a dynamic or kinetic quantity. Rather it is a thermodynamic quantity in the sense that it is purely a function of the microstate of the system dictated by its location in phase space. The generalized compressibility is easy to compute numerically, and it is simpler than the dielectric constant which involves both the translation and orientation of electric dipoles. In addition it does not suffer from finite size effects that can often plague measurements of the ordinary compressibility deduced from simulations. The generalized compressibility can be calculated in either the canonical or grand canonical ensembles. In particular it is well defined for a system with fixed volume $V$ and particle number $N$ in contrast to the ordinary compressibility which is defined for a system that has fluctuations in $N$ or $V$. The generalized compressibility should be directly measurable experimentally in colloidal suspensions of polystyrene spheres [@Weeks00] and possibly in other systems as well. In this paper we present measurements of this quantity in a molecular dynamics simulation of a two component system of soft spheres. We find that the linear generalized compressibility drops sharply as the temperature decreases below the glass transition temperature $T_g$. The drop becomes more and more 