240 Mr. Gompertz’s analysis applicable to the 
and also = — L r , 9 + i £ + L r + e , ; this appears by merely- 
writing 0 for n and e for t in the above formulae. And if we 
now write s for n, and e' for t in the forms of Art. 1, we shall 
+ x • L r + x 0 L ? + x . L r — Lr + t , q + * + 
have 0 
«+«' 
T ^?+ £ > r + e + £/ T ^? + £ + £/ > r + £ 4“ T" ^ r + £ + £ '> ?+ £ + e ' an< ^ also = 
x 
T\ 
0 
^q+x • ^r+x j+s + ^e 4 “ L^+e+e', And by con - 
j q+xr 
tinuing in this manner, we shall arrive at the value of 0 
n 
*L j where n = * + «'+ £ "+ &c. ; and therefore by dividing 
the intervals into a sufficient number, we may find the fluent 
of L^+tf.L , r+x to the utmost degree of accuracy, that the 
tables of mortality will admit of ; and for most purposes, by 
dividing the time in but few intervals, the requisite accuracy 
will be obtained. 
Art. 3 And considering the decrements also equal during 
the interval m at the expiration of the interval n, we have 
L . L r+J , that is the fluent of L ?+a; . L r+X from x =0 
n+m q+x 
x 
0 
to x=n-\-m, = 0 
I I IT ! I T 
^q + X'-^r+x ~ ■ Lj q + n,r-{-ri~ir ~ ±J q+n,r+n-{-m, 
^ q-\-x • 
+ *' 
2 ^q-\-n-\m, 2 ^~ J q + n-\-m,r «tlld also® 
L r+«,g+ n + itn—^r+n + m, q + n+jm, these are obtained by wri- 
ting m in the place of t in Art. 1. 
Art. 4. And if z i z , e", &c. m, be each equal to, or less than 
