Researchers investigate in detail the motion of gas in the galaxy NGC 1058 using the very large array (VLA) to map the emission in the 21-cm line. This galaxy is so nearly face-on that the contribution to the line width due to the variation of the rotational velocity across the D-array beam is small compared with the random z-motion of the gas. Researchers confirm results of earlier studies (Lewis 1987, A. and A. Suppl., 63, 515; van der Kruit and Shostak 1984, A. and A., 134, 258) of the galaxy's total neutral hydrogen (HI) and kinematics, including the fact that the rotation curve drops faster than Keplerian at the outer edge of the disk, which is interpreted as a fortuitous twist of the plane of rotation in the outer disk. However, their very high velocity resolution (2.58 km s(exp -1) after Hanning smoothing) coupled with good spatial resolution, allows researchers to measure more accurately the line width, and even to some extent its shape, throughout the disk. One of the most interesting results of this study is the remarkable constancy of the line width in the outer disk. From radius 90 to 210 seconds the Gaussian velocity dispersion (sigma sub nu) of the 21-cm line has a mean value of 5.7 km s(exp -1) (after correcting for the spectral resolution) with a dispersion of less than 0.9 km s(exp -1) (after correcting for the spectral resolution) with a dispersion of less than 0.9 km s(exp -1). Translating this directly into a kinetic temperature (Doppler temperature): T sub Dopp equals 121K (sigma sub mu exp 2/(km s(exp -1) (exp 2) gives 4000 K, with a dispersion of less than 1500 K over the outer disk. This constancy is observed even when comparing the spiral arms versus inter-arm regions, which in the radius range from 100 to 150 seconds the surface density modulates (defined as the ratio N sub peak -N sub trough/N sub peak + N sub trough) from 0.5 to 0.25 in the range 150 to 200 seconds