334 Mr . Morgan 
which denotes the probability of A’s furviving B, is well known 
to be the difference between the foregoing feries and unity . 
The fum of this feries might eafily be determined from 
tables of the expectations of (ingle and joint lives *. But no 
fuch table as the latter having ever been computed, it will by 
no means be found a laborious undertaking to compute a table 
of the probabilities of furvivorlhip between two perfons of all 
ages immediately from this feries, without having recourfe to the 
expectations of life. For if the probability of lurvivorfhip between 
any two perfons be found, the probability between two perfons 
one year younger is obtained with little difficulty ; and by pro- 
ceeding in this manner a whole table may be formed in lefs time 
than would be necelfary for computing one of the expectations 
of two joint lives. To exemplify what I have faid, I (hall 
juft fet down a few operations for determining the probability 
of furvivorffiip, according to the Northampton Table of Ob- 
fervations t> between two perfons, whofe common difference 
of age is io years. 
* The above feries, exprefling the probability of furvivorlhip, may be eafily 
found, from the folution of the next prohlem, — ^ ^ ~ ~ c ' ^ ~~ ; K 
2 b 
denoting the expectation of one life one year younger than B ; C the expectation 
of a life one year older than B; AK and AC the expectations of the joint lives 
of A and K, and of A and C, refpeftively ; and 0, as in that problem, the 
number of perfons living in the table of obfervations at the age of K. 
-f See Dr. Price’s Treatife on Reverfionary Payments, Tab. 6. Vol. II.' 
Age 
