2 50 
Mr, Gompertz’s analysis applicable to the 
may be ; then since — (1- 
J a + x 
J b + x 
may if x = 
according to the notation we have used be written ( 1 
L' . \ . v 
a-f x 
| / k , 
4 - t— - + ) t — ■ — , our fluent between the limit x — n and 
h a J L b 
x=.n-\- m , will therefore become ( 1- 
L a + n\ L 'b + n , m* 
* m ~T— "T 2 
L' . 1 / 
. a + n ‘ b+n • that is agreeably to the hypothesis putting h a+n 
l . L, 
a b 
becomes ( l- 
m . L and ^b+n+m rn • L It 
^b+rt ^b-t-n+m . ^ a-\-n ^a + n+m 
r ~l~ t " * 
L * J 
b+ n b f n+ .HL: this if n were equal to o would be reduced to 
2L b 
i-fi . - a +.™'\ x (l which is just half the chance 
2 L a J 0 / 
that they shall both have died in that time ; an approximation 
frequently of service, and used in many cases by Mr. Mor- 
gan, and the Gentlemen who have followed him. If there 
be a term of possible joint existence, and that be when m=(x; 
and v be some positive quantity, the formula JL(i — ~ • 
2 a / 
T 
( i — . ^ +m N \ will not answer when m — if A be the oldest; 
L b J 
wheny™o it will answer and become _L(i — r— \ but when 
2 L b J 
v has a value, this must be increased by the chance that B has 
of dying beyond this time ; that is, it must be increased by 
1, k 
; but if A be youngest, it becomes when 
