[ 497 ] 
7 %e invcjligation of the probabilities of fur'vivorjhip 
between two perfons oj given ages. 
Let the complement of the younger life be de- 
noted by and that of the elder by p : Then, 
Firft, If the probability of the elder perfon’s fur- 
viving the younger be required, let the fymbol p be 
ufed inftead of the number 36, and it will (from the 
argument above ufed) appear, that the expectations of 
the furvivor’s life, for the firft, fecond, third, &c. 
years, will be reprefented by ( ^ — - -j- - — - *T 
\ p 2 p p 
— . t=i 4 -—. &c. or i t=2. Zt=l. 
2 . p 
P 2 p S 2 P 2 p 2 p 
Gfr. which expectations, being feverally multiplied 
into — , the yearly probability of the other’s dying, 
will give 
2 p — 1 
2 p n 5 
2 p — 7 2 p — e , r . 
— — -, — &c. for the pro 
2 p 72 2 p n 
Lability of the furvivorfbip’s taking place, in the firft, 
fecond, third, &c. years. 
Now fince, by the hypothefis, the furvivor cannot 
poffibly out-live p years ; therefore, only, p terms of 
the above feries are to be ufed ; which feries, being 
an arithmetical progreflion, whofe grealeft term is 
— lea ft term — — , and number of terms p j 
2 p n 2 p n 
the fum thereof will, by a well-known rule, be 
( 2 ft 1 — x - = 1 — x f = ) — > which 
V 2 fin 2 pn 2 m p 7 s 2 n 
Rrr 
ex- 
