  We investigate chiral properties of the domain-wall fermion (DWF) system by
using the four-dimensional hermitian Wilson-Dirac operator. We first derive a
formula which connects a chiral symmetry breaking term in the five dimensional
DWF Ward-Takahashi identity with the four dimensional Wilson-Dirac operator,
and simplify the formula in terms of only the eigenvalues of the operator,
using an ansatz for the form of the eigenvectors. For a given distribution of
the eigenvalues, we then discuss the behavior of the chiral symmetry breaking
term as a function of the fifth dimensional length. We finally argue the chiral
property of the DWF formulation in the limit of the infinite fifth dimensional
length, in connection with spectra of the hermitian Wilson-Dirac operator in
the infinite volume limit as well as in the finite volume.
