D, E, F, having been constructed from the requisite data (30 and 38,) the last six, Μ, N, O, P, Q, R, from mortuary registers only.

53. The numbers in the first column A have been taken from table III. in Mr. Milne’s Treatise on Annuities, and those in B from table E (p. 28) in the Equitable Assurance Society’s publication.^[22. The author of this article in reading the note on the 4th and 5th pages of Mr. Arthur Morgan’s introduction to the valuable work above mentioned, when that gentleman was so good as to send it to him on its first publication, had noted with a pencil in the margin, that the practice there stated was not quite correct; but the circumstance had long passed from his recollection, when he showed in No. 40 of the present article, how the law of Mortality in the Society might be determined from the large and valuable table marked A; therefore, by the words “age on admission,” at the head of the extreme left hand column over the age in the same horizontal line with the number of lives admitted in the first division of the large column with that age at its bead, he was naturally led to conclude that that was, as it ought to be, the number of lives which really were insured during the observations, when that was the age they had last completed. But by the note referred to, it appears not to be so; on the contrary, none of the lives insured during any year commencing with the first of January, are entered in these statements as having come into the Society until the first day of January next following the day of their actual admission. and then each is stated to be one year older than it was when insured; although whatever deaths may happen amongst them before the first of January next following the commencement of the insurances, are entered in the statements as having taken place amongst the lives previously insured. The manuscript being wanted immediately, was in the hands of the printer, 400 miles from the author, before these circumstances were called to his recollection, by his accidently seeing his original note on the subject; he is therefore anxious to give this explanation. The principle of the method of determining the law of mortality in such cases, remains just the same. But it now appears that the number stated in Table A to have been admitted at any age, should have been stated to be so at the next younger age; and any calculator who may choose to employ himself on the subject, had better make that correction before proceeding farther. The probable error arising from the fault will not be great; but it is incumbent upon us to state the right method of proceeding. ]

54. Deparcieux’s table C constructed from great numbers of accurate observations on the nominees in the French Tontines, resident principally in Paris and its environs, represents the duration of life too small after 60 or 65 years of age. (See Mr. Milne’s Treatise on Annuities, articles 867 and 868.)

55. Column D has been taken from the 45th table in Dr. Price’s Observations, E from the 5th in Mr. Milne’s Annuities, and F from the 3d table in this article. All these tables represent the duration of life in Sweden and Finland, after 45 or 50 years of age, to be less than according to the others; and it might reasonably be expected, a priori, that the excessive cold in Sweden would be unfavourable to the prolongation of life in old age.

56. Of the less correct columns, Μ has been deduced from the 7th table in Mr. Milne’s Annuities, and N from the 42d in Dr. Price’s Observations ; but, as the Montpellier and Chester tables, just referred to, give the expectations of life only for males and females separately, the numbers in columns Μ and N against each age, are arithmetical mean proportionals between the expectations for males and females against the same ages in those tables; which, though not quite correct, is fully sufficient for our present purpose.

57. The number in column O against each age has been derived from that given by Μ. Mallet in his table of mortality as the mean duration of life in Geneva from and after that age, by subtracting one half (0∙5) from each of them; which will be found to be a necessary correction.

58. Column P has been derived from Lambert’s table for mankind in general, already mentioned in the historical part of this article, in which he gives a column headed mean age. Thus, against the age of 20 in that column, stands 54∙3, by which he means that persons who survive 20 years of age, do, on an average, attain the age of 54 ’ 3 years; so that their expectation of life at 20, will be 34∙3. But his numbers in that column are all too great by ½, or 0∙5, as he has himself demonstrated; the last, therefore, should be 33 ’ 8; and
[table]
[7:15:553]

59∙ The reason assigned by Lambert for voluntarily admitting this error at each age, as well as the corresponding one in the number of the living at and above the same age, into his table, was, that he did not consider the data in his possession enabled him to determine the duration of life within half a year of the truth.

60. In both these errors Μ. Lambert has been followed by J. C. Baumann, in constructing the 21st, 22d, and 23d tables inserted at the end of the third volume of Süssmilch’s Göttliche Ordnung which were intended to represent respectively, the law of mortality among the country people in the churmark of Brandenburg, amongst the whole population of the churmark, and amongst the inhabitants of London.

