Survivorships. 2 $<) 
fhould die in the year, B having died before the beginning, and 
C lived to the end of it. ^dly, If B only fhould die in the 
year, A having died before the beginning, and C lived to the 
end of it. 4 thly, If A and B fhould both die in the year, 
and C furvive it. 5 thly, If C fhould die after A in the 
year, B having died in either of the foregoing years. 6thly, 
if C fhould die after B in the year, A having died in either 
of the foregoing years. The fractions denoting thefe fe- 
veral contingencies being added together will be found — 
s 
2 ac 
de . a" ,d 
® a ' bc j a"md a"ne 
A ~ + T ~~T~ 
6 abc 
S v a mc i a " nri i 
x — - -J * t - - — 
S a' bd a" me a r " nf 
X — + — 
babe 
+ -T^ + &C.+ 
2S ^ ci' md ci"ne a" of 
‘iabc r r r 3 
+ —X 
2 ac 
a ^ | 
r 
in r- 
+ &C. 
r 5 
F-A_x 
. a* 
,±. ne 
2 uber 
r 
i 
r % ’ T OTC. 
s 
- x 
nd . d 
0 * . 
2 aber 
r 
-j- . .. 
r * + ore. 
S me . a* 
nf. 
labor 
r 
T 
r z T" ore. 
S 
ne . 
X 
a' of, o' + a" 0 
2 aber 
r 
i ■ 
r z “t"Oce« 
The firft two feries are = D ; the third and fourth feries are = 
; the fifth and fixth feries are = — 
-xBC- ABC- 
S' 
0* . Jr K — APK 
6 . be 
* . BK- ABK m . i : C-APC 
; the feventh and eighth feries =s] 
0 . FC— AFC . d . BT3ABT . , 
; and the ninth and tenth feries = 
r * Hence the whole value of the 
3 C 
6b 
6 br 
3 cr 
md . P T — AF F 2 . iiC — AB‘ 
6bcr 3 
reverfion will be = D - 
2 - s _iLzi xBC-ABC- 
FC-AFC- 
S.« 0.FK-AFK. 
X — 7 
3 C w 
S . m 
BK *! 
BT-AB1 if— - FT ~ a1 ' t 
2 If 
K17 x PC - APC + S -~ x 
Mm2 
The 
