581 
expressive of the law of human mortality ^ &c. 
be not at the extremes of life, a consequence which follows 
from the near agreement to a geometrical progression which 
takes place in the number of living at each small equal in- 
crement of time ; that is to say, from the near coincidence 
Z' 7i • by Cy SCQ» • l 71 “1“ t • dy l)y C* 1 1 • • f% 
of n-i-a,b.c,Scc. "''‘h 1 : a. b.c. &c : ’ the Small Variation of ^ 
for the different values of t : and also, that when the number 
of years for which an assurance continues be not very long, 
and the ages be not at the extremes of life, the annual pre- 
miums will not differ widely from the premiums to be paid 
for an assurance of one year of a life older than the proposed 
life by about half the term : thus, according to the North- 
ampton table, at three per cent, to assure loo /. at the 
Age .... 
IS 
20 
30 
40 
50 
60 
For 7 years, the annual 
premium by the com- 
mon modes of calculation 
£i.. 2 ..I I 
1.. 9.. 5 
I .. 1 4.. 1 1 
2.. 4.. 1 
00 
d 
4 - 7 - 1 
And the premium for one 
year assurance for an age 
3 years older . . . _ 
> 
3 
I.. 9.. 8 
0 
2.4.. 6 
3.. I.. 0 
! 
4.. 7.. 8' 
the difference of which is very small. — As another example, let 
Age .... 
10 
20 
30 
40 
50 
60 
For 10 years, the annual' 
premium will be, by com- 
mon modes of calculation 
► 
£o..i9.. 2 
I. .9.. 1 
8 
2.. 5.. 8 
3 - 3 -- 4 
4.. 12.. 6 
Premium for one year as- 
2.. 6.. 8 
surance, age 5 years older j j 
0..17..1 1 
I.. 10.. 7 
3 - 5 - I 
4.. 15.. 2 
Here, except at the age lo, the excess is rather more in the 
approximation than in the first set of examples ; but it should 
be recollected, that we took the exact middle, instead of 
inclining to the early age. 