61. The numbers in column Q were calculated by Deparcieux from Dr. Halley’s table; and those in column R have been extracted from the 18th table in Dr. Price’s Observations.

62. Upon comparing the numbers in the first six of these columns, which are more correct, with those in the last six, which are less so; it will be found, that at the early periods of life, its future mean duration according to the tables formed from mortuary registers alone, is less than according to those formed from the requisite data; also that the difference is greater the younger the lives are, and diminishes while the age increases, so as at 60 or 65 years of age to be little or nothing, and to continue small, and variable both in kind and magnitude, through the rest of life.

63. This appears to have arisen from the number of the people having varied but little during the first 35 or 40 years of the century that ended at or about the middle of the term in which the observations were made; and having increased considerably by procreation, during the remainder of that century; such increase having been slow at first, but gradually accelerated afterwards.

64. Table V. is calculated to illustrate this part of the subject. The columns A and B represent the law of mortality among the whole population of Sweden and Finland without distinction of sex, having been merely copied from Table II.

Column C shews the proportion of 10,000 annual deaths in Sweden and Finland that took place in each year of age, on an average of five years ending with 1805. And the number in column D against any age, being the sum of of those in column C against that and all the greater ages, would be the number who annually attain to that age, if the number of the people of every age had remained stationary from the year 1700 till 1806 (7).

65. The table of mortality formed by the columns C and D therefore, is that which Dupre de Saint Maur, Süssmilch, Lambert, Baumann, Florencourt, Muret and others, for want of the mortuary registers of a whole country, endeavoured to form by combining the registers of different town and country parishes.

Those tables also have the same faults, which have been formed in a similar way for particular towns or other comparatively small districts, from the bills of mortality alone, where the population had been increasing during the century preceding the commencement of the observations or statements in the bills of mortality which each table was formed from, and also during the period of the observations.

66. But it has been ascertained by repeated enumerations of the people in Sweden and Finland, that the hypothesis of their number having remained stationary for the last 100 years or more, is far from the truth. And by i comparing columns A and B with C and D, it will be seen I in what manner, and to what degree, the falsity of the hypothesis in this case, has vitiated the table derived from it.

67. To facilitate this comparison, columns E and F have been added. Taking the age of five years for an example;

! the numbers against that age in columns C and D show, that, according to the hypothesis, out of 5988 children who annually enter upon their 6th year, 144 die in it; while it appears by columns A and B, that out of 7096 children who enter upon that year of their age, only 112 die in it: and 112: 7096 :: 144: 9123, so that 9123, inserted against the age of five years in column E, is the number of children annually entering upon their 6th year, out of whom 144 really die in the same year of their age; and the mortality as represented by the hypothetical table in this case, is to the true mortality, as 9123 to 5988, or as 3 to 2 nearly.

Then the number in column F against any age, is always the excess of that in E above that in column D against the same age.

68. Columns B and C both containing 10,000 deaths, it will be seen that in column C, they are greatly accumulated at the early ages, in comparison with those in column B; and that in old age, the deaths in column C are much less numerous than in B; which are necessary consequences of the people increasing by procreation; the numbers of the people in a progressive population, in comparison with a stationary one, being greater in early life, and less in old age. And, while the law of mortality remains the same, the numbers of deaths at the different ages, must necessarily be distributed in a similar manner.

69∙ This enables us to see clearly how the principal differences have arisen between the correct and incorrect tables of mortality AB and CD; whilst the number of annual deaths at all ages (10,000) is the same in both, the proportions of that number are necessarily in column C of the increasing population greater, and the deaths are more densely distributed at the early ages, and less so at the advanced ones than in column B of the population which has consisted of the same number of persons of every age, and has produced the same number of annual births and of annual deaths at every age for 100 years past. The increasing population is necessarily attended with a corresponding increase of the annual births and of young persons; while the elderly persons are only those left by the law of mortality out of the corresponding small numbers that were born annually, 50, 60, 70, or 100 years back. And as columns A and B represent the true law of mortality that prevails among the people, columns C and D cannot do so, although constructed from observations on the same people; for in an increasing population it is not true that the sum of the deaths happening annually above a given age will be the same as the number of persons annually arriving at or completing that age; it always falls short of it, and the more so as the given age is younger, there being deficiencies at all ages above that.

