estimation of the value of life contingencies . 
277 
is the sum of the assurances on A if he survives C, and on B 
if he survives C — the assurance on C if he survives A or B. 
This agrees with Mr. Baily's deduction. Note ; for fluent of 
^ kg-f X ' 
J-J | 7 
c+x . x:a,b,c 
-t — we may write -f 
g, b, c 
fluent of 
' x: a, b 
L T 
a, b 
J c+x 
. L ■, whence &c. } and this not containing the fluent multi- 
C 
plied by a variable, may be considered out of its place. 
Example 9. On the longest of the two lives A and B, pro- 
vided they be the last that fail of the three A, B, C. This is 
fluent of | a+X ’ fluent off 1 — ~-~r~ • — r + - H ^r— fluent of 
1 L g ' L c L b ^ L b 
1 
L 
^C+X L g + xl r, r f L a + X l 
- — • — j =nuent of j — ( 
L 
b+x 
c+x ' Lj b+x 
— 1 — fluent of 
L. , _ L 
a + x 
= correction — 
J a + x 
L, , L r s L . 
b+x . x:a,b n a + x 
— : f- -j fluent of 
a, q 
. fluent of — — -r — — fluent of f fluent of — r^—') 
L c,b l . \ L b L c . L a J 
— correction 
c+x ^ b+x ^ 
L , L, , 
a+x b+x , 
“lT lT 1 
L r L . 
x:a,b a+x a r 
-7 ; — fluent of 
V b L a 
J 
(fluent of — L “ +X 
^ c+x f ^x:a,b 
and we may write for fluent of -p rX - x ’ a,b \ 
^ a , l J c 
j-^j + fluent of 
f L ar :a,b\' 
1 1 
. , x:a,b,c 
its equal — 
g 3 b, c 
fluent of 
l , L , 
x:a,b x + c 
J a,b 
and each part, as 
O o 
MDCCCXX. 
