expressive of the law of human mortality, ^c. S 39 
shall be equal to the value of the whole life annuity at 
T"* 
1 , 05 —* 
five per cent, at such age, namely 'TL^ 5 consequently x 
1,05“' 1,05“* 1,05“' /l,05“* \ 
( 1 ) = i1^ ; AS = x(i[^)-f-x(i ,05) — x\ • / 
This table is constructed for Carlisle, Deparcieux, and 
Northampton, and is to be used in conjunction with Table IV., 
where only a rough value of the contingency is required ; 
and though this table applies as the other tables of accom- 
modated chances, to different rates of interest, still it would 
be of advantage more particularly here for the greater ap- 
proximation to have similar tables constructed from the 
formula x (€)= x ( 1 ) -|- X (r”^) — X ) for different values 
of r. 
Art. 9. In calculating the value of life annuities for long 
periods, by means of adding together the values of portions 
of those periods, the portions of the distant periods contain 
factors of the real chance of living to these periods, and 
likewise of the discounted value of the money of which the 
payment is not immediate; thus if t be greater than 10, 
a+io,6-j-io, c+io 
r r 
It will be therefore convenient to 
have a table of the logarithm of the real chance of living 
10, 20, 30 years, &c. and also for other terms ; and some of 
these are given by Tables VII., VIII. , IX. 
4 A 
MDCCCXXV. 
