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APPENDIX.
ON THE
MUTUAL RELATIONS OF THE BIRTH-RATE
AND DEATH-RATE.
BY J.S.Bristowe, M.D., F.R.C.P.
It will probably be recollected that Dr. Richardson
claimed as one of the benefits to be anticipated for those
living in his visionary city "Hygeiopolis," that their annual
death-rate should be reduced to .5 per cent. It will probably
also be recollected that immediately after the reading of
Dr. Richardson's celebrated paper an anonymous correspondent
of the "Times" asserted, with some show of argument,
that a mortality of ·5 per cent, implied an average duration
of life of 200 years, and that, a fortiori, Dr. Richardson's
anticipations were impossible of realization and absurd.
There is no doubt that under one special condition
(and that the condition which, on account of its simplicity,
would probably present itself most readily for computation)
the result arrived at by the "Times" correspondent is correct.
If an annual mortality of .5 per cent. be maintained in a
population which neither diminishes nor increases, and in
which the removals by death are exactly balanced by the
additions by birth, it is certain that the average duration of
life would be exactly 200 years. Thus, if in a population of
1000 persons five deaths and five births occur annually, and
it be assumed for simplicity's sake that every individual of
the population lives to the same (namely,the mean) age, it