Mr. Morgan on Survivorships. 261 
than when B is the older life, the error must necessarily bear 
a less proportion to the whole value than it does in the pre- 
ceding examples. 
With regard to the fifth problem, the error in some cases is 
greater, in others less than in the present problem. If B and 
C are both older than A it will be nearly twice as great. If 
one is older and the other younger, it will be altogether incon- 
siderable ; for the fractions which express the probability of 
the older of B and C dying after A will be as much above the 
truth, as the other fractions expressing the probability that the 
younger of these two lives die after A will be below it, and 
thus the errors of one correct those of the other, and render 
the computation almost perfectly accurate. I have not given 
any examples to that problem, not only as the correctness of 
its rules may be inferred from the examples which have been 
given to those of the present problem, but as I wished to make 
as few additions as possible to a paper, which having engaged 
a large portion of my time and attention for the last three 
years, has already become too long, and for which my only 
apology is the attempt to give correct, and not very laborious, 
solutions to some of the most difficult and complicated cases 
in the doctrine of survivorships. 
