  We probe the role of carbon in the ultraviolet (UV) extinction by examining
the relations between the amount of carbon required to be locked up in dust
[C/H]_dust with the 2175 Angstrom extinction bump and the far-UV extinction
rise, based on an analysis of the extinction curves along 16 Galactic
sightlines for which the gas-phase carbon abundance is known and the 2175
Angstrom extinction bump exhibits variable strengths and widths.
  We derive [C/H]_dust from the Kramers-Kronig relation which relates the
wavelength-integrated extinction to the total dust volume. This approach is
less model-dependent since it does not require the knowledge of the detailed
optical properties and size distribution of the dust. We also derive [C/H]_dust
from fitting the observed UV/optical/near-infrared extinction with a mixture of
amorphous silicate and graphite.
  We find that the carbon depletion [C/H]_dust tends to correlate with the
strength of the 2175 Angstrom bump, while the abundance of silicon depleted in
dust shows no correlation with the 2175 Angstrom bump. This supports graphite
or polycyclic aromatic hydrocarbon (PAH) molecules as the possible carrier of
the 2175 Angstrom bump. We also see that [C/H]_dust shows a trend of
correlating with 1/R_V, where R_V is the total-to-selective extinction ratio,
suggesting that the far-UV extinction is more likely produced by small carbon
dust than by small silicate dust.
