  We present a study of the compressibility, K, of a two-dimensional hole
system which exhibits a metal-insulator phase transition at zero magnetic
field. It has been observed that dK/dp changes sign at the critical density for
the metal-insulator transition. Measurements also indicate that the insulating
phase is incompressible for all values of B. Finally, we show how the phase
transition evolves as the magnetic field is varied and construct a phase
diagram in the density-magnetic field plane for this system.
