Mr. Morgan oh 
z£z 
SOLUTION. 
in the firft year the payment of the given fum depends 
npon either of four events, ift, That all the three lives (hall 
become extinct, the life of A having been the firft or fecond 
that failed, adiy, That A and B fhall both die, and C live to 
the end of the year. 3 dly, That A and C fhall both die, and 
h live to the end of the year. 4 thly, That only A fhall die, 
and B and C both live to the end of the year. In the fecond 
and following years the payment of the given fum will depend 
upon either of eight events happening, ift, That all the 
three lives fhall drop in the year, A having been the firft or 
fecond that failed, adly, That C furvives, and only A and B 
die in the year. 3 dly, That B furvives, and only A and C 
die in the year. 4 thly, That both B and C furvive, 'and A only 
dies m the year. 5 thly, That A dies in the year, B having 
died before the beginning, and C lived to the end of it. 6th!y, 
That A in like manner dies in the year, C having died before 
the beginning, and B lived to the end of it. ythly, That C dies 
after A in the year, B’s life having failed ineither of the preced- 
ing years. Sthly, That B dies after A in the year, C’s life having 
failed m either of the preceding years. The fractions denoting thefe 
feveral contingencies are = 
® . a c , a" 
— X — J r 
Zac r r 
4- &C. -f* 
S a* d 
— X — 4 
2 ac r 
r 
4~ &c. 4" — 
1 x — 4- *— 
2 ub r y 
m 
, « n 
+ Tf 
+ &c. + 
o ^ am a n a" t 
2 ab r r 2 y z 
4- &c. — 
X 
a'bc 
- 4* 
a ,lf ne 
4- &c. - 
S ci'mr cd'nd 
babe r r 2 
+ &C ‘ “b^ X 
*' bd a" me 
— - 4” r- 
r r a 
, <r ’nf A 
T “TT + &C. — 
S ^ a' rnd t 
“ t X 4 
yk r 
+ ~ + &c. = D + E-M. 
This 
