£ 22 J 



II. On the Method of determining^ from the real Probabilities 

 of Life, the Values of Contingent Reversions in which three 

 Lives are involved in the Survivorship. By William Morgan, 

 Esq. F. R. S. 



Read December 12, 1799. 



ON SURVIVORSHIPS. 



1 he several papers which I have had the honour of communi- 

 cating to the Royal Society, on the doctrine of contingent re- 

 versions, contain the greater number of those cases in which 

 three lives are concerned in the survivorship. With the view of 

 completing this subject, I have been induced to investigate the 

 remaining problems ; and, having succeeded in the solution of 

 them, I hope the following will not be considered as an impro- 

 per addition to my former communications. 



Being anxious to render this paper as concise as possible, I 

 have omitted to state at length the different contingencies on 

 which the payment of the given sum depends ; trusting that, 

 from an attentive perusal of my former demonstrations, these 

 will appear to be so plainly expressed by the several fractions 

 in each problem, as to render a more ample description of them 

 unnecessary. 



problem 1. 

 To determine the value of a given sum, payable on the death 



