The 2A 0335+096 cluster of galaxies was observed in X-rays with the Position Sensitive Proportional Counter (PSPC) and the High Resolution Imager (HRI) on ROSAT. Spatially resolved X-ray spectra show a decrease in the ambient temperature of the X-ray emitting gas in the inner regions of the cluster, indicative of a cooling flow. The spectra also confirm the presence of an absorbing column density in excess of the measured Galactic value toward the cooling how region, which must be intrinsic to the cluster. The mass of this absorbing matter is 7.4 x 10(11) M. within 170 kpc of the center of the cluster. A deprojection of the surface brightness profile combined with the observed temperature profile yields electron density, gas and gravitational mass, and mass deposition rate profiles. Within 1.2 Mpc the total gravitating mass is 1.9 x 10(14) M.. A cooling rate of 400(-65)(+90) M. yr(-1) is found within the cooling radius of 166(-18)(+28) kpc. This value is consistent with the cooling rate obtained by fitting a cooling flow model to the spectrum of the central 166 kpc. Although the cooling rate is proportional to radius for the inner 60 kpc, it is essentially constant beyond this point, which suggests that the gas cools homogeneously in this region. A similar result was found for the NGC 5044 group of galaxies by David et al. (1994). This disagrees with earlier observations of other clusters, which suggested that the gas within the entire cooling flow region was inhomogeneous.