We present ROSAT PSPC and HRI observations of the galactic wind from t
he starburst galaxy M 82. X-ray emission from the wind is detected to
a distance of similar to 6 kpc from the plane of the galaxy. Making us
e of the PSPC's mixture of good spatial and spectral characteristics,
we separate point source and diffuse emission, and investigate the spe
ctral variation of the diffuse emission through the wind. The intrinsi
c X-ray luminosity of the wind in the 0.1-2.4 keV band is found to be
approximately 1.9 x 10(40) erg s(-1) outside the immediate vicinity of
the nucleus. The temperature of the diffuse emission is found to decr
ease weakly from similar to 0.6 keV to similar to 0.4 keV along the mi
nor 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 t
hese results with those expected from two simple models for the emissi
on: 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.