estimation of the value of life contingencies. 
275 
4±i, which we will suppose to commence with x , write 
its approximate value — ■§■(! — 
+ * 
+ 2 
J b+x 
L . 
1 c+x 
2 T. 
W + X 
V 
L. 
x)(i 
‘ b+x 
; we get the contingency 
* L 
J i!+I 
•i fluent of 
"c + * ' £-fx 
W + x 
c b a 
an approxi- 
= + i fluent of 
\ a \ c cl J 
f]f± * 
\ 
mation during the term of joint existence of B and C; and 
hence the method of finding the assurance for that term ; for 
each part is evident from what has been shown ; and how to 
proceed beyond that term, will be evident by considering the 
accurate fluent. But this last method throws the approxima- 
tion on the whole value. 
Example 5. On the death of A, provided he be the first or 
second of the three A, B, C ; and provided C in the latter 
L. 
case dies before B. This contingency is = — fluent of' 
b -j- X C -f* X 
of 
c 
b+x ^ a-\-x 
■ fluent of (i- 
J c+x 
TT 
J b+x a-\~x 
= fluent 
; and the assurance is the same as the as- 
surance of A's death, on condition that he dies before B ; as 
Messrs. Morgan, See. makes it. This does not contain the 
double fluent or the variable quantity multiplied by a fluent, 
and therefore may be considered out of its place. 
Example 6. On the death of A, provided he be the 2d or 
3rd that fails of the three A, B, C ; and provided C dies be- 
