228 
Mr. Gompertz's analysis applicable to the 
sions respectively n 
y 
• n 
. w 
a, by Cy See . p 
a, b, c, &c. 
c 
> ’ 
', when p — o, 
and the time m is not the utmost limit, they will stand « 
m 
b ’ c ’ &c - : and when m is the utmost limit, and 
r 
w 
0 
n 
m 
a, b, c, &c. o 
— . .... . n 
m 
r 
p=o, they will stand 
r 
o 
n 
a, b, c, 
These denote 
the assurances of one pound to be received after the failure 
takes place ; and if they be multiplied by r*, they will denote 
the value of the assurance, if the money be to be received at 
the time p after the event takes place, whenever that may 
happen between the times n and m; and this is properly what 
should be called the assurance of the sums, though writers call 
r r 
what I denote by n 
m 
a, b, c, &c. 
> &c. the assurance. See 
Scholium. 
Art. to. It is often necessary in calculating from tables, to 
have a method of interpolation for the discovery of terms not 
explicitly contained in the tables ; if, for instance, we had the 
function M , calculated in a table, for values of x,y,z, 
x , y$ z y oc c. 
&c. taken in as many series proceeding in arithmetical pro- 
gression, according to certain scales of differences, and we 
wish to have the value of the function, when some only, or 
neither of them are in those series. And for this purpose the 
method of finite differences, when the differences converge* 
Is applied with great advantage, as is well known. 
