  We present the results of a CCD imaging survey for gravitational lensing in a
sample of 38 X-ray-selected clusters of galaxies. Our sample consists of the
most X-ray luminous (Lx>= 2x10^{44} erg s^{-1}) clusters selected from the
Einstein Observatory Extended Medium Sensitivity Survey (EMSS) that are
observable from Mauna Kea (dec > -40deg). The sample spans a redshift range of
0.15 < z < 0.823 and includes 5 clusters with z > 0.5. CCD images of the
clusters were obtained in excellent seeing. There is evidence of strong
gravitational lensing in the form of giant arcs (length l > 8'', axis ratio l/w
> 10) in 8 of the 38 clusters. Two additional clusters contain shorter arclets,
and 6 more clusters contain candidate arcs that require follow-up observations
to confirm their lensing origin. Since the survey does not have a uniform
surface brightness limit we do not draw any conclusion based on the statistics
of the arcs found. We note, however, that 60% (3 of 5) of the clusters with Lx
> 10^{45} erg s^{-1}, and none of the 15 clusters with Lx < 4x10^{44} erg
s^{-1} contain giant arcs, thereby confirming that high X-ray luminosity does
identify the most massive systems, and thus X-ray selection is the preferred
method for finding true, rich clusters at intermediate and high redshifts. The
observed geometry of the arcs, most of which are thin, have large axis ratios
(l/w > 10), and are aligned orthogonal to the optical major axes of the
clusters, indicate the cluster core mass density profiles must be compact
(steeper than isothermal). In several cases, however, there is also some
evidence, in the form of possible radial arcs, for density profiles with finite
core radii.
