  We present the results from a study of the spatial distributions of cooling
gas and intrinsic X-ray absorbing material in a sample of nearby, X-ray bright
cooling flow clusters observed with the Position Sensitive Proportional Counter
(PSPC) on ROSAT. Our method of analysis employs X-ray colour profiles, formed
from ratios of the surface brightness profiles of the clusters in selected
energy bands, and an adapted version of the deprojection code of Fabian et. al
(1981). We show that all of the cooling flow clusters in our sample exhibit
significant central concentrations of cooling gas. At larger radii the clusters
appear approximately isothermal. In detail, the spatial distributions and
emissivity of the cooling material are shown to be in excellent agreement with
the predictions from the deprojection code, and can be used to constrain the
ages of the cooling flows. The X-ray colour profiles also indicate substantial
levels of intrinsic X-ray absorption in the clusters. The intrinsic absorption
increases with decreasing radius, and is confined to the regions occupied by
the cooling flows. We explore a range of likely spatial distributions for the
absorbing gas and discuss the complexities involved in the measurement of
column densities from X-ray data. Comparison of our results with previously
reported observations made with Einstein Observatory Solid State Spectrometer
(White et. al 1991) shows reasonable agreement, but requires that the absorbing
material only partially covers the X-ray emitting regions. The results
presented in this paper provide strong support for the standard model of
inhomogeneous cooling flows in clusters of galaxies.