Columns E and F show what the errors of the hypothetical table are at the different ages, and they are of a similar kind in all tables similarly constructed from records of the number of deaths at the different periods of life in an increasing population; and such are probably 99 out of 100 of those hitherto published; many of them for people increasing their numbers much faster than the Swedes have done, and the errors of such tables must be greater than those of the table CD.

70. Table VI., which needs no further explanation than is placed at the head of it, will also illustrate the difference between tables of mortality formed from the requisite data, and those constructed from mortuary registers only.

It is better fitted for this purpose than Table IV., with which, however, it will be found to correspond very well. But the 4th table has other uses which this has not.

71. From what has already been advanced, it would appear probable, that the number of annual births in Sweden and Finland had been nearly stationary, and rather decreasing than increasing, upon an average, from about 1700 till 1735.

The numbers both of the annual births and deaths, from the year 1749 till 1803, will be found in Milne’s Treatise [7:15:554] on Annuities, art. 698: these kind of returns to government were not made before 1749, neither have we any satisfactory account of the population before that period.

72. But the statements in our 7th table corroborate the inferences just drawn from the 5th and 6th, as they shew that during the 43 years ended with 1800, the total population increased, while the proportion above 90 years of age diminished through the whole term, and increased very little during the next 10 years.

The numbers in that table include both sexes, and the long continued diminution of them past 90, cannot be explained by supposing the males to have fallen in battle; for the females were reduced in the same proportion, their number throughout, having been to that of the males above 90 years of age, as nine to five nearly.

From the 7th table, therefore, it appears probable, that the annual births in the years

1698, 1705, 1710, and 1715, were respectively proportional to the numbers 907, 637, 837, and 786.

The last number, 786, has been calculated upon the supposition that the proportion of the population in Sweden and Finland to those in Sweden alone, was the same in 1810 as in 1805.

73. It should also be observed here, that the disastrous career of Charles the Twelfth commenced with the eighteenth century, and terminated in 1718, when the country was in such a state of exhaustion as it could not have recovered from for many years; whence there appears reason to believe, that the annual births during the succeeding fifteen or twenty years, did not increase fast.

Cantzlaer informs us, that between the 10th of August 1710, and the month of February 1711, near 30,000 persons were carried off by the plague in Stockholm alone. (Mem. du Royaume de Suède, t. i. p. 29∙)

74. It will be seen that the numbers in col. F of Table V., in proceeding back from four years of age to birth, continually decrease, contrary to what generally obtains; and as we ascribe the general increase of these numbers, when taken in the retrograde order of the ages, to the annually increasing number of births, so will this anomalous appearance be found to arise partly from the average number of annual births having actually decreased for a few years; for
[table]

But it appears to have arisen principally from the practice of vaccination during the years 1804 and 1805, by which the mortality among children, or the numbers in col. C, in a few of the first years from birth, were reduced below what they otherwise would have been (50) while those in col. D remained nearly the same (64); consequently, the numbers in col. E were reduced in nearly the same ratio as those in C (67), and the reduction in col. F. was in each case nearly the same as in E (61).

75. The numbers relating to Sweden and Finland in the 7th table, have been derived from the Stockholm Transactions for the years 1766, 1801, 1809, and 1813.

Those relating to Spain and the Spanish possessions in Europe and Africa, including the Canary Islands, from the Censo de la Poblacion de Espana en el ano de 1797, mentioned in the first section of this article. These last have been included in this Table, to show the difference in the proportion of aged persons between Spain and Sweden, and still more between the Canary Islands and both.

76. If the population of Spain had remained invariable from 1697 to 1797, the law of mortality there, might have been easily derived from the statements above mentioned of the enumeration in 1797; but in the actual state of things, that cannot be determined without comparing these with exact accounts of the numbers that died annually in each interval of age. And, as was observed in the first section of this article, the author has obtained satisfactory information that no such returns from the parish registers throughout Spain, as are there mentioned, ever were published, nor is it probable they were ever made.

