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is obvious that exactly 200 years will elapse before the whole
of the original 1000 will have died out, and that the turn of
each annual litter to die will arrive exactly 200 years from
the date of birth. But 200 years would still be the mean
duration of life, even if the population were to die as they do
now at different ages; only in this case while many would
die below the mean age, many would exceed it, and some
might easily attain to the years of Methuselah. The author
of this calculation might have added that if a mortality of .5
per cent, were to be maintained in a population uniformly
diminishing by that amount, the population would never die
out; and that if it commenced with 1,000 individuals the
last whole man would live for somewhat over 1,379 years,
and would then perish only bit by bit in a diminishing
geometrical series throughout all eternity. On the other
hand, an annual death-rate of .5 per cent, with an annual
birth-rate of 20,000,000 per cent, (a condition of things conceivable
in the case of certain intestinal worms) would imply
an average duration of life of little more than a year.
It is obvious that if with a uniform annual mortality
of only ·5 in the 100 the mean duration of life may vary,
with variations of the birth-rate, from zero to infinity, even
a low death-rate means per se neither healthiness nor unhealthiness,
neither a long nor a short span of life, and that
in order to determine its significance in these respects its
relation to the birth-rate must be taken into account. It is
because as an officer of health I have hitherto practically
overlooked this important relation, and because, as I believe,
the great majority of my colleagues have been equally
neglectful—often, indeed, falsely boasting that while the
birth-rates of our districts have been higher, and their death-