s8o 
Mr. Gompertz’s analysis applicable to the 
- fluent of . iH; + fluent of 
a+x 
a, c i 
. fluent of ^ - ^ +-y . — fluent of 
Note. This result may be obtained in rather a more simple 
manner ; for the chance depends on the two events ; namely, 
that A shall be dead, and that B dies whilst C is living ; the 
former is 1 ; and the latter is — fluent of . -4^— 
and the rectangle of the two gives the expression above. 
Example 12. On the death of A and B, provided another 
/L L , 
life C, dies before B. This is fluent off - j — fluent of (1 
v l 
^ a 
-fluent At-*. 1-^ 
u b a 
. 1 — 
c-f x 
fluent of 
(1 — 
''c + .r 
^ — fluent of (1 — 
c- \-x ^ n-\-x ^ b-\- 
£ ) 
fluent of - y + * . 1 
— 1 J — t 
L * 1 L 1 
a c 
J a+x 
J b+x 
— 4^ - fluent of 
. n c +* 
-J- fluent 
J £+x 
If the contingencies begin with x. 
There are some observations to be made on the manner 
we have corrected the fluents ; and also on the manner of 
calculating without the usual tables, for which consult the 
Scholium. 
