estimation of the value of life contingencies . 2 6g 
of the equal periods p, from n — p, after the event, provided 
it be not beyond the time m is . « 
b -j-£ n 
m 
■ ' "T" 71 c 
m 1 
a, c 
a,b,c\ that is half the sum of the assurances 
P 
m 
for the term on B’s life, on A’s life, on EC’s joint life, and 
on AC’s joint life; — the assurance on A, B, C’s joint life for 
the term : on the supposition that if two persons are both to 
be dead, in a certain time less than their possible time of joint 
existence, it is an equal chance which is the survivor; our 
theorem therefore only goes to that term ; after this, by con- 
sulting the formula, constant * ' -j b -~- . fluent of - y— 
. -* +J -J- —~f fluent of ~t + " . we find that if C be the 
one which must of necessity die before the extreme age of B 
or A ; and if there is a possibility of his living as long as x is 
less than ; we shall have L , —0: and the fluents of 
1 C + /X 
L , L , L , L, , 
c-\-x a-\-x 1 c + x b-\-x r 1 . -» it 
— — . “ — and -j — . — 7— after that time equal ~g and — h 
if — g and — h be the values at that time ; after that time, the 
L b 
contingency, is constant — — f — — — g . 
b 
L, . L , 
b- \-x 7 a + x ■ c 
h.~ ( ; it 
the whole assurance be required, find the whole value whilst 
r r r 
is not greater than to which add 7k b 4. g J'b + h 7 
m 
b . 
But if A be the oldest, and there is a possibility of his living as 
long as x is less than fi,but not longer ; use the theorem as long 
mdcccxx. N n 
