on Survivorships, 34 3 
and AK the value of an annuity on the joint lives of A 
and K. The whole value of the furvivorlhip is therefore = 
Sx 
I . B- 
2 r 
■AB 0 
— 
K. 
2 /; 
AK 
— 
A -AC 
2 br 
Q. E. D. 
Having now the value of the fum S payable on the contin- 
gency of B’s furviving A,, the value of the lame fum, payable 
on the contingency of A’s furviving B, is eafily obtained by 
the well known method of fubtradting the value found above 
from the whole value of the reverlion after the extinction of 
the joint lives of A and B. It is evident, that the exadhiefs 
of the above rule muft depend on the accuracy with which the 
values of the fingle and joint lives are computed. Being pof- 
felfed of luch tables for all ages* even with refpedt to the joint 
lives, I have computed the following values, in order that it 
may be feen how far Mr. Simpson’s approximation * (the only 
rule now in ufe)' may be depended on. 
* It muft be remembered, that the correction explained by Dr. Price, in 
Vol. I. p. 29, &c. of his Treatife on ReverfionaFy Payments, muft be applied 
to Mr. Simpson’s rule ; that is, when the reverlion is a and notan eftate, 
the value found by the rule muft be divided by £. 1, increafcd by its intereft for 
a year. 
Age 
