258 
Mr. Morgan on Survivorships. 
of that series is 
solution is = 
BC 
_ VL 1 + pc . . . . The first series in this 
2 zbr 
+ ABC rf-HFC the second is = x 
6 ab 
NB — NBC — 
. AF — AFC 
6b 5 
the third is = — x HB — HBC 
3 a 
m . AP — A PC 
3 br 
fifth is = 
, the fourth is = -r-r x 1 + NPC 
ABC 
, the 
r — 1 • V 
— , and the sixth is = * — 1 + ~ -■ The 
whole value therefore of the given sum may be found — S . 
JL 
zb 
into ~ x V - 3 C' + S BC- ABC + + 4k x 
FC — F'C' 
AF _ AFC 
HFC 4. 2 ■ HB - HBC , 
~ r ? x 1 
3 a 
-f-^xNB-NBC + Il^^. 
zbr 
xi + PC-f- 
z. AP — APC 
p k . r — 1 
+ + T x TTh 17 
V — C*. 
When the lives are all equal, the expression |3x ( ^ K in the first 
and second rules becomes = 1 the expression 
wirf.PT 
3 ccr 
, CC rfrf j ^ C rf.T _ C' ■ 
becomes = — — , and the expression — — 
or — 
— becomes = 
. c 
, so that those rules become 
CCT 
S into i x CK3CCK + £ x i + , 
** . CKK 
6cc 
3 ccr 
X 1 -J- CTT. In the third rule the expressions 
T' — B'T' 
C'—B'C 
become = — 4zr x 1 — CT, 
zr 
so that in this case the value is = S into 
“ ** . CKK 
zcr 
“ . V-L 
6 r 
+ « 
1 JT x 
CCK 
CT — CCT — 17 x CK + — + 
See 
6ccr 
x 1 + CTT, 
