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A model is proposed for determining the distances to falling interstellar clouds in the galactic halo by measuring the cloud velocity and column density and assuming a model for the vertical density distribution of the Galactic interstellar medium. It is shown that falling clouds with N (H I) < ∼ 10 19 cm −2 may be decelerated to a terminal velocity which increases with increasing height above the Galactic plane. This terminal velocity model correctly predicts the distance to high velocity cloud Complex M and several other interstellar structures of previously determined distance. It is demonstrated how interstellar absorption spectra alone may be used to predict the distances of the clouds producing the absorption.If the distance, velocities, and column densities of enough interstellar clouds are known independently, the procedure can be reversed, and the terminal velocity model can be used to estimate the vertical density structure (both the mean density and the porosity) of the interstellar medium. Using the data of Danly and assuming a drag coefficient of C D ∼ = 1, the derived density distribution is consistent with the expected density distribution of the warm ionized medium, characterized by Reynolds. There is also evidence that for z > ∼ 0.4 kpc one or more of the following occurs: (1) the neutral fraction of the cloud decreases to ∼ 31 ± 14%, (2) the density drops off faster than characterized by Reynolds, or (3) there is a systematic decrease in C D with increasing z. Current data do not place strong constraints on the porosity of the interstellar medium.

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