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female population who are of child-bearing age. This age
extends from puberty to 45, or in a well-ordered population
may be taken to extend practically from 20 to 45. With
the object of arriving at some kind of notion of the possible
reproductive capacities of populations existing under the
several conditions which I have assumed for the purposes
of Table 1., I have calculated the percentage number
of persons between 20 and 45 years of age living under
each several combination of the birth and death-rates.
Now, if males and females existed in equal numbers,
and every woman gave birth to a child once in two years,
the fourth part of each number arrived at should give the
highest possible number of births per cent, per annum
attainable in the case to which it relates. Hence it w T ill be
readily seen that a birth-rate of 6 per cent, might be
maintained in such a population with a death-rate of either
.5 or 1 per cent. ; a birth-rate of 5.5 per cent, in a population
dying at the rate of 1 5 or 2 per cent. ; a birth-rate of
5 per cent, in a population dying at the rate of 2.5 per
cent.; a birth-rate of 4.5 per cent, in a population dying at
the rate of 3 per cent.; and a birth-rate of 4 per cent, in
populations dying at the rate of 3.5 and 4 per cent.
It is obvious, of course, that these calculations do not
represent anything that would actually obtain under the
continuance of the combined birth and death-rates to which
they severally relate; for we know that females and males
do not exist in equal proportion; that not all women marry;
and that of those who marry some marry early, some late,
some have no children, some but few, others large families;
and we know further that the mean age, the attainment of
which was an essential element in my calculations, does not