Geoscience Reference
In-Depth Information
Fig. 6.2
Point boundary between two regions
6.5
The Regional Boundary as a Line
While this single-point perspective on the boundary indicates the approach adopted,
it is too restrictive, and needs to be broadened. The boundary between two metro-
politan area-based regions is now regarded as a line, the more conventional view of
a boundary. At any point on this line the two regional density functions are equal in
value, with the common value of density varying along this line.
6.5.1 The General Case
We again consider two regions
A
and
B
, which have
A
0
and
B
0
as their respective
metropolitan areas. The density functions for the two regions again have unequal
central densities (
N
A
>
b
). The boundary can be
determined by first setting
M
(
x
) in Eq. (
6.1
) equal for region
A
and region
B
, so that
N
B
) and unequal slopes (
a
>
