Mr. Morgan on Survivorships . 
" should die before A, and the value of an annuity equal to 
“ the interest of S during the life of C after A, provided A 
“ should survive B/ J Let the first of these values be denoted 
by W, and the second by X, and the required value will be = 
W — x X. When the three lives are equal, the value 
of the reversion evidently becomes = ~~ l x V— L, which 
expression may be easily derived from either of the rules given 
above, or immediately from the series themselves. 
Having given so many examples of the accuracy of the 
rules in the first and second problems, it becomes unnecessary 
to add any further examples in regard to the two foregoing 
problems, as the solutions of the latter are derived from those 
of the former, and consequently are equally correct in all 
cases. 
PROBLEM V. 
To find the value of a given sum payable on the decease of 
B and C, should their lives be the last that shall fail of the 
three lives A, B, and C. 
SOLUTION. 
In the first year the given sum can be received only pro- 
vided the three lives shall have failed, and the life of A have 
been the first that became extinct. In the second and fol- 
lowing years it may be received provided either of four events 
shall have happened: ist, If all the three lives shall have 
failed in that year, A dying first. 2dly, If A shall have died 
in any of the foregoing years, and B and C both died in that 
