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 \left [ { C / H } \right ] _ { dust } with the 2175 { \AA } 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 { \AA } extinction bump exhibits variable strengths and widths .
We derive \left [ { C / H } \right ] _ { 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 \left [ { C / H } \right ] _ { dust } from fitting the observed UV/optical/near-infrared extinction with a mixture of amorphous silicate and graphite .
We find that the carbon depletion \left [ { C / H } \right ] _ { dust } tends to correlate with the strength of the 2175 { \AA } bump , while the abundance of silicon depleted in dust shows no correlation with the 2175 { \AA } bump .
This supports graphite or polycyclic aromatic hydrocarbon ( PAH ) molecules as the possible carrier of the 2175 { \AA } bump .
We also see that \left [ { C / H } \right ] _ { 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 .