qj 6 Mr. Gompertz’s analysis applicable to the 
fore B; this is = — fluent of x |(i -~- 
fluent of 1 
l . l, , 
c+x b + x 
= fluent of 
a+x 
^±f . ii±f )) = h*l fluent of i^±f . 
L b c J J a L b c 
L i L , 
x:a,o c + x 
(fluent of 
fluent of 
^,6 
, and each part has been already treated on. 
Example 7. On the death of A, provided he be the first or 
last which fails of the three lives A, B, C; and provided C in 
the latter case dies before B. This is evidently = — fluent 
of(. 
, , f L r 
a-\-x J x\b, 1 
_ < 
a ^ c 
j , r L t 
a + # J x\b y c 
L a 1 L h, c 
■fluent (1 
k c + x \ 
1 = — fluent of 
- b ~- -j- 1 -j- fluent of — ~- 
hb + x 1 
‘ h J"" 
a+x 
fluent of 
L . L . 
x:b,c . a-\-x 
u b,c 
L 
+ fluent of 
L , L, . 
a-\-x b-\-x 
J a-\-x 
. fluent of — + fluent of — i-— c . - A~h - , and each 
c b a, c b 
part has been already considered. 
Example 8. On the death of the longest of the two lives 
A and B, provided they be the first which fail of the three 
L 
A, Band C; this is evidently fluent of xj 
x 1 1 — 
a+ x 
J b+x 
L 
b J 
= — fluent of - —jy— — fluent of— ^ — 
c a c 
b-\-x 
4- fluent of jy— • ~' l + ^ j ~r ~ » an< ^ the assurance 
