Survhorjhips. 
This general rule gives the true value whether the life of A 
be older or younger than both or either of the lives of B and 
C. When the three lives are of equal age, the value of S for 
the fir ft year will be- S -x-+ d *-~, for the fecond year = 
ee 
dd 
? X P ~7e + and io on for the other years. Hen 
ce 
the whole value in this cafe will be = 5 X 2 V - iCC ~ CCC, 
which expreffion may alfo be derived from the general rule juft 
given above, or D + E - M. 
The folution of this problem may alfo be obtained either 
from the firft and fecond, or from the third problems. In the 
one cale the value ot S is evidently equal to th & Jutn of the 
two values determined by the two firft- mentioned problems, 
or D -f E — 2 M -f M = D E — M. And in the other cafe its 
value is equal to the difference between the abfolute value of 
the reverfion after A ( = G) and its value depending upon the 
contingency that A {ha ll be the lap life that (Ball fail, which 
being = G + M — L) + n. by the third problem, it follows, that 
the general rule on this fuppofition will be alfo = D-fc-E - M 
Q^E. D. 
PROBLEM VI. 
To find the value of a given fum payable on the death of A. r 
Ihould his life be the fieond or third that {hall fail of the three 
lives A, B, and C. 
SOLUTION- 
The payment of the given fum in the firft year will depend 
upon the contingency of either of three events, ift, That 
7 all 
