-,264 Mr . Morgan on 
all the three lives fhall become extind, A having been the fe- 
cond or third that has failed. 2dly, That A ihall die after 
13 , and C live to the end of the year. 3dly, That A Ihall die 
after C, and B live to the end of the year. In the fecond and 
following years the given fum will become payable, provided 
either of eight events fhould happen, lft, If all the three 
lives fhould fail in the year, A having been the fecond 
or third that died. 2dly, If A fhould die after B in the 
year, and C live to the end of it. 3dly, If A fhould 
die after C in the year, and B live to the end of it. 4thly, If 
A and C fhould both die in the year, B having died before the 
beginning of it. 5thly, If A and B fhould both die in the 
year, C having died before the beginning of it. 6thly, If A 
only fhould die in the year, the lives of B and C having be- 
come extinct in either of the preceding years, /thly. If A 
fhould die in the year, B having died before the beginning, and 
C lived to the end of it. 8thly, if A fhould die in the year, 
C having died before the beginning, and B lived to the end of 
fit. Hence the whole value of the reverfion will be found = 
s -x 
a r 
/ n Q 
1 + + &c. - l-x 
r z r$ 
a be , a"md , a"'ne 
4- &c. - 
JLx— + — +^+ &c. - A-x — + a ^+ a -T- f + &C. - 
babe r r" r 3 babe r , r 3 
JL V &C. -G - M, 
%abc r r z r z 
SI* 
This rule is corred in all cafes ; but when the three lives 
e equal it becomes more Ample, and is 
S . r— i 
- X 
zV - 3C — CCC ; which expreffion may likewife be obtained 
immediately from the feries given above. 
The folution of this problem, like that of the foregoing 
one, may alfo be derived from the firft three problems ; for the 
value 
