REVERSE

In Numismatics, the opposite to the obverse or face of the coin or medal. See Obverse, Numismatics. REVERSION, in Law, is defined to be the residue of an estate in lands, tenements, or hereditaments, left in the grantor, to commence in po e ion after the determination of some particular estate granted by him. REVERSION OF SERIES, in Algebra, is a method of expre ing the value of an unknown quantity which is involved in an infinite series of terms, by means of another series of terms involving the powers of the quantity to which the proposed series is equal. Thus, if the proposed series be 2 = a jr + 6 ^2 ^ c *3 + d j: to commence upon the death of an individual, and to continue for a term of years certain, its value is found by computing the value of the annuity for the a igned period, and proceeding as in the above example; but when it consists of an annuity commencing upon the death of one individual, and terminable upon the death of another, it becomes nece ary to have recourse to tables of annuities on joint lives. Thus, if A. becomes entitled upon the death of Z?. to an annuity of 1/. for the remainder of his life, the present value of the rev<jrsion, or of A:s interest, is equal to B — A B; where B denotes the present value of the annuity on the life of B., and A B the value of the annuity on the joint lives of A. and B., that is, to continue only so long as both remain alive. The four following rules give the solution of all the cases of reversionary annuities which can arise when three lives are concerned, and it is seldom that a case occurs in practice involving a greater number. It is to be observed, that the two letters A B standing together denote, as above, the value of an annuity on the joint lives of ^. and B., B P that of an annuitj^ on the joint lives of B. and P., A P Q that of an annuity on the joint continuance of the three lives A.,P.,(i., and so on. Let R be the value of the reversionary annuity in each case. 1. On a single life A., after the longest of two lives P. and e. y R = A - A H — A Q -f A P Q. 2. On the longest of two lives A., B., after a single life P.; R = A + B — AB — AP — BP+ [s. 1063]