HISTORY OF BILLS OF MORTALITY.

From the Encyclopedia Britannica.

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 (4to.) The first, dated March 1, 1738, was entitled, Eerste Verhandeling toteen Proeve om te weeten de probable menigte des volks in de provintie van Hollandt en Westvrieslandt. The second, dated May 15, 1742, Tweede Verhandeling bevestigende de Proeve om te weeten de probable menigte des volks in de provintie van Hollandt en Westvrieslandt; and the third, dated August 31, 1742, Derde Verhandeling over 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 proper 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.

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, 5,500 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 writers on this subjeet (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 number of lives, whose current year of age at the time of their nomination was given precisely in these tables, were,

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

These, however, are only specimens of M. 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 one 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 Uitreekening der Lyfrenten," published at Amsterdam in 1740, at the end of the quarto volume, commencing with his "Inleiding 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 five 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 staat 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. M. 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 twentyfive 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, M. 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 M. 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 M. Kersseboom's, together with the expectation of life at, or its average duration after each age, both according to his own and M. 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 M. 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, M. Deparcieux published (at Paris, in 4to.) his addition à l'Essai sur les Probabilités de la duree 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 the documents.

In these the sexes were not distinguished. The other table of mortality M. Deparcieux constructed from statements sent to him by M. Wargentin 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.

M. Deparcieux states, (p. 28,) that in 1744, he suggested to M. 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 Recherches Statistiques.

M. 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 M. Dupre de Saint Maur, from the registers of twelve country parishes in France, and three parishes of Paris; which M. 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 M. Kersseboom on this table may be seen in the Philosophical Transactions for 1753. M. de Saint Cyran, corrected some of its most obvious errors, and inserted both the original and his corrected copy in his Calcul des Rentes Viageres. (Paris, 1779, in 4to.)

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 Mém. de l'Acad. Roy. de Berlin 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 show how it may be