  We report on the detection of dark matter in the cluster of galaxies
Abell~2163 using the weak gravitational distortion of background galaxies, and
an analysis of the cluster X-ray emission. We find that while the qualitative
distributions of the cluster light and the dark matter are similar -- shallow
and extended, with significant substructure -- the X-ray morphology shows a
more regular overall appearance. We interpret the joint lensing and X-ray
observations as a signature of a merger event in the cluster. We present new
ROSAT/HRI data and reanalyze ROSAT/PSPC data, accounting for the effect of a
varying background to determine the best fit parameters in the $\beta$-model
formalism. We combine the surface brightness fits with two determinations of
the radial temperature profile to determine the total mass. Although there are
slight variations in the total mass determinations introduced by the
uncertainties in the $\beta$-fit, the main contributor to the error arises from
the uncertainties in the temperature determinations. Even though the
morphologies of the dark matter/light and X-ray gas are quite different, we
find that the total mass determined from the X-ray and weak lensing estimates
are consistent with each other within the $2\sigma$ error bars, with the X-ray
inferred mass a factor of $\simeq 2$ larger. However, as the lensing mass
estimates are differential (the surface density at any point is determined
relative to the mean in a control annulus), the shallow, extended nature of the
mass profile biases the lensing inferred mass downwards. We estimate the
correction for this effect and find very good agreement between the corrected
lensing and X-ray results. We determine the gas mass fraction and find $f_g
\simeq 0.07h^{-3/2}$ at all radii and a constant mass-to-light ratio of $M/L_V
