We present ROSAT PSPC and HRI observations of the galactic wind from the starburst galaxy M 82. X-ray emission from the wind is detected to a distance of ∼6kpc from the plane of the galaxy. Making use of the PSPC's mixture of good spatial and spectral characteristics, we separate point source and diffuse emission, and investigate the spectral variation of the diffuse emission through the wind. The intrinsic X-ray luminosity of the wind in the 0.1-2.4keV band is found to be approximately 1.9x1040erg/s outside the immediate vicinity of the nucleus. The temperature of the diffuse emission is found to decrease weakly from ∼0.6keV to ∼0.4keV along the minor axis, whilst the inferred gas density drops as z–0.5 and z–0.8 along the northern and southern minor axes respectively. We compare these results with those expected from two simple models for the emission: Chevalier & Clegg's adiabatically expanding free wind and emission from shocked clouds in a wind, and find that the emission cannot come from a free wind, but that shock heated clouds could be the source of the emission.