C §RS ) 
may be better underftood, by putting N for the num- 
ber of the younger Age, and n for that of the Elder ; 
T, y the deceafed of both Ages refpedively, andi?, r 
for the Remainders,* and + Wand r^ry = n. 
Then fhall N n be the whole number of Chances j 
— Ty be the Chances that one of the two Perfons 
is living, Ty the Chances that they are both dead • 
R y the Chances that the elder Perfon is dead and the 
younger living ; and r T the Chances that the elder is 
living and the younger dead.Thus two Perfons of 18 and 
35 are propofed, and after 8 years the(e Chances are re- 
quired. The Numbers for 1 8 and 3 5 are 610 and 490, 
and there are 50 of the Firft Age dead in 8 years, and 
73 of the Eider Age. There are in all 610x490 or 
298900 Chances of thefe there are 50x73 or 3650 
that they are bothdead. And as 298900, to 298900 
— 3650, or 295250 : So is the prelent value of a Sum 
of Money to be paid after 8 years, to the prefent value 
of a Sum to be paid if either of the two live. And as 
560 x 73, fo are the Chances that the Elder is dead, 
leaving the Younger,* and as 417x50, fo are the 
Chances that the Younger is dead, leaving the Elder. 
Wherefore as 610x490 to 560x73, (bis the prefent 
value of a Sum to be paid at eight years end, to the 
Sum to be paid for the Chance of the Youngers Sur- 
vivance ; and as 610x490 to 417x50, fo is the fame 
prefent value to the Sum to be paid for the Chance of 
the EldersSurvivance. 
This poflibly may be yet better explained by ex- 
pounding theft Products by Re&angular Parallelo- 
grams, as m Fig. 7. wherein AB or C D reprefents the 
number of perfons of the younger Age, and£>£, EH 
thofe remaining alive after a certain term of years; 
whence C E will anfwer the number of thofo dead in 
that time : So A C, ED may reprelent the number 
D 2 , of 
