  We consider a 2D electron system in a strong magnetic field, where the local
Hall resistivity $\rho_{xy}(\vec r)$ is a function of position and
$\rho_{xx}(\vec r)$ is small compared to $\rho_{xy}$. Particularly if the
correlations fall off slowly with distance, or if fluctuations exist on several
length scales, one finds that the macroscopic longitudinal resistivity $R_{xx}$
is only weakly dependent on $\rho_{xx}$ and is approximately proportional to
the magnitude of fluctuations in $\rho_{xy}$. This may provide an explanation
of the empirical law $R_{xx} \propto B \frac{dR_{xy}}{dB}$ where $R_{xy}$ is
the Hall resistance, and $B$ is the magnetic field.
