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9
This net movement has been estimated by means of the two following methods, allowance
having been made for any variation in the census dates:—
(a) Life table—Advancing age group.—The expected survivors at the end of the period
of a given age group as at the commencement of the period were obtained from the life table of
the period and the actual survivors, i.e., those 10 years older, were taken from the census at
the end of the period, the difference between these giving the net movement in or out of the
county during the period of an advancing age group (see table 10).
(5) Age at migration.—The net movement in or out of the county during the intercensal
decennium was estimated according to age at migration. The method is based on the
formula:—

* Excludes 74,000 war losses.
applied to each year of the period under consideration where
M = the migration occurring between ages o—x each year.
B = the births during the year.
D — the deaths between ages o—x during the year.
If there has been a net migration out of the community between ages o—x during the
period, the summation of the above expression will be positive and if a net inward migration the
result will be negative. For all ages the expression reduces to the difference between the
" natural " increase (excess of births over deaths) and " actual " increase of the whole population
during the period.
The data required for the calculation are the populations
at each census and the total births and deaths (o —x) during the period, as recorded by the
Registrar-General. The migration at the various age groups is finally obtained by differencing.
It was only possible to use this method after 1891, the requisite data not being available prior
to that year (see table 11).
It may be noted here that as regards any age group a movement in may mask a movement
out, the net movement shown for the group being small. Generally speaking a movement only
becomes apparent when it is greatly in excess of one in the opposite direction ; on the other hand,
a negligible net movement one way or the other does not necessarily denote that there has been
little or no migration within that age group.
Similarly, a small total net movement (all ages) does not necessarily imply that there have
not been considerable compensating movements in different age groups. An examination of
tables 10 and 11 shows this.
Since the life table is calculated on the assumption that death is the only decrement of
population, migration being ignored, the effect is that in the case of migration out of the community
the deaths calculated on this basis will exceed the actual deaths occurring in the community.
As a consequence, the expected survivors according to the life table will therefore
be less than the actual survivors plus the migrants out. Hence the difference between the
expected and actual survivors will be less than the actual migrants out of the community.
It can be similarly shown that when there has been migration into the community the
difference between actual and expected survivors will be less than the actual migrants into the
community. Hence method (a) will, in general, under-estimate the net migration whether in
or out. The following table shows this to be the case.