77. When what we have advanced respecting the 5th and 6th tables is clearly understood, it will not be difficult to account for the greater part of the difference between the more and less correct columns in Table IV.

Most of the observations which the German tables were constructed from, were made between the years 1720 and 1750; and those who died then between 60 and 100 years of age, must have been born between 1620 and 1690; in which period nearly the whole of the thirty years’ war, ended in 1648, was included, during which, and for several years after, it is probable that the annual births increased little or nothing, if they did not decrease.

78. Amongst the less correct columns of Table IV., those for Montpellier, Chester, and Geneva, agree much better than the rest with the more correct ones, which has probably arisen in each case, partly from the mortality in these three places having really been less throughout life than in most large towns; and partly from the annual births in them, having increased less than in the other places, during the fifty or sixty years preceding the period in which the observations the tables were constructed from were made.

79∙ The Northampton table was constructed by Dr. Price, from the bills of mortality (from the year 1735 to 1780) of the single parish of All Saints, containing a little more than half the inhabitants of the town; and as the deaths exceeded the births in number, the Doctor applied a correction to the table under twenty years of age, which, if it had answered the intended purpose under that age, as we are satisfied it did not, could have no effect on any of the numbers above the same age; and almost all of the useful applications of such tables, are to ages above twenty.

80. The table so formed could only be correct, provided that the numbers, both of the living and the annual deaths at every age above twenty years, had continued invariable during the 146 years that intervened between 1634 and 1780; provided also, that no migration from or to the town took place, except at twenty years of age, and that the annual increase the population received by migration at that age, was just equal to the excess of the annual deaths above the annual births.

81. But we consider it to be much more probable, that during these 146 years, Northampton partook of the prosperity and adversity that prevailed in the rest of the kingdom; and, consequently, that its population was generally progressive, though sometimes stationary, and sometimes retrograde.

82. We have not room here to support this opinion by numerical statements and calculations, but from the population abstracts, and an enumeration of the inhabitants of Northampton, given in Dr. Price’s Observations on Reversionary Payments, (vol. ii. p. 94,) it wall be found, that both the annual births, and annual settlers in that town, have been increasing ever since about the year 1715 or 1720; also, that although the burials exceeded the baptisms till the year 1802, the supply by migration was much greater than that excess; and, consequently, that the numbers of the living have been accumulated more at the early ages, and less at the advanced ones, than they would have been had the population remained stationary.
[7:15:555]

83. Thus it appears, that the faults in the Northampton table are of the same kind as those of the others constructed from mortuary registers only. And the civil war in the time of Charles the First, with the unsettled state of the kingdom for some years before and after it, would probably have prevented or greatly retarded, the increase of the annual births, during the time in which those persons were born, who died past sixty years of age between the years 1734 and 1781, and may account for the table after that age being near the truth; while the comparatively rapid increase of the people during the sixty years ending with 1780, appears to explain the great excess of mortality in that table at the early periods of life.

84. As it was only from the Carlisle and ^ Northampton tables of mortality, that tables of the values of annuities on single andjointliveshad been calculated, sufficiently copious to admit of the values of interests dependent upon the continuance or the failure of human life being accurately derived from them. When the first edition of this article was published in the year 1820, the author gave the following comparison between the mortality represented by each of these tables to take place at the different periods of life, with that which had been observed to obtain among the members of the Equitable Assurance Society.

85. From an address delivered at a general court of that Society, by Mr. Morgan the actuary, on the 24th of April 1800, it appears, that according to the result of an annual experience of thirty years, the decrements of life (22) among the members of the society, were to those in the Northampton table,

Between the ages of 10 and 20 as 1 to 2.

20 — 30 — 1 —2.

30 — 40 ’ — 3 — 5.

40 — 50 _ 3 — 5.

50 — 60 —5 — 7.

60 — 80 — 4 — 5.

