I 40 ] 
'W. On the Method of determinings from the real Probabilities of 
Life , the Value of a contingent Reverfon in which Three 
Lives are involved in the Survivorfoip . By Mr. William 
Morgan ; communicated by the Rev . Richard Price, D . D . 
S. 
Read January 29, 1789. 
I N a Paper which I had lately the honour of communicating 
to the Royal Society, refpedting the method of deter- 
mining the values of reverfions depending on furvivorfhips 
between two perfons from the real probabilities of life, I ob- 
ferved, that the inveftigation of thofe cafes in which three 
lives were involved in the furvivorffiip (though attended with 
much more difficulty) might, however, be effedted in a fimilar 
manner. The further purfuit of this fubjedt has now con- 
vinced me that, as it is never fafe, fo likewife it can never be ne- 
ceffary to have recourfe to the expectations of life in any cafe; 
and that the foiution even of thofe problems which include three 
lives is far from being fo formidable as at firft fight it appears to 
be. I am fenfible of the impropriety of entering minutely in 
this place into the vaft variety of propofitions which refer to the 
different orders of furvivorffiip between three lives ; but as the 
following problem feems to be of confiderable importance on 
account of its being applied to the foiution of many other pro- 
blems, the demonftration of it, perhaps, may not be thought 
an improper addition to my formepPaper. 
PROBLEM. 
