  The isothermal compressibility of a general crystal is derived and discussed
within (classical) density functional theory. Starting from the microscopic
particle density, we carefully coarse grain to obtain the thermodynamic
compressibility and the long wavelength limits of the correlation functions of
elasticity theory. We explicitly show that the isothermal compressibility is
not the wavevector to zero limit of the (total) density correlation function.
The latter also cannot be obtained from the static structure factor measured in
a scattering experiment.