The same information may also be found in two notes in Dr. Price’s Observations on Reversionary Payments, (vol. i. p. 183, and vol. ii. p. 443.)

86. From the preceding statement, the Carlisle table of mortality, (No. II. in Mr. Milne’s Annuities, or No. V. at the end of the article Annuities in this work, and the Northampton table, (No. XVII. in Dr. Price’s Observations], we have derived the following :—
[table]

87. This table shows that the law of mortality exhibited in the Carlisle table is almost exactly the same as that which has prevailed among the members of the Equitable Assurance Society. And although the members of such a society, when they first enter, are select lives, they are not, even then, so much better than the common average, as many persons suppose; for the more precarious a life is, the stronger is the inducement for parties interested in its continuance, to get it insured, so that bad risks are frequently offered to such companies. And many proposals for insurance are accepted by the directors, that are not thought very eligible at the time, in cases where they are not aware of any specific objection to the life proposed.

88. Besides, it is to be considered, that of the number in a society at any one time, but a small proportion can have been recently admitted, and in a few years from the time of admission, the members will generally have come down to the common average of persons of the same ages.

89. It ought also to be observed, that most of the tables of mortality that have been published, have been constructed from observations made upon the whole population of very large towns, such as London, Paris, Vienna, and Stockholm; in each of which there are particular quarters inhabited only by the very lowest of the people, who, unfortunately, are also very numerous, badly clothed and fed, therefore exposed to serious injury from the inclemencies of the weather; extremely ignorant and vicious, indulging in the abuse of spirituous liquors, and inattentive to cleanliness both in their persons and habitations, which lastare crowded, badly ventilated, and surrounded with mud and the putrid remains of animals and vegetables. These are the nests of contagious diseases, in which they are generated and kept alive, where they at all times occasion greatmortality, though not so much within the last forty-five or fifty-five years as previously, and from which, when circumstances favour them, they spread amongst the rest of the people.

90. It is, therefore, obvious, that in such places, the average mortality at every age, must be considerably greater than that which prevails only among the middling and higher classes of society, even in such towns.

91. But the lives upon which leases, annuities, reversions, and assurances depend, are very seldom exposed to the influence of the causes of mortality mentioned in number 89∙ Whence it follows, that a table of mortality on which those causes have had no great influence, is best adapted to the valuation of such interests.

And these kind of valuations are the most important purposes to which tables of mortality can be applied.

92. The number of years in the mean duration of life from birth according to a table of mortality properly constructed from the necessary data, will, when the population has remained stationary for a century or more, be the same as the number of persons in the whole population, out of which one dies annually (20). When the population has been increasing, the mean duration of life, according to the table, will be less than the number out of which one dies annually in that population; but the difference will be small, except under particular circumstances, as appears by the following statement.
[7:15:556]
[table]

93. The above mentioned table of mortality for Glasgow, which the author has had by him several years, he expects to publish soon.

The high number in the column of differences for females in that place, arises from the small mortality amongst them, which was occasioned principally by the great influx of healthy females between the ages of 15 and 30, at which period of life the rate of mortality amongst them was small; its minimum for them being in their 18th year.

Between the ages of 10 and 15 the numbers of the two sexes were just about equal, whilst between the ages of 15 and 30 the females were more numerous than the males in the ratio of 3 to 2; and this accounts for the great number of females (42∙32), out of which one died annually there, which necessarily raises the number out of which one died annually in the whole population of both sexes, and therefore the number in the column of differences (in the line numbered 10) for the whole population of both sexes in Glasgow.

94. Similar causes probably produced similar effects, although in a much less degree in Stockholm.

95. When tables of mortality are constructed from the numbers of deaths only in the different intervals of age, without comparing them with the numbers of living persons in the same intervals; such as that formed by columns C and D of Table V. at the end of this article, and the population is increasing. The number ofyears in the mean duration of life from birth, according to that table, will fall short of the number of the people, out of which one dies annually,by a much greater number than in the case we have just been considering, of the table of mortality having been properly constructed from the necessary data: as the following statement willshow.
[table]

96. In both of the above statements, where the sexes are not mentioned, the table is for both without distinction.

97∙ In places where the increase of the population was slow, the numbers set against them in the column of differences are smaller than where the population increased more rapidly.

