  We study the effective quark mass induced by the finite separation of the
domain walls in the domain-wall formulation of chiral fermion as the function
of the size of the fifth dimension ($L_s$), the gauge coupling $\beta$ and the
physical volume $V$. We measure the mass by calculating the small eigenvalues
of the hermitian domain-wall Dirac operator ($H_{\rm DWF}(m_0))$ in the
topologically-nontrivial quenched SU(3) gauge configurations. We find that the
induced quark mass is nearly independent of the physical volume, decays
exponentially as a function of $L_s$, and has a strong dependence on the size
of quantum fluctuations controlled by $\beta$. The effect of the choice of the
lattice gluon action is also studied.
