A table of yearly rates may be converted into a table of decre ments, as follows. Assume it number to be born, then from the table of yearly rates, 1, = (1 — = (1 — sa,)1„ &c.
If the population, say of a town, remained unaffected, or sensibly unaffected by immigration or emigration, that is, if all who were born in the place, and no others, were registered in the burials of the place, the burial registers would form a mortality-table, provided the rate of increase of the population were steady and known. For, firstly, if the population had remained stationary for a long time preceding the com mencement of registration, the yearly deaths and births being equal, and if the mortality had also remained stationary, the burials of any one year, tho parties being distributed according to age, would show the law of mortality as follows :—Suppose the registers of a year showed that x„ died in their first year, )4, in their second year, and so on. the equality of births and deaths shows that Si,, + x, + m, +... trout have been born in that year, and the stationary character of the law of mortality being assumed, it follows that of m„ • at + persona born, it is the law of the mortality that Si,, die in their first rear, or that Si, + + ...survive ; similarly that m, + aurvivo two years, and so on. But if the population be in a state of Mercer:4e, and if the annual ratio of increase be that of 1 : 1 + p, those who die at the age x — 1 and .e cannot be incorporated in the same table, since the first are a portion of a table beginning with a larger number of births. The former then must be reduced, or the latter increased, in the proportion of 1 : 1 + p: so that if m,, &c., be the deaths In the first second, &c. years of age by the register, the table must. run thus : of Si,, + m + + 0 + + • • • • persons bum, die in their first year, as, (1+A) in their second, and so on.
A table of mortality may also be given in the form of a table of the mean durations of life, calculated as in LIFE, M KAN DURATION OF. Or the table of mean durations may be calculated from the table of yearly rates, as follows :—Let e, be the mean duration of the lives aged it, and ea, the yearly rate at the same age: then e • -4 by which, beginning from the end of life, the mean duration at each age may be computed from that at the ago next higher.
Various tables of these several kinds have been constructed, begin ning with that made by Halley from the town of Breslau, and ending with that formed by the Equitable Insurances Office from its own materials, and with the Actuaries' Table presently mentioned. If we were to look to the wants of the subject, whether as a physical inves tigation or a statistical one, wo should find that it is everywhere in the merest infancy. The fact of a difference of mortality between the two sexes is established, and it also seems to be known that whero the occupations of females are not above their strength, their mortality is leas than that of males ; but no settled determination of the amount of difference his been obtained. As to whether married or single life
is the longest, whether the age of the parents, or the relative age, affects the mortality of the children, whether the earlier children of a marriage differ in their law of mortality from the later, &c.. we have no trustworthy information at alL In some foreign countries, as in Sweden and Belgium, the attention laid by the government to statistical subjects has produced some results which are worth a good deal ; the reader may consult the article in the ' Encyclopedia Britan niin; already cited, for reference to them. Wo shall now give merely We dates and titles of the most remarkable earlier tables connected with the subject.
1638. Parish registers first kept in England.
1540-41. The statute 32 Henry VIII., c. 28, enabling ecclesiastical persons and corporations to grant, leases for three lives, or turn ty-ane years. From this permission springs, we think, much of the attention which has been paid to the subject of life leases in England. It gave rise to certain tables of the value of leases which were called' dEcroid's Tablas,' and which were put together, as was thought by later writers, about the end of the reign of Henry VIII. They assume a rate of interest greater than 11 per cent. After the Restoration, when the interest of money had very much fallen, the ecclesiastical lessors began to rake their fines. This occasioned great dissatisfaction, and frequent representations to the House of Commons, which, though it panned no law, in several cases recommended to particular bishops, &c., an adherence to the old rule. Attention began to be turned towards the actual value of life. In 1662 John (3raunt published ' Natural and Political Observations on the Bills of Mortality.' often reprinted. lo 1074, Sir William Petty, in a paper in the Philosophical Trans actions,' proposed a law of mortality of the following kind : the probability of one life surviving another, after the ago of 16, is inversely as the square roots of the ages In 1635 were published the well known "Fables for renewing and purchasing the leases of Cathedral Churches and Collisges; the methods of which were certified to be correct by Newton, and which therefore have been frequently called Newton's Tables. About 1720, If not before, a letter called ' The Value of Church and College Leases considered,' was appended to these tables, and a very sharp controversy took place, which produced a great many pamphlets; the party of the lessees appealing to custom, the lessors showing from the value of life and interest of money that the church landlord dealt more leniently with his tenant than the layman, as was indeed the case. Among the writings which arose out of this controversy was ' The Gentleman's Steward Instructed, 1730, by John Richards, containing the most complete tables of annuitiee which had been published.