98. In thetablesof mortality for Belgium and Montpellier, the sexes were distinguished, but not in the given number of the whole population, as well as the whole number of deaths in each of those places, and for that reason the sexes could not be distinguished for those two places in this last table.

99- When what we have shewn here is clearly understood, and the proportion of the people dying annually is known, it will not be difficult to judge whether a table of mortality for that people has been constructed properly from the necessary data; or, what is much more common, and more easily effected, merely by summation of the deaths at all ages. For in the case of the correct table of mortality, the difference obtained in the manner stated above, will probably not exceed 2; nor in the case of the incorrect table, will it be likely to be less than 7, upon the supposition of the population having increased generally for a considerable number of years preceding the termination of the observations; if for a whole century, so much the better.
[7:15:557]

100. The probable life at birth, or the age to which half the number born attain, will also be a good criterion for enabling us to judge, by comparison, whether a table of mortality has been correctly constructed from the necessary data or not; provided that, in the places the compared tables have been constructed from, the children have been similarly circumstanced, or nearly so.
[table]

In Belgium vaccination was practised during the whole period of the observations, in Sweden only during about 1½ out of the 5 years’ observations.

101. From all that has now been stated, we are entitled to conclude, that the Belgian table of mortality has been constructed either from the registers of burials alone, or only from the statements of the numbers living in the different intervals of age at the time of the enumeration; most probably from the burials alone. Μ. Quetelet appears now to be aware that such tables are very incorrect. In his late work sur V Homme et le Dévelopement de ses Facultés, ou Essai de Physique Sociale, 2 torn. Paris 1835, in 8vo, after giving the above mentioned table of mortality for Belgium, in which only the numbers attaining the different ages are given, without the decrements of life, or its mean or probable duration at the different ages, he states the mean duration of life from birth according to that table, and then proceeds thus, (tome i. p. 166) :—“D’après le dernier ouvrage de Μ. Rickman, la vie moyenne serait en Angleterre de 33 ans (32 pour les hommes, 34 pour les femmes).^[24. Preface to the Population Abstract. 1831. ] On l’estime en France de 32∙2 ans d’après le chiffre des naissances.^[25. Annuaire du Bureau des Longitudes, pour tannée 1834, p. 102. ] Du reste, ces calculs supposent une population stationnaire, et nous aurons occasion de voir qu’ils peuvent conduire à des erreurs assez graves.”

102. Reasoning as in Nos. 68 and 69, it will be seen that when the number of the people has been decreasing for a series of years, the deaths will be more densely distributed among the advanced ages, and more rarely in the early periods of life, than if the number of the people at every age, and the law of mortality had remained always the same. Consequently, in the table of mortality constructed from such data, merely by taking the successive sums, in retrograde order, from extreme old age to birth; those successive sums, which are the numbers of the living at the different ages in the table so constructed, will be greater at advanced ages and less in early life than if the population had remained stationary, as stated above. So that the errors of the incorrect table would, in this case, be of the opposite kind to those of the common tables, constructed in á similar way from the deaths only, in an increasing population. From the general increase of arts, manufactures, commerce, and civilization, ever since tables of mortality were first formed, the population has been increasing more or less rapidly in almost every place, for which a table of mortality has been constructed. But in Amsterdam we have an instance of the population having continued to decrease for half a century or more. We here present a view of it since the year 1622.

Population of Amsterdam.
[table]

103. The information on this subject is scanty and difficult to procure. Kersseboom took much pains in endeavouring to make just estimates of the population from the annual births and deaths; and taking it to be 35 times the number of annual births, he estimated the population of Amsterdam in 1742 at 241,000 persons.

