The boundary-layer resistance and the difference in sheath potentials between a pair of electrodes were measured in a shock tube. Using a small, square electrode and a strip electrode flush with the wall of the shock tube, the electric current could be drawn across the shock tube was measured as a function of the shock wave position for several applied voltages and load resistances. All measurements were made in air at a shock speed of 4.35 mmn/ mu sec and an initial pressure of 1 mm Hg. In the range of applied voltages considered, the boundary-layer resistance was not a function of the current level. The change in the sheath potential was of the order of several volts. A continumm theory is developed to predict the boundary-layer resistance for small current levels and the sheath potential. The sheath solution is separated from the convective compressible boundary-layer problem where ambipolar diffusion dominates. In the sheath, the transport equations for ions and electrons in and electric field are solved numerically. Resulting integrals for the dimensionless boundary-layer resistance and sheath potential are evaluated, both in the sheath and in more » the compressible boundary layer, to obtuin results that can be compared with experiment. Values of the resistance obtained, assuming the ionization reaction to be frozen, are not in agreement with experiment. Reasonable agreement between theory and experiment is obtained for the magnitude of the sheath potential. (auth) « less