  HIRES on the Keck I telescope has been used to measure the first radial
velocities for stars belonging to eleven, heavily-reddened globular clusters in
the direction of the inner Galaxy. The question of kinematic substructuring
among the Galactic globular cluster system is investigated using an updated
catalog of globular cluster distances, metallicities and velocities. It is
found that the population of metal-rich globular clusters shows significant
rotation at all Galactocentric radii. For the metal-rich clusters within 4 kpc
of the Galactic center, the measured rotation velocity and line-of-sight
velocity dispersion are similar to those of bulge field stars. We investigate
claims that the metal-rich clusters are associated with the central Galactic
bar by comparing the kinematics of the innermost clusters to that of the atomic
hydrogen in the inner Galaxy. The longitude-velocity diagram of both metal-rich
and metal-poor clusters bears a remarkable similarity to that of the gas,
including the same non-circular motions which have traditionally been
interpreted as evidence for a Galactic bar, or, alternatively, a
non-axisymmetric bulge. However, uncertainties in the existing
three-dimensional Galactocentric positions for most of the clusters do not yet
allow an unambiguous discrimination between the competing scenarios of
membership in a rigidly rotating bar, or in a bulge which is an oblate
isotropic rotator. We conclude that the majority of metal-rich clusters within
the central 4 kpc of the Galaxy are probably associated with the bulge/bar, and
not the thick disk. (ABRIDGED)
