Spectral study of three observations of the accreting X-ray pulsar Her
X-1 during RXTE observing round 1 show that the values of two spectra
l parameters, the cut energy and the cyclotron line centroid, appear t
o be much more stable than for the other shape parameters. These two p
arameters have been closely linked to the strength of the teragauss ma
gnetic field above the polar cap of the neutron star. The RMS stabilit
y of 1% implies an equal constraint on the average value of the magnet
ic field at the site of emission, and in a dipole field this constrain
s the average height of emission to within 50 meters. It may be possib
le to discriminate between emission in the very thin neutron star atmo
sphere and in an extensive accretion mound.