estimation of the value of life contingencies. 279 
expressions of this formula are derived from the resolution of 
fluent of ^ ~ m £ ~ a ’ h 'j ’ nto 
a, b, c 
fluent of 
Us bj c 
: a, b 
L , 
a, b 
J c+x 
Example 10. On the death of the longest of the lives A 
and B; provided they be the first and last of the three A B 
k’- 1 -'” - ^b- f-x . 
andC. This is fluent of j fluent of (1 
L Aj a 
fluent of ( 1 
h 6 
L L , 
a+x c+x 
fluent of 
l , /L , 
a + x f c+x 
— 1 — fluent of —jg— • + fluent of — (■ 
^ b c J ^b \ 
L,, /L„, 
b+x 1 c+x 
— 1 
— fluent of 
L , L , 
a+x c+x 
= correction 
L , l, , 
a+x b + x | 
T — 
fluent of . -~ L _|» fluent of . - y— 
a+x 
fluent 
of • lf±f fluent of -f- x . - c - x — 2 fluent of 
L 5 L C L h a c 
L , L. , 
x . a j b c -|- x 
~L 7 ' T * 
a, b c 
Example 11. On the death of the longest of the lives A 
/L , 
andB; provided B dies before C. This is fluent off- -* 
("" ^ ¥)) - 
fluent of — r +X ( 1 
a+x 
c + x 
= influent of 
fluent of 
x: a, c 
a, c 
2±£\ 
L * ) 
