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The author points out a short-cut to the proof of the results stated by Maci et al. (see ibid vol.45, no.1, p.183, 1997). Maci et al. reply that Lee's (see ibid., vol.46, no.2, p.296, 1998) proof is interesting, but not completely satisfactory. Indeed, Lee's equation for the E-field is valid only in free-space, thus requiring that the field and its first and second derivatives be continuous everywhere. Instead, for the problem under investigation, the field is discontinuous on the waveguide walls. However, the idea can be refined by applying the equivalence principle to the same surface as that suggested by Lee.