  We place observational constraints on a recently proposed Galactic
population, dubbed the shroud (Gyuk & Gates 1999, Gates & Gyuk 2001). The
shroud would be a very thick Galactic disk of low luminosity objects, most
likely old white dwarfs, proposed to explain the optical depth seen in
microlensing surveys towards the Magellanic clouds. The shroud is a simple
alternative to the lenses being distributed in a classical, near-spherical dark
halo; the advantage of the shroud is that it would compose only a fraction of a
dark halo's total mass.
  In this paper, we argue that stars of the Galactic shroud would be detectable
in the recent proper motion survey of Oppenheimer et al. (2001) if their
absolute luminosities were brighter than M_R_59F = 19.4 or approximately M_V =
18.6. We adopt a range of simple models of the shroud's kinematics and
morphology, and the colours and luminosities of its white dwarfs; via
Monte-Carlo simulations, we predict the numbers expected in the Oppenheimer et
al. survey, which would be clearly separated from the numbers produced by white
dwarfs of the disk, thick disk and halo.
  The number of white dwarf detections in the proper motion survey (98) is
found to be well explained by the disk, thick disk and halo. With the most
conservative kinematic and density parameters for the shroud, and an absolute
luminosity of the white dwarfs of M_R_59F = 17.6, we find that the proper
motion survey would detect over 100 WDs, just from the shroud. For a M_R_59F =
19.4 shroud, the survey would find 5 +/- 2 peculiar objects, whereas only two
white dwarfs with such characteristics are found in the original data. M_R_59F
= 19.4 corresponds to M_V = 18.6 for WDs with V - I = -1.030.
