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We analyze high-resolution Na I and Ca II interstellar absorption line data obtained toward 57 stars along extended sight lines through the Galactic disk and halo. The low average H I column densities along these sight lines indicate that absorption should arise mainly within a warm intercloud medium with some contribution from diffuse clouds. We find that the Na I lines trace the cloudy medium and the Ca II lines trace both the cloudy medium and a more extended (intercloud) medium. The clouds detected along these sight lines are more diffuse than the typical diffuse interstellar cloud in the solar neighborhood. We find that high latitude and interarm sight lines that do not cross spiral arms have clouds that are more diffuse on average than those along sight lines that cross spiral arms. This result indicates that either spiral structure may play an important role in determining the average absorption properties along extended sight lines or that interesting physical differences may exist between sight lines that cross spiral arms and those that do not. On average 10 percent of the Ca II column density occurs at velocities forbidden by the Galactic rotation law by more than 10 km/s. In contrast, only a small percentage of the Na I column density occurs at these velocities. The Ca II to Na I ratio increases by a factor of 15 over forbidden velocities from 0 to 50 km/s and rises rapidly thereafter. We find little evidence in the Na I or Ca II data for the RfastS H I distribution seen in 21 cm studies. A two component model of the Ca II column density per unit velocity over the range l = 325 to 360 indicates that two distinct distributions exist with velocity dispersions of 8 km/s and 21 km/s. As much as 60 percent of the Ca II column density at forbidden velocities may be associated with the faster distribution we attribute to warm intercloud material. We estimate exponential scale heights of 0.4-0.5 kpc for the neutral gas traced by the E(B-V), Na I, and H I distributions along the low density sight lines, and we find that Ca II has a larger scale height of 0.8 kpc. We base the scale height results upon both the integrated column densities and kinematical considerations.
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