Mr. Morgan- on Survivorships. 23 5 
From this table it appears, that the approximations and ex- 
act values do not differ much from each other till the last 
years of B's life, and that the principal inaccuracy in adopting 
the approximation will arise after the extinction of the life of 
B, when it becomes necessary to multiply the fraction ex- 
pressing the probability of his dying after A into the remain- 
ing series of the solution. But this perhaps will be better 
understood from the following problems, and from the com- 
putations which are made to prove the correctness of the ge- 
neral rules. 
problem 1. 
To find the value of an annuity on the life of C after A, on 
the particular condition that A's life when it fails shall fail 
before the life of B. 
SOLUTION. 
As the approximation appears from the preceding table to be 
-always sufficiently correct, except in the two or three last years 
of B's life, it is evident, that if the fractions which express 
the probability of B's dying after A in those years, be either 
confined only to the value of the annuity during that short 
period, or be not involved at all in the computation, no 
great inaccuracy will arise from having recourse to the ordi- 
nary method of determining that probability, provided the so- 
lution be founded on real observations of life, and not on Mr. 
De Mo iv re's hypothesis. In the present problem, when C or 
A is the oldest of the three lives, the abovementioned fractions 
either never enter into the computation, or are confined to 
the last years of A s life ; and in both cases they are combined 
H h 2 
