  We present {\em ROSAT} PSPC and HRI observations of the galactic wind from
the starburst galaxy M82. \mbox{X-ray} emission from the wind is detected to a
distance of $\sim6\kpc$ 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
0.1-2.4\keV\ band is found to be approximately $1.9\times10^{40}$\ergps outside
the immediate vicinity of the nucleus. The temperature of the diffuse emission
is found to decrease weakly from $\sim0.6\keV$ to $\sim0.4\keV$ 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.
