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As part of an investigation of the velocity fields in the atmospheres of cool, luminous stars we used the Goddard High Resolution Spectrograph (GHRS) aboard the Hubble Space Telescope to obtain a high resolution spectrum of the Mg II h and k lines in the M supergiant $\alpha$ Ori. These strong, centrally reversed emission lines have been well studied by the IUE. While the h line in $\alpha$ Ori has nearly equal intensity in the red and blue peaks, the blue peak of the k line is always much weaker than the red peak. This asymmetry is normally explained as resulting from absorption by Fe I and Mn I in the circumstellar shell. An examination of the GHRS spectrum, however, reveals that the asymmetry results from a velocity shift between the emission wings and the central absorption core of the line. Further, while the central absorption profiles for the h and k lines agree very well when plotted on a velocity scale, the centroid of the k line emission wings was observed to be redshifted by approximately 23 km/s with respect to that of the h line. Examination of other high resolution GHRS observations of Mg II showed a similar, though less pronounced, relative redshift of the k line centroid on the normal M giant $\gamma$ Cru and the hybrid K giant $\gamma$ Dra. To date, no concrete model has been proposed to explain these shifts. Examining well exposed, high resolution IUE observations of $\alpha$ Ori shows a close agreement with the GHRS results. This gives us confidence that we can use IUE spectra to study the relative shapes and velocities of the Mg II h and k lines and we are currently involved in a program to use the IUE archive to quantify the behavior of the Mg II h and k profiles as a function of luminosity and spectral type for luminous, cool stars. The results of this program will be presented.