We present results of a 5.7 day duration BeppoSAX observation of the short-on state of Her X-1 and a short observation during the decline of the preceding main-on state. The 0.1-10 keV spectra can be fit with a power-law and blackbody model together with Fe emission features at 1.0 keV and 6.5 keV. During the later stages of the short-on state there are long intervals when the absorption is $approxgt$$5 times 10^{22}$ atom cm$^{-2}$. These intervals become longer and occur ~0.3 day earlier in each orbital cycle as the short-on state progresses. During the intervals of high absorption the 0.1 keV blackbody is still clearly detected. This may indicate the presence of separate scattered and absorbed spectral components, although other explanations such as partial covering or a partially ionized absorber cannot be excluded. During the rest of the short-on state the ratio of flux in the blackbody compared to the power-law is consistent with that in the main-on state. This supports the view that much of the 35 day modulation is caused by an energy independent process, such as electron scattering. The discovery of strong absorption late in the short-on state is consistent with the predictions of the warped disk model (Petterson 1977, see also Schandl & Meyer 1994) where the end of the short-on state is caused by the accretion disk moving into the line of sight to the neutron star. The pulse phase difference between the blackbody and the power-law maxima is 250 +/- 20 degrees in both observations (separated by 0.43 of a 35 day cycle). This constant phase difference is consistent with the blackbody originating at the inner edge of a precessing accretion disk.
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