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XVI r. 0 « 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 May 15, 1794. 
In the last paper which I communicated to the Royal Society 
on the doctrine of survivorships, I concluded with observing 
that, as far as my own judgment could discover, I had then 
given rules for determining the values of reversions depending 
upon three lives in every case which admitted of an exact so- 
lution, and that the remaining cases, which were nearly equal 
m number to those I had already investigated, involved a con- 
tingency for which it appeared very difficult to find such a 
general expression as should not render the rules too com- 
plicated and laborious. Since that period I have bestowed 
much time and attention on this subject, and have at length 
so far succeeded as to give me reason now to hope that it is 
capable of being entirely exhausted. It is not my present de- 
sign to enter into the investigation of all the problems which 
still remain to be solved. I shall here confine myself to a few 
of the most important, reserving the conclusion of the subject 
for some future opportunity. 
The contingency to which I have alluded in this and my 
former paper, as opposing the great difficulty in those pro- 
blems which I have not yet solved, is that of one life s failing 
