  Hercules X-1 is a nearly edge-on X-ray binary with a warped, precessing
accretion disk, which manifests through a 35-day cycle of alternating High and
Low flux states. This disk precession introduces a changing line of sight
towards the X-ray source, through an ionized accretion disk wind. The sightline
variation allows us to uniquely determine how the wind properties vary with
height above the disk. All the previous wind measurements were made in the
brighter Main High state of Her X-1. Here, we analyze the only Chandra
observation during the fainter `Short' High state, and significantly detect
blueshifted ionized absorption. We find a column density of
$2.0_{-0.6}^{+1.1}\times10^{22}$ cm$^{-2}$, an ionization parameter $\log
(\xi$/erg cm s$^{-1})=3.41_{-0.12}^{+0.15}$ and an outflow velocity of $380 \pm
40$ km/s. The properties of the outflow measured during the Short High state
are in good agreement with those measured at equivalent precession phases
during Main High. We conclude that we are sampling the same wind structure,
seen during both Main and Short High, which is precessing alongside with the
warped accretion disk every 35 days. Finally, the high spectral resolution of
Chandra gratings above 1 keV in this observation enabled us to measure the
abundances of certain elements in the outflow. We find
Mg/O$=1.5_{-0.4}^{+0.5}$, Si/O$=1.5 \pm 0.4$ and S/O$=3.0_{-1.1}^{+1.2}$,
whereas in our previous study of Her X-1 with XMM-Newton, we found an
over-abundance of N, Ne and Fe compared with O. These peculiar abundance ratios
were likely introduced by pollution of the donor by the supernova which created
Her X-1.
