2 9 0 
Mr. Gompertz’s analysis applicable to the 
P 
n ~P 
m — p 
L 
(( 
ir+p n:a,b,c + \p 
L , 
a, b, c 
^ir+p : a, b, c — \p : a, c+±p 
~“a, b, c 
J h ) c 
a, c 
P 
n — p 
• m — p 
• r 
a,b,c, + \p n — p 
-- m — p 
T 
a, l, c — \p — n 
m 
J b, c 
r 
a, c + \p — n — p 
m — p 
h,c—\p 
a, c 
L 
■x-b, c+\p L n+p:a,c — \p ^ L n+p: &,c—±py ^ _ ^ . 
c + iP 
*,c + $p 
J C-kP 
a,c—\p n 
m 
When the term is 
not very long, especially_when there are many lives concerned, 
it will be often preferable to calculate with the usual tables 
by calculating each term of the expression 
m — p 
• when put into the form N — N„. — N n+i <, 
2 2 
. M n +p -|- &c. And I think when many lives are concerned, 
2 
this will generally be the best way, if even the term should 
be long ; but for the sake of preventing great error in such 
cases, or for near approximation, the following hint may be 
serviceable. Suppose we wished to calculate the value of 
ir 
71 
i 
o 
A*, that is the sum of the first 8o terms of the series whose 
th term is A„; then since j 
K 
8 
i 
A^ 4- 8 
1 2 
A '+ 3 
8o 
73 
74 
75 
A*. . . . . &c. I 
Aw 
A„, that is the sum of eight terms of a 
