ItIORTALITY, LAW OF. While there are few future events the date of whose arrival is more uncertain than that of death to any one man, on the other hand, the average duration of a multitude of human lives is found to be in accordance with a law which operates as surely as that of gravitation. If it be asked how many lives must we have before we can depend on obtaining from them a duration equal to the general average, the only answer that can be given is, that the more we have the more nearly must we approach to this result; the fluctuation ultimately becoming so small as to lie of no effect. So long ago as early in the 17th e., a certain John Graunt of London pub lished what he called .gatural and Political Observations on the Bills of Mortality. This work has been called "the earliest movement in economical arithmetic, and the closest approximation to the data on which life assurance is founded." About the same time. sir William Petty gave to the world many curious calculations and speculations on the same subject. In 1693 Dr. Halley published the Breslau tables of mortality, and this was the first work which really raised the subject to the rank of a science. Ilalley's speculations had, however, been preceded by those of Pascal in France, and of De Wit in Holland; and the latter famous man is probably entitled to be considered as the first who has applied the doctrine of probabilities to the valuation of life in the question of annuities. Ilis treatise will be lound in the second volume of the Assurance Magazine. Halley's tables are printed in the Philosophical Transactions for 1693, No. 196. In 1713 J. Bernouilli's important work was published; and in 1742 Dr. Price, availing himself of the principles laid down by Ilalley, and of data previously published by "John Smart of Guildhall, London, gent.," gave tables of mortality for London. In 1716 M. Depar cieux published at Paris his Essai sur les Probabilias de la Vie llumaine, in which lie gave six valuable tables. In one of these, computed from the registers of different relig ious houses, it was shown, for the first time, that female life is superior to male. In 1770 appeared the first edition of Price's Observations on. Reversionary Payments, The epeculations Simpson, and De bloivre about the same time were of much importance. Mortality tables are tables showing the operation of the law of mortality. The correct method of framing them is by analyzing and collating accurate and suffi ciently extensive statistics of life and death. They enable us to form a fair estimate of the number of human beings who will die at the end of a given period out of a given number alive at the beginning of it; and hence, the chance of life and death to the indi vidual, and the mean duration of life at any age. Tables showing the mean duration of life have been constructed in two ways: 1st, From statistics of deaths alone; and 2d, From statistics of life and death. By the first plan, they would be deduced as follows: Suppose, on searching a parish register, that we found recorded 100 deaths of children in their first year. we should assume that, on an average, + a year of life would have fallen to each. This gives 50 years of life among 100. if we found that 60 had died in their second year,•assigning one year and a half to each, we should have 60 X 1.5 = 90 years among the 60: and so on for every age up to the oldest on the register. The sum of all the years enjoyed, divided by the numbers who have enjoyed them, will give the mean duration of life from birth; and the sum of all the yeats enjoyed after a given age, divided by the numbers who have enjoyed them, will give the Mean duration at the given age; in both cases as nearly as the data enable its to give it; but the data are insufficient. Suppose we found by a register for 1873 that 100 children had died in their first year and one man in his 96th, it is plain that, to make this ratio a fair one, there ought to have been a4 many births in 1778 as in 1873. If there have been only half as many born at the former date as at the latter. then we must put two lives into the cal culation to make it correct; and we must proportion our results similarly at all interme diate ages. Again, suppose four deaths at age 23 to be registered, we cannot tell how many of those born in 1850 may have emigrated from one parish, nor do we know how many horn elsewhere in that year may have come-into it. For the rule and formula for obtaining the mean duration of life under the second method, which is an absolutely pertain one see LIFE, MEAN DEEATION or. The following are the tables now most generally used by assurance and annuity offices in this country: I. The Northampton (Dr. Price's). This table was framed by Dr. Price from the register of burials in the parish of All Saints, Northampton, 1735-80. Being constructed on deaths alone, it has, as was to have been expected, proved faulty. It gives the probabilities of life too low at the younger and middle. ages; and those offices which still use it—and there are a good many—have some difficulty in kepiug themselVes right. II, The New North ampton (Nos. 1 and 2). These tables were constructed by Dr. Farr. See Eighth Report of the Registrar-General for England. pp.. 277-348. No. 2 is based on the deaths alone in Northampton during the seven years 1838-44. In its results it agrees almost exactly with that of Dr. Price. No. 1 was deduced from a comparison of the deaths during 1838-44 with the census returns of 1841. It differs widely from No. 2 and from Dr. Price. By the two latter, the mean duration of life is respectively found as 24.88 years and 25.18 years. By No. 1 it is 37.5 years. III. The Carlisle. This table was constructed from observations made by Dr. Heysham at Carlisle, 1780-87. It is now generally understood that the mortality in towns is understated at ages 15-35, owing to the immigration of healthy men and women from the country. Again, the female pop
