Mr. Morgan on Survivorships. 
*53 
* T + ^+£ + &c. + jL>4 
+ -L + i +& c_.L x 
= + H^fc + ^xi + i + £ + & c. = ^ 
V — L . Q . E . D. 
PROBLEM VI. 
To find the value of a given sum payable on the death of 
C, provided A should be the first, B the second, and C the 
third that shall fail of the three lives A, B, and C. 
SOLUTION. 
When C is the oldest of the three lives. To receive the given 
sum in the first year, it is only necessary that the three lives 
should become extinct in the order specified in this pro- 
blem, and therefore the value of S for this year will be = 
~ b ~l ' alc7 d ' U • Ih the second year the given sum may be 
received, provided either of three events shall take place; 
1st, That all the lives fail in the order required by the pro- 
blem. 2dly, That B dies after A in the first year, and C dies 
in the second year. 3 dly, That A only dies in the first year, 
and C dies after B in the second year. Hence the value of S 
for this year will be = s • m ~ n • d—e . d' s . b—m . d~ e , a' 
6abcr z • zubcr 7 - “ T 
S m—n . d—e . a' . , 
* J 0 receive the. given sum in the third year 
either of the same events must take place. 1st, The three lives 
must drop in the order stated above ; or 2dly, B must die after 
A in the first or second year, and C die in the third year ; or 
