537 
expressive of the law of human mortality, 
commencing with X (a) =T.7 ; 1,701 ; 1,702, &c. with the 
differences between them. I have not, in this table, had the 
proportional parts inserted, though it would be attended with 
advantage, as the table is not meant to be of general use ; 
but only given to be applied for rough purposes, or where 
accuracy is not particularly required for calculating at once 
the value of a life annuity for the whole term of life, or the 
whole remaining terms of life, after a given term, by con- 
sidering the present value of each successive payment to 
form the successive terms of a geometrical progression whose 
first term and common ratio are each equal to a. And as 
X will represent the log. of the sum of the said geo- 
metrical progression, it will likewise express approximatively 
the logarithm of the value required. For many purposes, a 
table of , answering to given values of a, would be pre- 
a~— I 
ferable, but not for general purposes. 
Art. 7. I have already, in Art. 4 and 5, Chap. II, intro- 
duced the term accommodated ratios, or chances, and endea- 
voured to explain the methods to be adopted to reap the 
advantage of the ideas there expressed. Table V, for Carlisle, 
Deparcieux, and Northampton, are the logarithms of tenth 
terms of the accommodated ratios, or the logarithms of the 
accommodated chances for living ten years, calculated ac- 
cording to a mode laid down in Art. 5, Chap. II ; that is, it 
expresses for every age, or value of b, the logarithm of 
when-l- X (i,o 5“*L -f &c. . . . 1,05 T L \ 
0 + 2 ^ ~i~P/ 
is equal toi 1 ,05'* f'^-f&c. ... 1 ,05 7^”^ *7 and to show, 
by example, how these are calculated, let it be required to 
find the logarithm of the accommodated chance for living 
