  In clean enough samples of the high-$T_c$ oxide materials, the phase
transition into the superconducting state occurs along a first order line in
the $H$-$T$ plane. This means that a two-phase region occurs in the B-$T$
plane, in which the liquid and solid vortex phases coexist. We discuss the
thermodynamics of this two-phase region, developing formulae relating
experimental quantities of interest. We then apply the 3D XY scaling theory to
the problem, obtaining detailed predictions for the boundaries of the
coexistence region. By using published data, we are able to predict the width
of the two-phase region, and determine the physical parameters involved in the
3D XY description.
