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In calculating the mean duration of life given in
Table 1., I assumed (as will be recollected) that every
person born into a population attains the same age, and
further that the children born in a group (so to speak) in
one year, die in a group in the course of some subsequent
year. But the truth of the table is not dependent on these
assumptions. The results as regards the duration of life in
relation to uniformly maintained birth-rates and death-rates
are in fact identical, whether the same length of life be
attained by every one of the inhabitants, or whether as
occurs in nature the mean duration be the resultant of lives
varying widely among themselves in length. And again, in
order to determine the mean duration of life, it is not really
necessary to assume that persons are born in groups and die
in groups. For if we take as the basis of our calculation
just so much of a population as yields one birth and take d
to be the mortality due to the same fragment of the population,
the duration of life will be determined by that index of
(1+r) which makes d (1+r)x =1; and the
log- i/d
equation becomes x =
log. (1+r).
* * *
In conclusion, and as hearing upon the questions
which have just been discussed, I venture to quote some
remarks which I addressed to the Vestry of Camberwell in
my report for the year 1863. They are subject, of course,
to correction in reference to the influence of the birth-rate
on the significance of the death-rate, which at that time I
overlooked.
"But supposing a death-rate to have been ascertained
with perfect accuracy; what does it teach? what do we