expressive of the law of human mortality, &c. 51 5 
living in each yearly increase of age are from 25 to 45 
nearly, in geometrical progression. If we refer to Mr. 
Milne's table of Carlisle, we shall find that according to 
that table of mortality, the number of living at each successive 
year, from 93 up to 99, forms very nearly a geometrical 
progression, whose common ratio is ^ ; thus setting out with 
75 for the number of living at 92, and diminishing continu- 
ally by i, we have to the nearest integer 75, 5^? 42, 32, 24, 
18, 13, 10, for the living at the respective ages 92, 93 , 94 , 
95, 96, 97, 98,99, which in no part differs from the table by 
jyth part of the living at 92. 
Art. 3. The near approximation in old a'ge, according to 
some tables of mortality, leads to an observation, that if the 
law of mortality were accurately such that after a certain 
age the number of living corresponding to ages increasing in 
arithmetical progression, decreased in geometrical progression, 
it would follow that life annuities, for all ages beyond that 
period, were of equal value ; for if the ratio of the number 
of persons living from one year to the other be constantly 
the same, the chance of a person at any proposed age living 
to a given number of years would be the same, whatever 
that age might be ; and therefore the present worth of all 
the payments would be independent of the age, if the annuity 
were for the whole life ; but according to the mode of cal- 
culating tables from a limited number of persons at the 
commencement of the term, and only retaining integer num- 
bers, a limit is necessarily placed to the tabular, or indicative 
possibility of life ; and the consequence may be, that the 
value of life annuities for old age, especially where they are 
MDCCCXXV. 3 X 
