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rates only a little lower, than those of our less prolific
neighbours, they were therefore in a twofold sense healthier
than theirs —that I determined to investigate it. The results
at which I have arrived form the more important part of the
present paper.
The death-rate implies healthiness or unhealthiness
only in so far as it implies long or short average duration of
life ; for example, there can he no difference in the healthiness
of two localities in one of which the death-rate is twice or
even thrice as high as that of the other, provided other conditions
are such that in both cases the inhabitants attain the
same mean age; or conversely, supposing different populations
to enjoy the same mean duration of life, any differences
which may be presented by their respective death-rates are
due to other circumstances than differences of health. From
the death-rate alone, however, it is impossible to arrive at
any definite conclusion in regard to the average duration of
life. But the birth-rate and the death-rate together supply
us with the necessary data. The primary object, therefore,
which I set before myself was the determination of the mean
duration of life under various conditions of the birth-rate and
death-rate.
For the purposes of my calculations I have assumed
the simplest possible condition of things; namely, Ist, that
in each case the death-rate and birth-rate continue uniform
from year to year; 2nd, that no immigration or emigration
takes place, and that, consequently, any annual differences
there may be in the number of the population are due simply
to the excess of births over deaths or conversely; and 3rd,
that every individual born into the population attains the
mean age, or, in other words, that all the inhabitants die at