[ 49 8 J 
expreffion is exaCtly the fame as Mr. De Moivre 
gives, in the 44th page of the 3d edition of his trea- 
tife of annuities on lives ; which by the demonftra- 
tion thereof, given in fol, 1 16. of the fame work, ap- 
pears to have been obtained by a fluxional procefs. 
Secondly, Jf the probability of the younger per- 
fon’s furviving the elder be required ; then, if 
in 
2.77— X 2.YI— C 
-, - , &c. the yearly expectations of the 
in m 
continuance of the life of the younger, be feverally 
multiplied by the yearly probability of the elder’s 
P 
dying j the products, 
in- 
-1 m 3 2*—5 
1 11 p' 1 n p ' i?ip ' 
will give the probabilities of the furvivorfbip’s taking 
place,, in the firft, fecond, third, &c. years. 
And here, as before, the furvivorfhip muft necef- 
farily take place, before, or at, the end of p years, the 
longed; time that the elder can poffibly live, by fup- 
pofition ; and therefore, the fum of p terms, of the fe- 
ries above given, will be the anfwer. 
Now this feries is, alfo, an arithmetical progreffion, 
whofe greateft term is 2W 
1 n p 
leaft, — and 
2 n p 
number of terms, p ; whence f — — -4-— — 2 ~ 1 
r V m p 2 np 
y P ^ 4^—2 P y P _ 4”— 2 P „ I _ 2 »— ; p __ ) 
2 2. n p 2 2 n 1 in y in 
will be the probability required 5 to which, if — , the 
pro- 
