Survivoffhips, 
261 
■■ ■» kk . KK — CKK . d 
TT - CTT. The two expreffions bic - + — X 
CT — CCT, by refolvlng them into their refpedlive feries, will 
be found — 1 -^- + ^ + 67? + 6773 4 $? + &c " and the - two 
expreffions 
iL ' - 1 - --• - - X CK - CCK. = 
beer c 
cc 
6 r 
ber 
de 
ef -f / iiL + &c. ; hence the fum of thefe four exprefc 
beer 1 bur 3 beer 
fions will be = 
i . v-cc 
0 r 
, and confequently the general rule 
in this cafe will be = X V — 3CC -2LCC, which is 
known to denote the true value from other principles*. 
As a further proof of the accuracy of the preceding invefti- 
gation, it may not be improper to obierve, that this rule may 
be immediately obtained from the different fractions which 
exprefs the value of the given fum in each year. For in this 
cafe the value of S in the firft year is = ~-X- in 
the fecond year = - X 4r— — — ~~ V“. + an< ^ 011 in *be 
J 3 C 3 r 2 ccr rr l ccr 
other years, which expreffions may be eafily found =2 
S . r — I 
X V — 3CC - 2CCC. Q, E. D. 
PROBLEM V. 
To find the value of a given fum, payable on the death of 
A, if his life Ihould be the jirji or fecond that fails of the three 
lives A, B, and C. 
# See my Paper in the Phil* Tranf, Yol, LXXIX, 
SOL U- 
