  Interstellar thermal pressures can be measured using C I absorption lines
that probe the pressure-sensitive populations of the fine-structure levels of
its ground state. In a survey of C I absorption toward Galactic hot stars,
Jenkins & Tripp (2011) found evidence of small amounts ($\sim 0.05\%$) of gas
at high pressures ($p/k \gg 10^4{\rm cm^{-3}K}$) mixed with a more general
presence of lower pressure material exhibiting a log normal distribution that
spanned the range $10^3 \lesssim p/k \lesssim 10^4{\rm cm^{-3}K}$. In this
paper, we study Milky Way C I lines in the spectra of extragalactic sources
instead of Galactic stars and thus measure the pressures without being
influenced by regions where stellar mass loss and H II region expansions could
create localized pressure elevations. We find that the distribution of low
pressures in the current sample favors slightly higher pressures than the
earlier survey, and the fraction of gaseous material at extremely high
pressures is about the same as that found earlier. Thus we conclude that the
earlier survey was not appreciably influenced by the stellar environments, and
the small amounts of high pressure gas indeed exist within the general
interstellar medium.
