Prompted by the H I Ly$alpha$ absorption associated with the X-ray ultra-fast outflow at -17,300 $rm km~s^{-1}$ in the quasar PG~1211+143, we have searched archival UV spectra at the expected locations of H I Ly$alpha$ absorption for a large sample of ultra-fast outflows identified in XMM-Newton and Suzaku observations. Sixteen of the X-ray outflows have predicted H I Ly$alpha$ wavelengths falling within the bandpass of spectra from either the Far Ultraviolet Spectroscopic Explorer or the Hubble Space Telescope, although none of the archival observations were simultaneous with the X-ray observations in which UFOs were detected. In our spectra broad features with full-width at half-maximum of 1000 $rm km~s^{-1}$ have 2-$sigma$ upper limits on the H I column density of generally <$2times10^{13}~rm cm^{-2}$. Using grids of photoionization models covering a broad range of spectral energy distributions, we find that producing Fe XXVI Ly$alpha$ X-ray absorption with equivalent widths $>30$ eV and associated H I Ly$alpha$ absorption with $rm N_{HI}<2times10^{13}~cm^{-2}$ requires total absorbing column densities $rm N_{H}>5times10^{22}~cm^{-2}$ and ionization parameters log $xi$ > 3.7. Nevertheless, a wide range of SEDs would predict observable H I Ly$alpha$ absorption if ionization parameters are only slightly below peak ionization fractions for Fe XXV and Fe XXVI. The lack of Ly$alpha$ features in the archival UV spectra indicates that either the UFOs have very high ionization parameters, very hard UV-ionizing spectra, or that they were not present at the time of the UV spectral observations due to variability.
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