238 
Mr. Gompertz’s analysis applicable to the 
=^T e* . + „ . £=iy— ee;* + »*•=?■ ^i* -2 • ^~ 2 
See. therefore in this case P (/i „ = E* P,,-,. , = w- ■ E“~' ’ 
P • — ,, <^zL p /x ~ 2 & c 
Section 3, being necessary Lemmata. 
Art. 1, on the fluentof L 
Suppose that between the intervals x=n and x=n-\-m, the 
decrements of life of persons arrived at the ages q-{~n, r-\-n , 
each in proportion to the time elapsed from the commence- 
ment of the interval, or that they may be considered so with 
sufficient accuracy. See Sect. II. Art. 1. Put x = n + t, L ?+X} 
^q+n+t -L'q+n ^ ^ q+n> ^“r + x ^r+n ^ ^ r+n ’ 
fluent of h q+x . L r+a willbe=fluent of (-L' r+n txL q+n -tL' q ^ n ) 
= correction - tL' r+n . L q+n + ^ . V r+n . L , (?+M ; and as 
L q+y . L r _|_ x (Art. 3. Sect. I.) expresses the fluent of L r+X 
. L r +x from x = 0 to x — n, this will be the correction, if the 
fluent be supposed to commence from x=o, and our fluent 
X 
^q+x • ^r+x stand = — 1 1 L r ^ n 
that is 0 
n-\-t 
t 
• L $-i-K+T • + K • Lfl+n — 
+ » ? + ) 
'ty+.r • 
^ r+« * (Lj-f-n 
T //L 9 + «) ; but because according to hypothesis t\J q + n — 
L , „ — L , , . ; L , , , , = L , — — t\J , ; and also 
q + w q n t ^ q-\-n-\-^t q'\~ n 2 
^LV +M =L r+ „~L r+M+f ; therefore 
• 4+* the fluent 
