The X-ray source in the Perseus cluster has been studied both by the Copernicus satellite and by sounding-rocket instruments flown by Columbia University. The spatial and spectral data from these observations are examined. A surface brightness distribution is obtained which shows that the source consists of a compact core associated with NGC 1275 and a more extended emission volume. The structure of the central core region has been examined by means of an image reconstruction technique, revealing a steeply declining luminosity function and north-south elongation. The spectrum of the emission of the core region is distinguished from that of the surrounding area and found to be consistent with a hydrogen column density of 2.5 x 10 to the 21th/sq cm. A comparison between the isothermal and adiabatic gas sphere models is presented which shows the need for at least two components to provide the X-ray emission.