Mr. Morgan on Survivorjhipf. 
*6 
S ci' md a n en 0 S a' en a 4 ' ci n . fo 0 $ 
— X “7“ + 1 “f* &C. — 7” X “7— H — r~" 4 * &C. are = — ■ - X 
3 awr #4^ 2r aocr abcr g 
dm a — ft 7 . £72 
* 
a— a — a 
jr 
be 
abcr 
- -X BC 
3 
bcr z 
- ABC - ( 
abcr‘ 
S 
en 0 S a'en a 4 - a’’ . fo 
_ + & c.--x^+__/+&c. 
md en 
7- X — X 
07 ' be mdr 
a — a » en 
amdr 
+ 
of 
mar 
a — a' — a" . of 0 N S md . PT — APT « j a 
-£ h&c. =)“ X , where PT and APT 
amdr J 6r be 
reprefent the values of the two and three joint lives of P and 
T, and of A, P, and T. If theft feveral expreffions be added toge- 
ther, &c. we fhall at laft have S - * * - x — A — - BK. - ABK. 
6 c 
+ ~ xFC~ AFC- 
3* 
S . r — 1 
y 
X BC - ABC 
S . m 
3 br 
x PC—APC+ 
teJ x BT — ABT - m - FT , APT , for the value of the fum S,. 
6 cr 0 
when either B or C are the oldeft of the three lives. 
In order to determine the value of the reverfion when the life 
of A is the oldeft of the three lives, let j*, t r u , w 9 &c.be the num- 
ber of perfon-s living at the end of the ift, 2d, 3d, 4th, &c. years 
from the age of A, and let b\ b'\ b //f , b u/ \ &c. be the decre- 
ments of life at the end of r, 2, 3, 4, &c. years from the age of 
B ; then, by reafoning as above, the value of the fum S for the 
firft year will be exprefled by the feries S * h + 
s xb . a t 4,^ f or t }ie ftcond year by the feries J -ft 
2 abcr 
S . b 
// 
. s~t . e S . b"a—s . e S • b" . a — s . a—e 
+ — 72 — ■ 
Q.abcr 
abed 
by the feries 
S . b rre , t—u . e 
2 abcr z 
S . b 
babcr z 
, for the third year 
t — u . / „ S . b" r , a — t . f 
+ - — rrzs + . 
S . b n/ . a — t . e-^j 
: zaber 3 
6 abcr 1 1 2 aber^ 4 abefi 
, and fo on for the remaining years of A’s life. 
p-r-^i r r 1 r • 1 r j S ab r c b cs ah' d b f ds 
Theleieverallenes maybe found— — x — — - — — — - — - -b 
/ ^ ^ 3 j 3 
ab f d 
