AbstractThe ground electronic state of neutral atomic carbon has three fine-structure levels. In the interstellar medium, the relative populations of the upper two levels are established by collisional excitations (and de-excitations) balanced against spontaneous radiative decay. Consequently, the fractions of C I in the upper two levels indicate acceptable combinations of local temperature and density, which in turn indicate the approximate thermal pressures of the medium. We can measure the values of these fractions and how they vary from one location to the next by observing the multiplets of C I seen in absorption in the ultraviolet spectra of hot stars.We have identified 102 stars for which the HST MAST archive has E140H STIS spectra that are suitable for measuring the absorption features of C I at velocity resolutions of 3 kms⁻¹(or better). A special analysis method developed by Jenkins & Tripp (2001) permits determinations of the amounts of C I in each of the three levels as a function of radial velocity over a wide dynamic range in column density, since several multiplets of vastly different strengths can be considered simultaneously.The C I data reveal that the much of the diffuse, cold, neutral medium has pressures that are distributed in an approximately log-normal fashion, spread over a range 1000 < p/k < 10⁴ cm⁻³ K (FWHM), but with low level tails outside this range. The dispersion of pressures increases slightly for gases that have radial velocities outside the expected range for quiescent material along each line of sight. This link to the kinematics of the gas is consistent with the picture that pressure fluctuations are driven by the dynamics of a turbulent medium. If the gas is a single medium that is being driven by turbulent forces, its barytropic index (slope of log p vs. log n) is more than 0.9, which is inconsistent with the value 0.72 for material that is expected to be in thermal equilibrium. Slightly less than one part in a thousand of the gas is at pressures of order or greater than ~10⁵cm⁻³ K and seems to nearly always accompany the gas at normal pressures.