  We give results for the $B$ and the $D$ meson spectrum using NRQCD on the
lattice in the quenched approximation. The masses of radially and orbitally
excited states are calculated as well as $S$-wave hyperfine and $P$-wave fine
structure. Radially excited $P$-states are observed for the first time. Radial
and orbital excitation energies match well to experiment, as does the
strange-non-strange $S$-wave splitting. We compare the light and heavy quark
mass dependence of various splittings to experiment. Our $B$-results cover a
range in lattice spacings of more than a factor of two. Our $D$-results are
from a single lattice spacing and we compare them to numbers in the literature
from finer lattices using other methods. We see no significant dependence of
physical results on the lattice spacing.
  PACS: 11.15.Ha 12.38.Gc 14.40.Lb 14.40.Nd
