M/\ Morgan on 
greater accuracy. But when the number of years, and the 
difference between the ages of the two lives are, confiderable, 
thofe chances muft vary in proportion ; and, therefore, unlefs 
the contingency is blended with another which (hall very much 
diminifh the probability of the event, the folution, by thus 
indifcriminately fuppoling the chances to be equal, muft be 
rendered extremely inaccurate. In Mr. Simpson’s 36th pro- 
blem the folution by this means appears to be abfurd : for, in 
the particular cafe in which C is the oldeft of the three lives, 
the value of the reverfionary annuity becomes = ; that 
2 
is, the value of an annuity in this cafe during the life of C 
after B and A, provided A dies firft, is the fame whatever be 
the age of B ; for no mention is made of his life in the fore- 
going expreffion. It (ho aid be obferved, however, that the 
rule itfelf is ftriCHy true, and that the error arifes from Mr. 
Simpson’s having been milled by the hypothelis in determin- 
ing the probability of B’s dying after A in his inveftigation of 
the 34th problem, which is applied to the folution of this 
problem 
I have declined giving fpecimens of the different values of 
the reverlions as deduced from the foregoing rules and thofe 
which have been hitherto publilhed, not only from an appre- 
henlion of becoming tedious, but alfo from the conviction 
that at prefent they are unnecelfary ; thofe which I have for- 
merly given being, I think, fufficient to prove the inaccuracy 
of M. de Moivre’s hypothelis. In thofe inftances in which I 
have compared fome of the foregoing rules with the approxi- 
* It is proper to obferve, that I have followed Mr. Simpson’s method of 
-determining this contingency in the 23d, 27th, 28th, and 29th Problems in my 
Treatife on Annuities, 
4 
matrons 
