  We reconsider the ordinary impurity effect on the transition temperature
$T_{c}$ of superconductors using the Eliashberg formalism. It is shown that the
correspondence principle, which relates strong-coupling and weak-coupling
theories, works only when Anderson's pairing condition between the
time-reversed scattered-states is used. For an Einstein phonon model, the
change of the electron density of states caused by the impurity scattering
leads to a $T_{c}$ decrease proportional to ${1/ E_{F}\tau}$ in the dirty
limit. It is pointed out that the phonon-mediated interaction decreases by the
same weak localization correction term as that of the conductivity.
Accordingly, for strongly localized states the phonon-mediated interaction is
exponentially small. We also discuss the case of Debye phonon model.
