SURVIVORSHIP

, the doctrine of reversionary payments that depend upon certain contingencies, or contingent circumstances.

Payments which are not to be made till some future period, are termed reversions, to distinguish them from payments that are to be made immediately.

Reversions are either certain or contingent. Of the former sort, are all sums or annuities, payable certainly or absolutely at the expiration of any terms, or on the extinction of any lives. And of the latter sort, are all such reversions as depend on any contingency; and particularly the Survivorship of any lives beyond or after other lives. An account of the former may be found under the articles Assurance, Annuities, and Life-annuities. But the latter form the most intricate and difficult part of the doctrine of reversions and lifeannuities; and the books in which this subject is treated most at large, and at the same time with the most precision, are Mr. Simpson's Select Exercises; Dr. Price's Reversionary Payments; and Mr. Morgan's Annuities and Assurances on Lives and Survivorships. The whole likewise of the 3d volume of Dodson's Mathematical Repository is on this subject; but his investigations are founded on De Moivre's false hypothesis, viz of an equal decrement of life through all its stages, and which is explained under Life-annuities: but as this hypothesis does not agree near enough to fact and experience, the rules deduced from it cannot be sufficiently correct. For this reason, Dr. Price, and also the ingenious Mr. Maseres, cursitor baron of the exchequer (in two volumes lately published, entitled the Principles of the Doctrine of Life Annuities), have discarded the valuations of lives grounded upon it; and the former in particular, in order to obviate all occasion for using them, has substituted in their stead, a great variety of new tables of the probabilities and values of lives, at every age and in every situation; calculated, not upon any hypothesis, but in strict conformity to the best observations. These tables, added to other new tables of the same kind, in Mr. Baron Maseres's work just mentioned, form a complete set of tables, by which all questions relating to annuities on lives and Survivorships, may be answered with as much correctness as the nature of the subject allows.

Rules for calculating correctly, in most cases, the values of reversions depending on Survivorships, may be found in the three treatises just mentioned. Mr. Morgan, in particular, has gone a good way towards exhausting this subject, as far as any questions can include in them any Survivorships between two or three lives, either for terms, or the whole duration of the lives.

There is, however, one circumstance necessary to be attended to in calculating such values, to which no regard could be paid till lately. This circumstance is the shorter duration of the lives of males than of females; and the consequent advantage in favour of females in all cases of Survivorship. In the 4th edition of Dr. Price's Treatise on Reversionary Payments, this fact is not only ascertained, but separate tables of the duration and values of lives are given for males and females.