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We have used the Very Long Baseline Array (VLBA) and the Very Large Array(VLA) to image Galactic neutral hydrogen in absorption towards four compactextragalactic radio sources with 10 milliarcsecond resolution. Previous VLBAdata by Faison et al (1998) have shown the existence of prominent structures inthe direction of the extragalactic source 3C~138 with scale sizes of 10-20 AUwith changes in HI optical depth in excess of 0.8 $\pm$ 0.1. In this paper weconfirm the small scale \hi optical depth variations toward 3C~147 suggestedearlier at a level up to 20 % $\pm$ 5% . The sources 3C~119, 2352+495 and0831+557 show no significant change in \hi optical depth across the sourceswith one sigma limits of 30%, 50%, and 100%. Of the seven sources recentlyinvestigated with the VLBA and VLA, only 3C~138 and 3C~147 show statisticallysignificant variations in HI opacities.  Deshpande (2000) have attempted to explain the observed small-scale structureas an extension of the observed power spectrum of structure on parsec sizescales. The predictions of Deshpande (2000) are consistent with the VLBA HIdata observed in the directions of a number of sources, including 3C~147, butare not consistent with our previous observations of the HI opacity structuretoward 3C~138

The Structure of the Cold Neutral Interstellar Medium on 10–100 AU Scales