522 Mr. Gompertz on the nature of the function 
The logarithms of the living at the age of 
15 are 2,92840 differences 
= ,03966 
= ^(Lk)- 
25 
2,88874 
>04738 
1 
> LT( 
N 
II 
■Khs) 
35 
2,84136 
>04757 
= Hhs)- 
'-r\ 
.< 
1 
45 
2,79379 
,07280 
= Hhs)- 
■^"'55) 
55 
2,72099 
on the supposi- 
tion of the possi- 
bility, though 
the thing cannot 
be accurately 
true. 
- m 
Here the three first differences, instead of being nearly in 
geometrical progression are nearly equal to each other, 
showing from a remark above, that the living, according to 
these tables, are nearly in geometrical progression ; and the 
reader might probably infer that this table will not admit of 
being expressed by a formula similar to that by which the 
Northampton table has been expressed between the same 
limits, but putting, 
^(^15) “ 
^ = X ^ -m- mp - mp^ - mp 
or its equal m + mp — ,08704, and — 
x(L^^) or its equal x w + pm — ,12037 ; = 
the log. oi p — — ^ — ,0703997 and 
/>=i,i76, — ,04. And to see how these 
values of m and p will answer for the approximate determi- 
nation of the logarithms above set down of the numbers of 
living at the ages 15, 25, 35, 45, and 55, we have the fol- 
lowing easy calculation by continually adding the logarithm 
of p 
— 2,92840 
— 2,88874 
and we 
=: 2,841 36 )> shall 
have 
= 2,79379 
= 2,72099 
