estimation of the value of life contingencies. 
273 
+ fluent of fluent of ( 1 
JL±f ^ ; but con- 
sidering all the fluents to commence with x = 0, the second 
term is = fluent of 
J a+x 
L — 1 
b + x — fluent of 
L c+r L b+x 
and the third term is = fluent of * (~j ~~ — 1 — fluent 
of- 4±5 . — an A therefore the sum of the two = fluent 
° f (& ■ »— »' ■ >0) 
L, 
4. fluent of — ~ fluent of 
J c + x 
J b -\-x 
+ 1 - 
4.1 7— f ; and the whole by comparison with the com- 
i 
mencement of the last example ; if the fluents are to be cor- 
rected in a similar manner to vanish with x—o shows imme- 
h a L £ 
diately that 1 - 4-1 jy— — that value is equal to 
a 
this ; and therefore that the assurance of the contingency 
here, is the excess of the sum of the assurances on A’s life 
and on B’s life singly, above that : this agrees with the inge- 
nious Mr. Milne’s observations on page 232 of his work on 
Assurances ; and therefore, according to our solution of that 
case, we have during the possible joint existence the value 
r r r r r 
. 7 
T • » 
m 
P 
+ 1 £ 
2 • M 
m 
' 2 • ” 
ht — j 
, P 
a, c 4 “ n 
a,b,c, and 
