Survivorjhips. 265 
value of S is either equal to the difference between the abfolute 
value of the reverfion after the death of A and its value de- 
pending on the contingency that A fhall be the firfi that fails 
(found by Prob. 1.), or it is equal to the fum of the two values 
depending on the contingencies that A {hall be the fecond or 
third that fails (found by Prob. 2. and 3.). In both cafes the 
general rule is — • G — M. Q. E. D. 
fc> 
PROBLEM VI I. 
To find the value of a given fum payable on the death of A, 
fhould his life be the firjl or lafi that fails of the three lives 
A, B, C. 
SOLUTION. 
In order to receive the given fum in the firfi year, it is necef- 
fary that either of four events fhould happen, ift. That all 
the three lives fhould fail, A having been the firfi; or third that 
died, adly, That B fhould die after A, and C live. ^dly. 
That C fhould die after A, and B live. 4thly, That A only 
ihould die, and B and G both live. In the fecond and follow- 
ing years the given fum may be received, provided either of 
feven events Ihould happen, ift, If the three lives fhould 
fail, A having been the firfi or laft that died, zdly, if B 
Ihould die after A in the year, and C live to the end of it. 
3 dly, If C fhould die after A ih the year, and B live to the 
end of it. 4thly, If A only fhould die in the year, andB and 
C both live to the end of it. 5 thly, If A’s life fhould fail 
after that of B in the year, C’s life having failed before the be- 
ginning of it. 6thly, If A fhould fail after C in the year, 
B having failed before the beginning of it. 7thly, If A only 
Vol. LXXXI. N n fo°uld 
