#i $* Mr. Morgan on Survivorships. 
~- Cr and the whole value of the given sum will he = 
r 9 
B'C'—C' 
S into - — — - + 
3 r 
r— i . V + B'-f AB + AC 
2 r 
+ 
a.HBK 
4- K' — B'K' 
2 . AK— ABK 
X NC-NBC + -xT 
d 
2 cr 
— — 25 . 1 +NBT at-abt , 
b 1 H « 3 ^ 
w.k.r— i • 
r— x V — C y + "f" "7 x 
* tiI=i x V — 
+ l ' ‘ * * c * r7 + 
If ^ lives be equal, the two first rules become S into 
2 dd 
3 ccr 
ELI3 + lxi+ — x 
3 r 
CKK — 
“ .V-L 
cr " ~ ' 3 
2 * x ck CCK, and the last rule becomes S into 
• CKK ■ * x CK — CCK. 77 x CT d 
+ 
+ 
6cc r 3 C 
dd 
6cr 
rrT JL. 4- — x i 4- CTT. If all the expressions, ex- 
X V'V-/ J- zcr i 3 ccr 1 
cept the first, in these rules be resolved into their respective 
series, they will be found to destroy each other^andfiie general 
, -i S • t — i * V k wVndi 
rule in both cases will become simply 3 r » 
is known from self-evident principles to express the true value 
in this particular case. The same general rule may also be 
obtained immediately from the series which denote the value 
of S in each year, for in the first year its value will m this 
S . d- 
case be = in the second year = + 
S.c—d.d—e\ 
+ 
S . c—d\ l . d— 
in the third year = + 
3 cJ r 2 
__ S .7ZJ] 3 . 
3 C 
+ 
s. 7 ^\ l -e-f and so on ; hence the whole value will be — 
L + X + i + &cT + Tc X T + F + £ + &C ' _ * r 
