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XVII. On the Method of determining , from the real Probabilities 
of Life , the V, dues of contingent Reverfions in which Three 
Lives are involved in the Survivor Jhip. By Mr. William 
Morgan, F. R. S. 
Read May 26, 1791. 
H AVING been encouraged to the further purfuit of the 
dodrine of furvivorlhips by the very honourable man- 
ner in which my two former Papers on this fubjed were 
received by the Royal Society, I think it my duty to fubmit 
the refult of my labours to their consideration. The folutions 
of fome of the following problems might have been derived 
from thofe which I have already communicated ; but the dired 
inveftigation of each feparate problem being certainly more 
fatisfadory, and the rules obtained by this means in general 
more fimple, I have confidered no problem as conneded with 
another, except the relation between them either immediately 
arifes from the folution, or is neceflary. to prove the truth of 
it. Being anxious to render myfelf as concife as poffible, I 
have been minute only in the inveftigation of the firft pro- 
blem, and have done little more than ftate the contingencies 
which will determine the furvivodhip in the others. By the 
affiftance, however, of thefe, and the operations which are 
detailed in my former Papers, the theorems which I have given 
may be deduced without much difficulty. 
In 
