We have carried out a soft X-ray survey of the sky using the ROSAT
Position Sensitive Proportional Counter (PSPC) in a region of very low
Galactic column density (N_H_ = 6-9 x 10^19^ cm^-2^). The data consist
of a deep >70 ks pointing (the Deep Survey) and six pointings at
lower sensitivity (13-20 ks; the Medium Survey). We detect a total of
141 sources over the 0.9 deg^2^ of sky area used. The faintest source
detected has a flux of 3.2 x 10^-15^ erg cm^-2^ s^-1^ (0.5-2.0 keV). We
present the source number-flux distribution, and we compare it with the
distributions constructed from other ROSAT observations and from surveys
carried out with X-ray instruments operating at higher energies. We
estimate the contribution of the resolved sources to the soft X-ray
background by direct comparison of their integrated spectrum with that
of the diffuse background: 44 per cent of the extragalactic X-ray
background between 0.5 and 2.0 keV is resolved directly into discrete
sources whose average spectrum is steeper than that of the background.
Integration of our number-flux relation to infinite flux produces a
background resolved fraction of 44+/- _5_^56^ per cent (0.5-2.0 keV).
Limits on the slope of the log N-log S curve at very faint fluxes are
set by the measured value of the X-ray background.