View report page

260
represent the populations of the two successive Censuses,
p=p (1 + r)t; and r = (p/p)1/t — 1. From this latter formula,
by an easy calculation, the value of r in figures may be
obtained. And, as this represents the annual increase or
decrease per unit by which at the end of ten years p
becomes P it represents the annual increase per unit by
which it may be presumed that P will go on increasing or
diminishing during the following years ; and therefore the
population for the first year after the Census, at which P
was enumerated, will be obtained by multiplying P by r,
that of the second year by multiplying Pr by r (which
equals Pr2), and so on. It must be pointed out, however,
that as the Census is always taken early in April, and as
for the purpose of ascertaining the birth-rate and death-rate
in a changing population we must take the mean population
for the year, or in other words the population assumed to be
present in the middle of the year, it is always necessary
even in Census years to make, in accordance with the above
rules, a correction from the three months that lie between
April and the middle of the year; and, further, that the
above method of calculation can only be expected to lead
to accurate results in the case of a population whose increase
or decrease depends only on the births and deaths, and that
of necessity it is apt to mislead in a greater or less degree
when the variations depend largely on emigration and immigration,
as is the case with most large towns.
Recognising the fact that the method of calculation
above considered almost certainly leads in the course of
years to serious and gravely misleading errors, it is not
unnatural to ask whether no better method of estimating
the number of the population could be devised. In former