[ 33' ] 
XX. On the Probabilities of Survivorships between Two Per fans 
of any given Ages, and the Method of determining the Values 
oj Reverfions depending on thofe Survivorf ips, By Mr . Wil- 
liam Morgan ; communicated by the Rev . Richard Price, 
D. D. F. R. S. 
Read May 8, 1788. 
T HE hypothefis of an equal decrement of life, adopted by 
M. de Moivre, for the purpofe of facilitating the com- 
putations of life annuities, has not only been rendered unne- 
ceflary by the late publication of many excellent tables deduced 
from real obfervations *, but has likewife been found fo very 
incorrect in fome cafes, that probably little or 110 recourfe will 
ever be had to it in future. But though the direct application 
of this hypothefis may be laid afide, there is danger of its not 
being entirely abandoned; and mathematicians may Rill be led 
to reafon from this principle, by deriving their rules fujm the 
expectations rather than from the real probabilities of life. The 
ingenious Mr. Thomas Simpson has contented himfelf with 
this inaccurate method in his Select Exercifes, and he has been 
followed in it by moft other writers on the fubje<5t -j- • Even 
in thofe cafes which involve only two lives, the errors are often 
* See Dr. Price’s Treatife on Reverfionary Payments, 4th edit.; and Mr. 
Baron Maseres on Life Annuities. 
f Dr. Price’s folutions of his 15th and 1 6th queftions are exceptions to this 
remark. 
Voi .. LXXVI1I. Y y 
con- 
