We present the analysis of an observation of the X-ray luminous cluster of galaxies Abell 478 made with the Position Sensitive Proportional Counter (PSPC) on ROSAT. The X-ray emission from the central regions of the cluster is shown to be absorbed by a column density in excess of the Galactic value obtained from 21-cm H I observations, confirming the results of previous observations with the Solid State Spectrometer on the Einstein Observatory. We have measured the radial variation of column density and temperature within the cluster, in annuli concentric with the peak of the X-ray emission. The PSPC spectra show that the excess absorption is concentrated within the inner approximately 300 kpc, and so must be intrinsic to the cluster. The X-ray absorbing matter has a mass > 10(12) M. and is a significant component of the intracluster medium in the cluster centre. At large radii, the measured temperature of the intracluster gas is consistent with the value of approximately 6.6 keV measured over the whole cluster by Ginga. Within approximately 300 kpc of the cluster centre the temperature drops rapidly, to a value averaged over the inner 150 kpc of approximately 3 keV. A simple deprojection analysis of the ROSAT image has been performed which confirms that Abell 478 has one of the largest known cooling flows, with an integrated mass deposition rate of approximately 1000 M. yr-1. Spectral fitting of the central 300 kpc of the cluster also demonstrates the presence of material significantly cooler than the ambient intracluster gas, which can be well modelled by a cooling flow with a mass deposition rate consistent with the deprojection result. The radius within which the intrinsic absorbing material is detected is well matched to the cooling radius of the cluster. We suggest that the absorbing matter may be cooled gas, which has been deposited by the flow and accumulated on time-scales of approximately few x 10(9) yr.