  We reexamine the charge transport induced by a weak electric field in
two-dimensional quantum Hall systems in a finite, periodic box at very low
temperatures. The resulting linear response coefficients consist of the
time-independent term $\sigma_{xy}$ corresponding to the Hall conductance and
the linearly time-dependent term $\gamma_{sy}\cdot t$ in the transverse and
longitudinal directions $s=x,y$ in a slow switching limit for adiabatically
applying the initial electric field. The latter terms $\gamma_{sy}\cdot t$ are
due to the acceleration of the electrons by the uniform electric field in the
finite and isolated system, and so the time-independent term $\sigma_{yy}$
corresponding to the diagonal conductance always vanishes. The well known
topological argument yields the integral and fractional quantization of the
averaged Hall conductance $\bar{\sigma_{xy}}$ over gauge parameters under the
assumption on the existence of a spectral gap above the ground state. In
addition to this fact, we show that the averaged acceleration coefficients
$\bar{\gamma_{sy}}$ are vanishing under the same assumption. In the
non-interacting case, the spectral gap between the neighbouring Landau levels
persists if the vector and the electrostatic potentials together satisfy a
certain condition, and then the Hall conductance $\sigma_{xy}$ without
averaging exhibits the exact integral quantization in the infinite volume limit
with the vanishing acceleration coefficients. We also estimate their finite
size corrections. In the interacting case, the averaged Hall conductance
$\bar{\sigma_{xy}}$ for a non-integer filling of the electrons is quantized to
a fraction not equal to an integer under the assumption that the potentials
satisfy certain conditions in addition to the gap assumption.
