s8 Mr. Morgan on Survivorships. 



assistance of the ist problem in my last paper,* supposing, 

 instead of a. given sum, it were required to know the value of 

 the reversion of a given estate. For, since the possession of 

 this estate is an event which must certainly take place, and the 

 only point to be determined is the time in which it will pro- 

 bably happen, it is obvious that no event can postpone the pos- 

 session, but the contingency of C's being the second that fails, 

 of the three lives. If, therefore, the sum of the values of an 

 annuity on the life of B after A, provided A should die before 

 C, and of an annuity on the life of A after B, provided B should 

 die before C, (both found by the problem just mentioned,) be 

 subtracted from the whole value of the reversion after the joint 

 lives of A and B, the remainder will be the value required. Let 

 X and Y respectively denote the annuities found by problem 

 ist, (Phil. Trans. Vol. LXXXIV.) then will the general rule 

 expressing the value of an estate be = V — AB — X + Y, and 



s 



consequently of a given sum == — : x V — AB — X -f- Y, 



which, when the lives are equal, may be reduced, as in the 



s 



former cases, to ~ x V — C — CC + CCC. Q. E. D. 



PROBLEM III. 



To determine the value of an estate, or of a given sum, after 

 the decease of A or B, should either of them be the first or last 

 that shall fail, of the three lives, A, B, and C. 



Solution. 

 The reversion of the estate in this problem, like that in the 



* Phil. Trans, for the year 1794, page 235. 



