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