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We establish the Bethe equation of the $\tau^{(2)}$-model in the $N$-statechiral Potts model (including the degenerate selfdual cases) with alternatingvertical rapidities. The eigenvalues of a finite-size transfer matrix of thechiral Potts model are computed by use of functional relations. Thesignificance of the "alternating superintegrable" case of the chiral Pottsmodel is discussed, and the degeneracy of $\tau^{(2)}$-model found as in thehomogeneous superintegrable chiral Potts model.

Bethe Equation of $\tau^{(2)}$-model and Eigenvalues of Finite-size Transfer Matrix of Chiral Potts Model with Alternating Rapidities