26 o Mr. Morgan on Survivorships. 
true values, I have in the following examples undergone the 
labour of separately computing each of those latter fractions, 
and the results appear to differ so little from the approximated 
values, that I think a greater degree of accuracy need not be 
required. 
Value of £ 100, payable on the contingency in this problem, com- 
puted from the Northampton table , at 4 per cent. 
A. 
Ages of 
B. 
c. 
Value by 
the rule. 
Correct 
value. 
Difference. 
IO 
85 
80 
I .467 
I.438 
O 029 
15 
75 
73 
2.233 
2.150 
O.083 
15 
75 
35 
2.761 
2.589 
0. 172 
15 
75 
78 
I.698 
1-513 
O.185 
20 
65 
64 
303 1 
2.912 
0. 1 19 
20 
65 
70 
2.388 
2.580 
0.008 
70 
80 
78 
9-457 
9.068 
O.389 
70 
80 
35 
10.109 
9.618 
O.49 1 
I have chosen those cases in which the approximation was 
likely to have been most inaccurate ; for if the ages of A and 
B are either both younger, or differ less from each other than 
they do in these examples, it is obvious that the foregoing 
rules must be still nearer the truth. I have also uniformly 
supposed the life of B to be older than that of A, and of conse- 
quence the approximated value always errs m excess ; if the 
life of A had been the older of the two, it would have been 
found to have erred in defect, and nearly to the same amount. 
But as, in this latter case, the value of the reversion is greater 
