  Analysis of several recent ROSAT HRI observations of the gravitationally
lensed system Q0957+561 has led to the detection at the 3sigma level of the
cluster lens containing the primary galaxy G1. The total mass was estimated by
applying the equation of hydrostatic equilibrium to the detected hot
intracluster gas for a range of cluster core radii, cluster sizes and for
different values of the Hubble constant. X-ray estimates of the lensing cluster
mass provide a means to determine the cluster contribution to the deflection of
rays originating from the quasar Q0957+561. The present mass estimates were
used to evaluate the convergence parameter kappa, the ratio of the local
surface mass density of the cluster to the critical surface mass density for
lensing. The convergence parameter, kappa, calculated in the vicinity of the
lensed images, was found to range between 0.07 and 0.21, depending on the
assumed cluster core radius and cluster extent. This range of uncertainty in
kappa does not include possible systematic errors arising from the estimation
of the cluster temperature through the use of the cluster
luminosity-temperature relation and the assumption of spherical symmetry of the
cluster gas. Applying this range of values of kappa to the lensing model of
Grogin & Narayan (1996) for Q0957+561 but not accounting for uncertainties in
that model yields a range of values for the Hubble constant:67<H_0<82 km s^-1
Mpc^-1, for a time delay of 1.1 years.
