  High-resolution spectra covering absorption features from interstellar C I
were recorded for four early-type stars with spectrographs on HST, in a program
to measure the fine-structure excitation of this atom within neutral clouds
inside or near the edge of the Local Bubble, a volume of hot (T ~ 10^6 K) gas
that emits soft x-rays and extends out to about 100 pc away from the Sun. The
excited levels of C I are populated by collisions, and the ratio of excited
atoms to those in the ground level give a measure of the local thermal
pressure. Absorptions from the two lowest levels of C I were detected toward
alpha Del and delta Cyg, while only marginal indications of excited C I were
obtained for gamma Ori, and lambda Lup. Along with temperature limits derived
by other means, the C I fine-structure populations indicate that for the clouds
in front of gamma Ori, delta Cyg and alpha Del, 10^3 < p/k < 10^4 cm^{-3}K at
about the +-1 sigma confidence level in each case. The results for lambda Lup
are not as well constrained, but still consistent with the other three stars.
The results indicate that the thermal pressures are below generally accepted
estimates p/k > 10^4 cm^{-3}K for the Local Bubble, based on the strength of
x-ray and EUV emission from the hot gas. This inequality of pressure for these
neutral clouds and their surroundings duplicates a condition that exists for
the local, partly-ionized cloud that surrounds the Sun. An appendix in the
paper describes a direct method for determining and eliminating small spectral
artifacts arising from variations of detector sensitivity with position.
