estimation of the value of life contingencies. ■ 
281 
Scholium. 
As the Tables calculated for the valuation of annuities or 
yearly incomes may be serviceable for the valuation of in- 
comes payable at less periods, it will be proper to show how r 
the value of such incomes depend on each other ; and also to 
show how to compare the value of assurances on lives, when 
the sum assured is to be received at some one of a number of 
periods which is to happen after the death, reckoning from a 
fixed period, with the value of the assurance, if the sum is to 
be received at a given distant time from the death ; for in- 
stance, what is commonly called the assurance of £1. on a 
life, is the value of one pound to be received at the first anni- 
versary from the payment of the premium, which shall hap- 
pen after the death ; but it is not the value of one pound to 
be received at the death; and it is, as will appear farther on, 
very nearly the value of one pound to be received a half 
year after the death shall happen. 
a,b,c,Sec. tO find n 
. m 
Art. 1 . Problem. Given « 
m 
Y being a whole number, and p a small period ? 
r 
Solution. We shall have n L, b, c , See. — n 
m I n 4- p — q 
r r 
a, b, c, Si c. x_£_ nearly, 
u, b, Cj Sec. — |— 
9 
n+p 
n + 2p — q 
L 
r m * 
a, b , c 9 &c. + n+2p 
«+3 P—9 
a, b, c, Sc — p 
* m — q 
a, b, c, See. -j- 
m:a,b, c, Sec. 
J a, b, c, Sec. 
But considering that during the whole of 
