254 
Mr. Morgan on 
of three events fhould happen; ift, if the three lives fhould 
become extind, and A be the fecond that fails ; 2dly, if A 
fhould die after B, and C live; and, 3<dly, if A fhould die 
after C, and B live. But in the fecond and following years* 
the given fum may be received, provided either of feven events 
fhould happen, ift, If the three lives fhould fail in the year, 
A’s life having been the fecond that failed. 2dly, If A only 
fhould die in the year, B having died before the beginning and 
C lived to the end of it. 3dly, If A only fhould die in the 
year, C having died before the beginning and B lived to the 
end of it. 4thly, If A fhould die after B in the year and C 
live. 5 thly. If A fhould die after C in the year and B live* 
6thly, if A and C fhould both die in the year (A dying firft) 
and B’s life fhould have failed in one or other of the foregoing 
years ; and, ythly, if A and B fhould both die in the year (A 
dying firft) and C’s life fhould have failed in the foregoing 
years. From the feveral expreftions denoting thefe contin- 
gencies the whole value of the reverfion may be found = 
s 
lac 
a'c a" d , , , S t a'd . a "e , a"'/ , « 
X T * &C. + — + — + — + -—■ + &C. + 
r r r 3 lac r r r 3 
S ab , 
— * — -f 
2 ab r 
. o . S am a 
+ &C. + — X — + - 
2 ab r r 
■ a o , 0 
+ — + &c. - 
2 S a' be a!'md a" \ 
- — x — -r — r — r — : 
^abc r r 4 r- 
+ &c. - J - S x" + ^ + a 4 / + &C. - 
3 abc r ? 
S a me , a " 
— X -f — 
3 abc r r 
-f &C. — 
S a'bd 
X 
\abc r 
+ 
a'"nf 
+ &C. 
The two firft of thefe feries are^D, . . the two next = E . . . 
and it appears from the folution of the preceding problem that 
the four remaining feries exprefs double the value of the fum 
S, depending on the contingency of A’s dying firft (when B 
'or C are the oldeft of the three lives) with a negative fign. 
The 
