  We observed several nearby face-on spiral galaxies with the ROSAT PSPC. The
apparent deficiency in soft X-ray surface brightness observed at the outer
portion of their disks is consistent with the absorption of the extragalactic
soft X-ray background by material associated with these galaxies, and allows us
to place a lower limit on the intensity of this cosmologically important
background. From the depth of the soft X-ray shadow observed in NGC 3184, a 95%
confidence lower limit was derived to be $32 keV cm^{-2} s^{-1} keV^{-1}$ at
1/4 keV. This was obtained by assuming that there is no unresolved 1/4 keV
X-ray emission from the outer region of the galaxy which may otherwise
partially fill in the shadow: any such emission, or any unresolved structure in
the absorbing gas, would imply a larger value. In the deepest exposure to date
in this energy range, Hasinger et al. (1993) resolved about $30 keV cm^{-2}
s^{-1} keV^{-1}$ at 1/4 keV into discrete sources; our current limit is
therefore consistent with an extragalactic origin for all of these sources. Our
results can also be directly compared with the corresponding upper limit
derived from the ROSAT PSPC detection of soft X-ray shadows cast by
high-latitude clouds in Ursa Major, $\simeq 65 keV cm^{-2} s^{-1} keV^{-1}$ at
1/4 keV. The lower and upper limits are only a factor of 2 apart, and begin to
provide a reasonable measurement of the intensity of the 1/4 keV extragalactic
X-ray background.
