  We present the results of a pencil-beam survey of the Kuiper Belt using the
Keck 10-m telescope. A single 0.01 square degree field is imaged 29 times for a
total integration time of 4.8 hr. Combining exposures in software allows the
detection of Kuiper Belt Objects (KBOs) having visual magnitude V < 27.9. Two
new KBOs are discovered. One object having V = 25.5 lies at a probable
heliocentric distance d = 33 AU. The second object at V = 27.2 is located at d
= 44 AU. Both KBOs have diameters of about 50 km, assuming comet-like albedos
of 4%.
  Data from all surveys are pooled to construct the luminosity function from
red magnitude R = 20 to 27. The cumulative number of objects per square degree,
N (< R), is fitted to a power law of the form log_(10) N = 0.52 (R - 23.5).
Differences between power laws reported in the literature are due mainly to
which survey data are incorporated, and not to the method of fitting. The
luminosity function is consistent with a power-law size distribution for
objects having diameters s = 50 to 500 km; dn ~ s^(-q) ds, where the
differential size index q = 3.6 +/- 0.1. The distribution is such that the
smallest objects possess most of the surface area, but the largest bodies
contain the bulk of the mass. Though our inferred size index nearly matches
that derived by Dohnanyi (1969), it is unknown whether catastrophic collisions
are responsible for shaping the size distribution. Implications of the absence
of detections of classical KBOs beyond 50 AU are discussed.
