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mortality, the mean duration of life is raised to 70 years,
we shall find that in the first column of Table I. the conditions
become impossible when the birth-rate falls below
3.5 per cent.; in the second column, when the birth-rate
falls below 2 per cent.; in the third column, when the
birth-rate falls below 1.5 per cent.; in the fourth, fifth, and
sixth columns, when the birth-rate falls below 1 per cent.;
and in the seventh and eighth columns, when the birth-rate
falls below .5 per cent. Beneath these several birth-rates
and their associated estimates of the duration of life I have
again drawn horizontal lines ; so that the conditions which
may be regarded as possible conditions are in each column
included between the upper and lower horizontal lines. It
may be added that the apparent irregularities in the table
presented by the upper and lower limits of the assumed
possible conditions are due simply to the small number of
birth-rates which have been employed; and that it would
be easy, if it were worth while, to ascertain for each
column, on the one hand, the exact birth-rate which would
allow of a mean duration of life of 70 years, and, on the
other hand, the exact birth-rate which in accordance with
my assumptions is compatible with the lowest possible mean
duration of life. It may also be added (what is, however,
sufficiently obvious) that a population in which there are no
births must gradually die out, and that it is impossible in
such a case that a uniform annual death-rate can be maintained.
Indeed, however healthy and long-lived such a
population might be, and however low its initial death-rate,
the death-rate must of necessity increase year by year until
it becomes with the extinction of the population cent,
per cent.