* 5 6 
Mr. Morgan on Survivorships. 
of three events: ist, Of C’s dying after B in that particular 
year, adly, Of C only dying in that year, B having died in 
either of the preceding % + 1, % -fi 2, &c. years : or, 3dly, Of 
C only dying in the year, B having died after A in the first z 
years. Hence the whole value of S, after the nece ssary ex- 
tinction of the life of A by the table, will be = ^ x + 
+ &c. + 
s 
bcr cJ r l 
X 
r 1 
+ &C. + 
Lz v inL* ini j_ inJ _l & c . The last of these series is = 
cr* * r ' r' ' r 3 1 
s . ir . k . r—i x y __,q % . t ] ie other two series being added to the 
four first series in this solution, their sum will be found = 
—1 . V-C+BC , F c _ ».BK 4_ x x' — B'T' 4- i — BT 
Tr 1 zr 2 c ‘ 2 cr 
(T ; , B'T', and B'C' denoting the values of annuities on those 
single and joint lives respectively for z years.) The fifth and 
, . <*,. . HBK AC 7ZT. aV— ABC 
sixth series in the solution are = — — 2t . or 
, a, . HO — HBO . d 
the seventh and eighth series are = — ~r 6cr x 
AK — ABK, and the tenth is = x 1 + NTB — 
Hence the whole value of the given s um in this 
ABC 
case is 
„ . . TZT.V-l , B'C'_AL + C'_J^ 
S into — 1 
x BK + AK i -— + 
d AT 
— — X — — 
6r ' 2 r 2c i 
+ r+T— BT + B'T' + c*NC- NBC V 
d . i+NBT 
HC- HBC 
.HBK 
6ar 
irk . r 
V 
. .JIIL * a " c ' cr~+' 
When A is the oldest and C the youngest of the three lives , the 
