  We discuss the propagation of electromagnetic waves on a rectangular lattice
of polarizable point dipoles. For wavelengths long compared to the lattice
spacing, we obtain the dispersion relation in terms of the lattice spacing and
the dipole polarizabilities. We also obtain the polarizabilities required for
the lattice to have the same dispersion relation as a continuum medium of given
refractive index m.; our result differs slightly from previous work by Draine &
Goodman (1993). Our new prescription can be used to assign dipole
polarizabilities when the discrete dipole approximation is used to study
scattering by finite targets. Results are shown for selected cases.
