  We have made ROSAT PSPC and HRI X-ray observations to study the intracluster
gas surrounding the powerful radio source Hercules A. The cluster is luminous
in X-rays (L_bol = 4.8x10^37 W), and the host of the radio source is the
central dominating galaxy of the cluster. The X-ray surface brightness profile
is well fitted by a modified King beta model, but the cluster is elongated
parallel to the radio source, especially on the scale of the radio lobes. Fits
to individual quadrants give a core radius 50 per cent larger along the radio
axis. Part of this elongation appears to be associated with enhanced X-ray
emission superimposed on the outer radio lobes. There are no obvious
depressions in the X-ray emission coincident with the radio lobes, as expected
if the relativistic plasma displaces the ICM. However, we show that these
depressions may be quite weak. From the surface brightness profile for the PSPC
data the X-ray emission extends out to ~ 2.2 Mpc radius. In the absence of the
powerful jets, we would expect a cooling flow at the centre of the cluster, but
currently it must be substantially disturbed by the expansion of the radio
lobes. The PSPC spectrum reveals a cool component of the ICM with 0.5 < kT < 1
keV. The central cooling time could be as low as 2 Gyr if the cool component is
centrally concentrated, otherwise it is around 6 Gyr. The modelled central
electron density is typical for modest cooling flows. Finally, we have detected
faint X-ray emission from a compact central source.
