  The free energy of the chiral Potts model has been obtained in two ways. The
first used only the star-triangle relation, symmetries and invariances, and led
to a system of equations that implicitly define the free energy, and from which
the critical behaviour can be obtained. The second used the functional
relations derived by Bazhanov and Stroganov, solving them to obtain the free
energy explicitly as a double integral. Here we obtain, for the first time, a
direct verification that the two results are identical at all temperatures.
