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With far-ultraviolet spectra of B stars taken with the Hopkins Ultraviolet Telescope (HUT) aboard the ASTRO-1 space observatory, we determine the far-ultraviolet extinction by galactic dust and hydrogen absorption in the local spiral-arm clouds toward HD~25443 (B0.5~III), HD~37903 (B1.5~V), and HD~200775 (B3~Ve). Respectively, the number fractions of H-atoms in molecular hydrogen relative to the total hydrogen are $f = 0.31$, 0.56, and $> 0.8$, showing that the Galactic media are different. The shape and strength of the HD~25443 FUV extinction is the same as a diffuse-medium mean extinction extrapolated from mid-UV wavelengths (Cardelli, Clayton, and Mathis 1989) [normal]. The HD~37903 FUV extinction through a bright \htwo\ photodissociation region is higher than a mean FUV extinction, as is the HD~200775 extinction. Another star from the literature, $\rho$~Oph, probes the dense medium and exhibits an FUV extinction of normal mean strength but steeper shape.
The ``normal'' FUV-extinction of HD~25443 implies that the small FUV-extinction dust in the diffuse medium forms in part from larger grains as the grains shatter under shocks. The normal strength of the $\rho$~Oph FUV-extinction indicates that the minute dust condenses onto or coaggulates into larger grains in the dense medium. The high extinction of the HD~37903 PDR (and HD~200775 PDR) shows that FUV radiation from hot stars with $T_{eff} \approx$~21,000--23,000~K can evaporate some of the FUV-extinction dust from grain surfaces in photodissociation regions. In contrast, previously-measured extinctions in Galactic \hion\ (H~II) regions shows that FUV radiation at $T_{eff} > 26,000$~K can destroy some of the dust in \hion\ (H~II) regions. Thus, some of the FUV-extinction dust is highly volatile.
We find that the dust carrier of the variable FUV extinction is correlated with the mid-IR (12~\um) radiation from hydrocarbon dust.
