248 Mr. Gompertz’s analysis applicable to the 
please by taking the intervals sufficiently small. When for 
the purpose of approximation a long interval is divided into 
smaller intervals, one of which, for instance, is from n to 
it will not be immaterial for obtaining the nearest approxi- 
mation, what vaiue we take for x between n and n-\-m, in 
the above value for ~-L' y+n \ an off-hand idea might be, that 
x should be taken somewhere about n + 2 ?U - 
L, ' 
Section IV. Art. 1. Because 1 -A— is the chance that 
L b 
a person of the age b shall be dead in the time x, is the 
fluxion of the chance ; that is the measure of the chance that 
he would have of dying during a finite time x, on the conside- 
ration that that cause, if any should subsist, to make the deaths 
disproportionate to the time, should cease at the term x. And 
L 
if this be multiplied by — ■ , the product will represent the 
Lj 
a 
fluxions of the chance of the person of the present age b dying 
in the life time of the person of the present age a, and conse- 
L . Lr 
quently, — fluent of — did . — is the chance that the person 
a, b 
of the present age a has of surviving the person of the pre- 
sent age b. The calculation of this fluent between any limits 
is effec'ed from the articles of Section 3, referring to the 
fluent of L . L . . If for q and r we write a and b, and 
we wish to have the part of the contingency corresponding 
to the intervals between x = n and x — i, taking t= 1 in 
the first of the two forms we have it = -- - - id T [ a + n 
a, b 
and by taking n successively o, 1, 2, 3, &c. and adding the 
+ L a +n-i-i) 
