Mr. Morgan on 
272 
it will be = S - L ^- 
i . V-AB 
r 
When the lives are equal, the rule may be found either im- 
mediately from the feries, or from the foregoing expreffions, = 
x V-3CC-2CCC. Q. E. D. 
To find the value of a given fum payable on the deceafe of 
B or C, fhould either of them be the lajl that fails of the three 
lives A, B, and C. 
The fum S can be received in the firft year only on tne ex- 
tinftion of the three lives, reftrained to the contingency of 
A’s life having been the firft or fecond that failed. In the 
fecond and following years it may be received provided either 
of fix events fhould happen, ift, If the three lives fhould fail 
in the year, A having been the firft or fecond that died. 2dly, 
If B and C fhould both die in the year, A having died before 
the beginning of it. 3 dly, If C only fhould die in the year, 
A andls having died in either of the preceding years.. 4thly, 
If B only fhould die in the year, A and C having died in either 
of the preceding years. 5thly, If B fhould die after A in the 
year, C having died before the beginning of it. 6thly, If C 
fhould die after A in the year, B having died before the 
beginning of it. From the fradions expreffing thefe feveral 
contingencies, the whole value of the reverfion will be found s 
problem X 
SOLUTION 
md.a' + a'' && 
s_ 
6 ah 
4 
