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 gress of the science, had been, to direct the public attention to these inquiries, by showing their important uses in the affairs of life; and to procure the requisite data for forming tables of mortality, that should illustrate the laws according to which human life wastes under different circumstances, by exciting the curiosity of intelligent men who had the necessary leisure and means of information. The ingenious author had, accordingly, been furnished with the necessary abstracts of mortuary registers which had been kept with these views, by Dr Haygarth at Chester, Dr Aikin at Warrington, and the Rev. Mr Gorsuch at Holy-Cross, near Shrewsbury, since the publication of the first edition; also by Mr Wargentin, with the mean numbers both of the living, and the annual deaths in all Sweden and Finland, for twenty-one successive years, in all of which the sexes were distinguished; and from these data, he constructed tables of mortality that threw great light on the subject. He also inserted in this edition, an improved table of mortality for Northampton; and, what had been so long wanted, a complete set of tables of the values of annuities on single lives, at six rates of interest, and on two joint lives at four, all calculated from the new Northampton table. The combinations of joint lives were sufficiently numerous to admit of all the values not included being easily interpolated. Besides these, he also gave tables of the values of annuities on single lives from the Swedish observations, both with and without distinction of the sexes, and on two joint lives without that distinction.

The values given in these tables are too low for the general average of lives, at all ages under 60; but in the treatise af Mr Baron Maseres on the Principles of the Doctrine of Life-Annuities, which was published in the same year (1783), others were given, calculated from the table of mortality which M. Deparcieux constructed from the lists of the Nominees in the French Tontines. The tables for single lives are calculated at twelve different rates of interest from 2 to 10 per cent.; but these for joint lives, only at 3½ and 4½ per cent.; and the combinations they include are only those of ages that are equal, or that differ by 5 or 10 years, and the multiples of 10.

There is reason to believe that the values in these tables, at all ages under 73 or 80 years, are nearer the truth, for the average of this country, than any others then extant; but certainly for the average of lives on which annuities and reversions depend. After that period of life, however, they are too small; and, in most cases, it is difficult to derive the values of joint lives from them with sufficient accuracy, on account of the contracted scale they have been calculated upon.

It was not Dr Price’s object to deliver the elements of the science systematically; but he treated most parts of it with great judgment, enriched it with a vast collection of valuable facts and observations, and corrected several errors into which some of the most eminent writers upon it had fallen. The mathematical demonstrations (which are given in the notes) are much inferior to the rest of the work.

The values of reversionary sums and annuities, which depend upon some of the lives involved failing according to assigned orders of precedency, had been approximated by Mr Simpson in his Select Exercises, and by Mr Morgan in his Doctrine of Annuities; but the latter gentleman first gave accurate solutions of problems of this kind, in the Philosophical Transactions for the years 1788, 1789, 1791, 1794, and 1800.

Except by the solution of these problems, the science had not been materially advanced, during a period of mere than thirty years that had elapsed since the appearance of the fourth edition of Dr Price’s work, when Mr Milne published his Treatise on the Valuation of Annuities and Assurances, on Lives and Survivorships, in the beginning of last year (1815).

The work consists of two volumes; the first is mathematical, the second entirely popular, except the notes, and a few of the tables. The algebraical part of this article is merely a short abstract of the first volume, and may serve as a specimen of the manner in which the subject has been treated there; but the construction of tables of mortality, which forms the subject of the third chapter, has not been noticed here; neither is the valuation of reversionary sums or annuities depending upon assigned orders of survivorship, treated in the present article; and these are parts of the work, which will not be found the least interesting to mathematicians.

The second volume contains upwards of fifty new tables, with a few others that had been published before, but have been reprinted either on account of their value, or scarcity, or both. Four of the new ones are tables of mortality constructed by the author, from registers kept at Carlisle and Montpellier, and in all Sweden and Finland, since the period of the observations Dr Price made use of; the sexes are distinguished in the tables for Sweden and Montpellier, but not in that for Carlisle. This last is the only table, besides those for Sweden and Finland, that has been formed from the necessary data,—enumerations of the living, as well as registers of the deaths in every interval of age.

Twenty-one of these tables, being the seventeenth to the thirty-seventh inclusive, in the collection at the end of the work, render it easy to apply the algebraical formulæ to practical purposes, and numerous examples of such applications are given. They have all been calculated from the Carlisle table of mortality; those of the values of life-annuities on the same extensive scale, with those which Dr Price derived from the Northampton table. It is the author’s opinion that the values of interests dependent upon the continuance of the failure of life, may be derived from them more correctly than from any others extant, and he has taken considerable pains to assist his readers in judging of this for themselves.

Besides the tables, the principal contents of the second volume, are explanations of their construction and uses; many of them relate to the progress of population,—the comparative mortality of different diseases—of different seasons,—and of the two sexes at every age—the proportion of the sexes at birth—and that of the born alive to the still-born of each sex.