  We discuss the Whitham deformation of the effective superpotential in the
Dijkgraaf-Vafa (DV) theory. It amounts to discussing the Whitham deformation of
an underlying (hyper)elliptic curve. Taking the elliptic case for simplicity we
derive the Whitham equation for the period, which governs flowings of branch
points on the Riemann surface. By studying the hodograph solution to the
Whitham equation it is shown that the effective superpotential in the DV theory
is realized by many different meromorphic differentials. Depending on which
meromorphic differential to take, the effective superpotential undergoes
different deformations. This aspect of the DV theory is discussed in detail by
taking the N=1^* theory. We give a physical interpretation of the deformation
parameters.
