  We present the results of a detailed investigation into the physical
conditions in interstellar material interacting with the supernova remnant IC
443. Our analysis is based on a comprehensive examination of high-resolution
far-ultraviolet spectra obtained with the Space Telescope Imaging Spectrograph
onboard the Hubble Space Telescope of two stars behind IC 443. One of our
targets (HD 43582) probes gas along the entire line of sight through the
supernova remnant, while the other (HD 254755) samples material located ahead
of the primary supernova shock front. We identify low velocity quiescent gas in
both directions and find that the densities and temperatures in these
components are typical of diffuse atomic and molecular clouds. Numerous high
velocity components are observed in the absorption profiles of neutral and
singly-ionized atomic species toward HD 43582. These components exhibit a
combination of greatly enhanced thermal pressures and significantly reduced
dust-grain depletions. We interpret this material as cooling gas in a
recombination zone far downstream from shocks driven into neutral gas clumps.
The pressures derived for a group of ionized gas components at high positive
velocity toward HD 43582 are lower than those of the other shocked components,
pointing to pressure inhomogeneities across the remnant. A strong very high
velocity component near -620 km/s is seen in the absorption profiles of
highly-ionized species toward HD 43582. The velocity of this material is
consistent with the range of shock velocities implied by observations of soft
thermal X-ray emission from IC 443. Moderately high-velocity gas toward HD
254755 may represent shocked material from a separate foreground supernova
remnant.
