Five observations of the hard X-ray spectrum of Her X-1 from RXTE show that the ~41 keV energy of the cyclotron scattering line is constant within statistics of a few percent per observation. The overall spectral shape, on the other hand, varies somewhat, with an rms of 2%. If the 41 keV feature truly originates as cyclotron resonance scattering in an unchanging 3 × 1012 G dipole field not far above the neutron star surface, these observations constrain the average height of scattering to within a range of 180 m. This is consistent with models that put the radiating structure within meters of the surface of the neutron star. In other pulsars, observed line centroid changes have been correlated with luminosity changes, and if interpreted as variations of the height at which scattering takes place, many hundreds of meters are required. These RXTE data, which sample nearly a factor of 2 in unabsorbed luminosity, are in conflict with a particular model for such an extended radiating structure. Comparison with other observations over many years indicates strongly that the centroid energy of this absorption line has increased some time between 1991 and 1993 by 23%, from 34 to 41 keV. Moreover, the cutoff energy of the spectral continuum increased at the same time from 16 to 20 keV, which is, within the statistical error of 5%, in direct proportion to the centroid. This may be a sign that both these characteristics of the spectrum are controlled in the same way by the magnetic field strength in the region of scattering.
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