uhtion of Carlisle was excessive during the period in question, and the extent of the observations was limited. Owing to these facts, this table gives rather too low a rate of mortality, and is a little irregular In its graduation. In a table prepared by W. 'I'. Thom son, esq., in a Report on the Ministers' Widows' Fund of the Church of 'Scotland, 1861, he shows that the lives of the Scotch clergy are about half a year better up to 44 than the Carlisle; at 45, they are equal; and at 45 to 80 they are half a year worse. There after they vary. The widows are half a year better up to 61, equal at 62. and nearly so to the end. Probably the Carlisle gives a fair mortality rate for a healthily cirettia stances] papalation. IV. The Government. These were computed by Mr. Finlaison on the lives of 22,000 nominees for government annuities. They are chiefly important as giving a- view of the value of female life, but this view is one which differs widely from those given either by the "Experience" or by the "English" table. At age 20. for instance, the mean duration of female life is, by the Government table, 5i years more than the male; by the Experience, it is 4 years less. In some measure this wide diver gence may [wimps be accounted for by the fact slut the Government results are deduced from annuitants, th • Experience from assured lives. The experience of late years has, however, led to som modification in the relative values of male and female life in gov ernment tables. V. The English (Nos. 1, 2, and 3). No. 1 is deduced from the living by the census of 1841, and from the deaths at corresponding ages in the same year. See 5th and 6th Reports of the Registrar-General for England, where the tables will be found, and their construction explained. No. 2 is deduced from the living in 1841, and from the deaths in the seven years 1838-44. No. 3 is deduced from the population in 1841 and in 1851, and on the deaths for the 17 years 1838-54; male and female life being calculated separately and in combination. These " English" tables probably give the results of the average mortality of England more correctly than any others which we have. They are the result of enormous labor on the out of Dr. Farr. The observations were taken on the plan recommended by prof. de Morgan and Mr. Griffith Davies. VI. The Experience. These were prepared by a committee of eminent actuaries on the data afforded by the combined experience of 17 life assurance offices The objections to which they are liable are, that certain lives, having been more than once assured, have appeared twice or oftener as elements in the calculations; that tha average term over which the observation of the offices extends is only eight and a half years; and it is prob able that the mortality which will prevail in assurance societies when they have reached maturity is somewhat understated. See letter by Dr. Farr in Appendix to 10th Report of Registrar-General, p. 11. Further, the data for old ages were deficient, and this of course affects the whole. Many curious results are brought out by this table. It shows that "town" assured life is superior to "country;" that female assured life is on the whole inferior to male: and that Irish life is worst of all. At arre 20, "town" mean duration is 41 years, 2 mouths; country, 40 years, 4 months: Irish, 34 years, 11 months. The observations of the Standard assurance company do not, however, bear out these results; and they are doubtless so largely affected by the elements of care in selection as to render it impossible to found on them any conclusion of practical value. A new set of "Experience" tables was published in 1872, based on the mortality experiences of twenty offices, ten English and ten Scotch. They do not show any widely different results from the former Experience tables. These form a very valuable set of tables. They give the results of English and Scotch experience united, and of Scotch sepa rately.
In all tables deduced from the experience of assurance and annuity soeieties, the fact of selection must not lie lost sight of, either in using them for the sake of comparison, or as the basis of other tables. Actuaries, however, seem to be generally of opinion that the selection exercised by assurance societies does not really lowertheir rates of mor tality below the general average; without selection, their rate would he above the gen eral mean; for, it will be observed, that the public are continually selecting against the offices by offering inferior lives, and good lives often surrender their policies, while lives which have become had hardly ever do so, Again, the value of medical examination gradually disappears, and in ten years at most it is quite lost. Five to seven years is indeed now held by the assurance offices to exhaust its value. See •1inutes of the House of Commons' Committee on Assurance Associations, 1853; and Life-Contingency Tables by E. .J. Farren, pp. iii.-xiii. Though female life is, as a whole, undoubtedly superior to male, yet as there are more critical periods in it, it is probable that the public may more frequently select it than male life against the societies. A valuable report on the Madras military fund (Leuidon, 1863) gives tables coastineted on the mortality rates veiling among the officers, wives, and widows interested in the fund. As they have been prepared by eminent men on very ample data, they will probably he very valuable to societies transacting business in India.• The following is a view of the mean dura tion of life, at the beginning and at each decennial period, according to sonic of the tables mentioned above: In the present article we have considered the law of mortality chiefly as it bears on insurance and other monetary transactions. The wider view of the subject, as varying with occupation and in different ages and countries, will be illustrated under the head of VerAL STATISTICS.