[ 49i ] 
pofed to be due at the end of one, two, three, &c. 
years) be found, and added to the value of the an- 
nuity, according to the former cafe, the fum will be 
the value of an annuity, fecured by land, to continue 
during the life of a perfon who may poffibly live 3 6 
years. 
Now fince the fums, whereby the former annuity 
is to be increafed, confiff of the prefent worths of 
that fraction of a pound fterling (whofe numerator is 
unity, and denominator twice the number of years 
that the annuitant can poffibly live) fuppofed to be 
due at the end of each of one, two, three, years y 
it will follow, that their amount, or the difference be- 
tween the values of the two annuities, will be equal 
to the quotient, found by dividing the value of an an- 
nuity of 1 /. certain, for as many years as the an- 
nuitant can poffibly live, by twice that number of 
years : And, therefore, if to the value of an annuity 
for life, of the firft kind, we add the quotient fo 
found ; the fum will be the value of an annuity, of 
the fecond kind, for the fame life. 
When I had thus inveftigated the value of this an- 
nuity, I compared the refult with that Mr. De Moivre 
has deduced from fluxions, which is published in 
N° 473. of the Philofophical Tranfattiom ; and found, 
that they agree to more than a fufficient exacflnefs, for 
computations of this nature : I have, therefore, an- 
nexed that comparifon hereto. 
The above-mentioned author, and others, have alfo 
calculated the probabilities of furvivorfhip, by a flux- 
ional procefs ; which probabilities will flow from what 
is above premifed, by a very eal'y calculus ; in the 
doing which, the above vearly probabilities of the an- 
CLq q 2 nuitant 
