  We investigate the relation between the diagonal ($\sigma_{xx}$) and
off-diagonal ($\sigma_{xy}$) components of the conductivity tensor in the
quantum Hall system. We calculate the conductivity components for a short-range
impurity potential using the linear response theory, employing an approximation
that simply replaces the self-energy by a constant value $-i \hbar /(2 \tau)$
with $\tau$ the scattering time. The approximation is equivalent to assuming
that the broadening of a Landau level due to disorder is represented by a
Lorentzian with the width $\Gamma = \hbar /(2 \tau)$. Analytic formulas are
obtained for both $\sigma_{xx}$ and $\sigma_{xy}$ within the framework of this
simple approximation at low temperatures. By examining the leading terms in
$\sigma_{xx}$ and $\sigma_{xy}$, we find a proportional relation between
$\mathrm{d}\sigma_{xy}/\mathrm{d}B$ and $B \sigma_{xx}^2$. The relation, after
slight modification to account for the long-range nature of the impurity
potential, is shown to be in quantitative agreement with experimental results
obtained in the GaAs/AlGaAs two-dimensional electron system at the low
magnetic-field regime where spin splitting is negligibly small.
