estimation of the value of life contingencies. 
2 67 
Article 7. I shall now offer in the same order as in Mr. 
Baily’s work, some other questions of Mr. Morgan's papers, 
which are most of them of a nature in point of solution diffe- 
rent; in as much as that they contain in my method double 
fluents; or, as we have reduced them, contain fluents multi- 
plied by variable quantities. 
Example 1 . The contingency of the first of the deaths of A 
and B, which shall, be the second or third which happens of the 
three A, B and C, will be — - fluent of ( 1 — —iii ) 
J x . a, b 
1 “ 
a, b 
L 
-{- fluent of f ~r~- ' fluent of + fluent of 
V 0 C £ / ^ CL 
. L 
. fluent of — r —~ l * Since the first part is by Article 5, No. 
C ■ 0 
2, of this Section ; the contingency of the joint lives A and B 
failing after C, and the second by No. 5, denotes the chance 
of B’s dying after the event has taken place of A’s dying in 
the life time of C : and the third denotes the chance of A's 
dying after the event has taken place of B dying in the life 
time of A; and independent of the correction, the first part is 
evidently == 
‘ x : a, b 
J a, b 
L 
fluent of 
^ c-\-x * {fa- {-x * 
'‘a, b, c 
second part is = ~ f +x fluent of — a —~ — fluent of 
the 
L , . L 
x:c, b a-\-x 
c, a 
J a, b, c 
ju a , x 
and the third part is equal to - L - - fluent of 
a 
L 
^ c+x ' ^b+x 
^ c , b 
fluent of 
• L , . 
x:a,c b+x 
J a, b, c 
; and the sum of the three or the 
contingency in question is independent of the correction 