Three only of the six numbers stated above, viz. those for the years 1622, 1826, and 1830, were determined by actual enumerations at the times stated. Although Μ. Smits, the secretary of the Statistical Commission, relative to the population of the Netherlands, is not mentioned in the above table, we are greatly indebted to him. In his Statistique Nationale he gave a table, (No. 10, p. 82), shewing the number of deaths that took place in Amsterdam in each year of the 18th century. Μ. Lobatto has given them in the place above referred to for each of the ten years 1816-1825; and Μ. Quetelet, in the part of his work referred to above, has given them for each of the 17 years, 1816-1832, and states that in the year 1777 the mortality was 1 in 27; the number of deaths in that year was 8939, whence the population inserted in the table is derived. Μ. Lobatto states, on the authority of Professor Van Swinden and of Μ. Nieuwenhuys, that from 1774 to 1813 there died annually 1 of 26; the deaths in 27 years, 1774- 1800, were 233,510, the annual average number, therefore, was 8648∙5, and multiplying this by 26, we obtain 224,862, the mean number of the people during these 27 years, which is stated in the above table to have been the population in 1787, the middle year of the 27.

104. The enumeration in 1622 was made in levying a capitation tax, which was exacted with great strictness, even in every receptacle for paupers, the master or owner of it was obliged to pay the tax for each inmate. This enumeration appears not to have been known of, either by Kersseboom or by Struyck at the time of his first publication on the subject; but an original paper, with many particulars which he gives, was afterwards communicated to him. Struyck, after taking great pains with the subject, stated his opinion, that in 1753, Amsterdam did not contain 200,000 inhabitants.

105. Μ. Lobatto, at the end of his Beschouwing ^[26. Beschouwing van den <ιard, de voordelen, en de inrigting der Maatschappijen van Levensverzekering, &c., door R. Looatto; Amsterdam, in 8vo, 1830. ] , &c. gives two tables of mortality for Amsterdam, one for males, the other for females, constructed from the deaths that took place during the ten years 1816-1825, with the expectation of life at every age, and we here give the same particulars for it as are given for some others above, but marking the difference (—) as it is of the opposite kind to those which resulted from an increasing population.
[table]
[7:15:558]

106. This low mortality of one in 29∙22 was obtained by Μ. Lobatto stopping at the year 1825, which he himself states was on account of the mortality having been high in the two following years, 1826 and 1827. He obtained the annual mortality of 1 in 29, by dividing the number of the people in 1826, the year after the end of the term, by the annual average number of deaths during the term. During the 12 years 1821-32, of which 1826 was the middle one, the annual average number of deaths was 7,336∙18, and there died annually, on an average, one of 27’369; the dif ference in the above statement should therefore be —4∙8δ or nearly 5; which is the true excess of the number 0 f years in the mean duration of life, above the number of persons out of which one died annually.

107. For some of the most important applications of the facts and inferences stated in this article, the reader is referred to the article Annuities in this work, where he will find that the valuation of Assurances or Reversions dependent upon lives is also treated of.

TABLE I.

In all Sweden and Finland during the Five Years ending with 1805.
[table]

The Numbers of Births during the same Five Years were,
[table]
[7:15:559]

TABLE II.

Exhibiting the Law of Mortality which prevailed in all Sweden and Finland, during the Five Years ending with 1805.
[table]
[7:15:560]

TABLE III.

According to the Law of Mortality that prevailed in all Sweden and Finland during the Five Years ending with 1805.
[table]

TABLE IV.

Showing the Number of Years in the Expectation of Life at every fifth year of age, from birth to 90 years, according to different Tables of Mortality.
[table]
[7:15:561]

tn cC

I'

? in

“e 0

5<⅛ if h α

≡ 3 g 1

+ § ∣t l, „

O - u £u fS - g o g ⅛r ⅜~ ∙

S ⅛ ft .Γs∙ £- ÿ e o<⅛ O ÿ § § f fl≡ J≡-

I·® STS*? I

Pf‰

§ ≡'

<Q s

⅛ A
[table]
[7:15:562]

TABLE VI.

Exhibiting the Expectation of Life in Sweden and Finland, both according to Columns A and D of the preceding Table.
[table]

TABLE VII.

Exhibiting the Increase of the Total Population of Sweden and Finland, and the Decrease of the Absolute Number above 90 Years of Age, as well as of the Proportion of the whole Population above that Age, throughout the latter half of the Eighteenth Century.
[table]

(A. A.)