244 Mr. Gompertz's analysis applicable to the 
and the excess of this above the other, that is 
0 
0 
n + e + e' 
_ x 
^‘p+n+z+i', q + x * ^r+x) ° 
K-f t 
(^+w+£, q + x*^r+ x) will 
be ( o 
V n 
^q + • ^q+x 2 ^ q+n , r+n) • ( L^ + w + f + s' « + e) “I" 
“ ^q + n • ( ^K + e + e' :/>» r ^n+e:p, r) 2" + w (^ Jn + S + £,; P» ? 
L K -j- 6 ; p, q) H ~ ( L„+ e +6' r ““ ■ L w _|. £ : p f q> r ) Seethe nota- 
tion, Art. 4, Section i. 
Art. 8. If when x—v and greater, + ^ . L r+r is equal to 
0, and the fluent of L . L generated from x equal to o 
becomes equal to v, be <y, then L x . fluent of (L^ +x . L r+X 
commencing with x=o), will when x=v-j-m be =yLp +f+vi} 
pt being positive. 
Article g. On the fluent of Lp +X . L q _ x . L r+>J: , that is, if 
L x . p >q . L r+X by notation, Article 4. Section 1. 
If between the limits x=.n and x=n-\-m, the decrements 
of each life be sufficiently nearly proportional to the times to 
admit of their being considered proportional, and x being 
put = n 1 , we use the notation L^ +x = Lp +B — tL'p +n , 
^ '‘q+n ^ ^ q + n’ ^r+x ^r+n r+n > ^ ^ shall ha\ e 
^ x : p,q * ^r+x = ^ L r +n * C : p, q ‘ ^ + « ^ 9 + n)”!" 
f.L^ +H . h 1 +w ). Hence the fluent generated whilst jr fromo 
becomes == 72 4- m is = 0 
M 
^x : p, q ' L'r + x r + n * ( ^« : p, q 
2 ( Lp + n • L' ? + n 4- L q + n . Up + „ ) + — L' p + n . L' q + n ) 
