  Rich and massive clusters of galaxies at intermediate redshift are capable of
magnifying and distorting the images of background galaxies. A comparison of
different mass estimators among these clusters can provide useful information
about the distribution and composition of cluster matter and their dynamical
evolution. Using a hitherto largest sample of lensing clusters drawn from
literature, we compare the gravitating masses of clusters derived from the
strong/weak gravitational lensing phenomena, from the X-ray measurements based
on the assumption of hydrostatic equilibrium, and from the conventional
isothermal sphere model for the dark matter profile characterized by the
velocity dispersion and core radius of galaxy distributions in clusters. While
there is an excellent agreement between the weak lensing, X-ray and isothermal
sphere model determined cluster masses, these methods are likely to
underestimate the gravitating masses enclosed within the central cores of
clusters by a factor of 2--4 as compared with the strong lensing results. Such
a mass discrepancy has probably arisen from the inappropriate applications of
the weak lensing technique and the hydrostatic equilibrium hypothesis to the
central regions of clusters as well as an unreasonably large core radius for
both luminous and dark matter profiles. Nevertheless, it is pointed out that
these cluster mass estimators may be safely applied on scales greater than the
core sizes. Namely, the overall clusters of galaxies at intermediate redshift
can still be regarded as the dynamically relaxed systems, in which the velocity
dispersion of galaxies and the temperature of X-ray emitting gas are good
indicators of the underlying gravitational potentials of clusters.
