264 Mr. Gompertz’s analysis applicable to the 
l r .L 
^5 +x ' ^a-\-x 
^ b, a 
L , .L 
c + 
x' a-\-x . x:b,c' a-4-.r\ i ,1 
j — -] 7 — ] ; hence the 
L c,a L a,b,c ) 
as- 
surance on this contingency is equal to the assurance on A’s 
death, assurance on A’s death if survived by B, — assurance 
on A’s death if survived by C -{- assurance on A’s death if 
survived by B and C, as Mr. Morgan, &c. makes it. 
Example 4. If K"= 1 —(1 . (1 and K 7 " 
l 
= — ~~ , we shall see that the contingency of A’s dying, and 
that he is the 1st or 2nd which dies, is equal to — the fluent 
L 
a - f * 
^“c+x . ^“b + x 
[- 
+ ' ^b-\-x 
Hence, &c. 
J b c, b 
Example 5. If A is to be the second or third which fails, 
L X-b c 
by taking K" = 1 namely, the chance that B and C 
o, c 
are not both living, we have the contingency of A’s death 
= — fluent 1 
L A L , 
x:b,c a+x 
hr „ * L • 
b,c a 
Hence, &c. And the assur- 
ance equal to the assurance of A’s life absolutely —the assur- 
ance of his life on condition that he dies first. 
Example 6 . If A is either to be the first or last to die : then 
L 
is the chance on his death equal to — fluent of — 
^x:b, c t # 
x v -r 1 r— 
h, c 
L 
b +x 
c + x 
. 1 — 
J x : b, c 
€ -j* X 
== — fluent of L a+X x 
Hence, &c. 
J b “b, c 
Example 7. To find the contingency on the first of the two 
