  We establish an extragalactic, zero-motion frame of reference within the
deepest optical image of a globular star cluster, an HST 123-orbit exposure of
M4 (GO 8679, cycle 9). The line of sight beyond M4 (l,b (deg) = 351,16)
intersects the inner halo (spheroid) of our Galaxy at a tangent-point distance
of 7.6 kpc (for Ro = 8 kpc). We isolate these spheroid stars from the cluster
based on their proper motions over the 6-year baseline between these and
previous epoch HST data (GO 5461, cycle 4). Distant background galaxies are
also found on the same sight line using image-morphology techniques. This fixed
reference frame allows us to independently determine the fundamental Galactic
constant, Vo/Ro = 25.3 +/- 2.6 km/s/kpc, thus providing a velocity of the Local
Standard of Rest, v = 202.7 +/- 24.7 km/s for Ro = 8.0 +/- 0.5 kpc. Secondly,
the galaxies allow a direct measurement of M4's absolute proper motion,
mu_total = 22.57 +/- 0.76 mas/yr, in excellent agreement with recent studies.
The clear separation of galaxies from stars in these deep data also allow us to
search for inner-halo white dwarfs. We model the conventional Galactic
contributions of white dwarfs along our line of sight and predict 7.9 (thin
disk), 6.3 (thick disk) and 2.2 (spheroid) objects to the limiting magnitude at
which we can clearly delineate stars from galaxies (V = 29). An additional 2.5
objects are expected from a 20% white dwarf dark halo consisting of 0.5 Mo
objects, 70% of which are of the DA type. After considering the kinematics and
morphology of the objects in our data set, we find the number of white dwarfs
to be consistent with the predictions for each of the conventional populations.
However, we do not find any evidence for dark halo white dwarfs.
