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which prevailed between the yeans 1871 and 1881. The
subject is a very interesting one, because the discordance
proves how little reliance can be placed on estimates of
population calculated on the most approved principles,
especially as we recede further and further from the periods
of exact determination; and a very important one, because
as the death-rate is the ratio between the number of
persons living in a year, and the number of persons who
have died in the course of it, any serious miscalculation of
the population falsifies the death-rate in a proportionate
degree. For these reasons I propose to consider this matter
at some length.
The usual method of calculating the population for
years lying between the Census-periods is to take the
populations enumerated at the last two Censuses, to ascertain
therefrom how much the population has increased during
the 10 years, or how much it has diminished, or whether it
has remained stationary ; to assume that during the succeeding
years the increase or diminution which had been
going on in the previous decennium will be maintained, or
that if the population was stationary it will remain
stationary ; and to calculate the populations of these succeeding
years in accordance with these premises. Thus, if
p represent the population enumerated at a certain Census,
and P the population enumerated at the next following
Census, the increase or the decrease, as the case may be,
will be the difference between these numbers. But, assuming
that the total decennial increase or decrease has been
effected at compound interest, or rather in geometrical progression,
then, if r stand for the increase or decrease of a
unit for one year, and t stand for ten years, and p and P