Mr. Morgan on Survivorjhips . 4 <; 
B and K, P and C, A, Band K and of A, P and C: then 
the fum of the third and fourth feries, or of - 
S 
x 
a' me d'nd n S a'dn a' + a n . eo _ . . S . * 
+ — + & e .^- rX — + —— + &C. being = - -r- X 
abcr abcr 
1 2 
abcr 
6 c 
me a — a.mc 
xbr 
ab*r 
dn 
+ bZ 1 
a — a —a 
" . dn 
ab’x.d 
+ 
eo 
buX 1 
a— a' — a" — a'" . eo 
ab<r~ 
&C. 
V v 
a' dn a' + a rr . eo 
y * abcr 
+ 
abcr 2 
n . S . m a'dn . a' + a" . eo n 
, See. = X — + ■ ■■ — -i - ■+ &c., 
3 fo 
acmr 
... . S k.H K-ABK S . FC — APC 
will be = — - x — x 7 — . 
O c y b 
acmr 
The fifth fe» 
s 
3 
a' db 
a" em 
g . S ft db 
neS » " X aba + 7 k? + &C -> IS = ? x b X 0 ?r 
a — a' . db , em 
-j- 
after @cr z 
jf 
a — a’ — a' r .em fn a — a' — a 
d” ftcr 3 
" ■ a"' .fn 
,&C. 
S a' em a' + a" . fn 
- x — + — 
y ' 
1 ftcr 3 tf&rr 3 a ^ cr abcr z 
= (putting FC and AFC for the values of the two and three 
joint lives of F and C and of A, F, and C)- x i zldz dld _ 
$ 
gr * abcr 
— 4. * + , &<:• The fum, therefore, of the fifth and 
-i*'"-' 1 abcr 
_ , - . S a' db a' 'em Q S a' em a' + a" . fn 
fixth feries, or ot - x ^ +^,&c. ^ + - eitr * + &c. 
S # . FC— AFC 
1-S = — X 7 
3 b 
/S a'~\~a" . fn Q . 
+ V6 r X Hb7r + abrc z ? &C * = ) 
S x d 
6 cr 
X 
em a — a! . em fn a — a — a . fn 
bdr 
+ hdr L ~ 
.. +&c. If T denote a life one 
abdr ! bdr L abdr ‘ T 
year older than C, and BT, and ABT denote the values of the 
two and three joint lives of B and T and of A, B, and T, this 
laft feries will be = f x — gT ~ A _ ; and confequently the fum 
, , ... , S 0 . FC— AFC , S 
of the fifth and fixth feries will be = — x 7 x 
J 
d . BT— ABT 
Laftlyy the feventh and eighth feries, or 
&* 
1 
