IUE observations of 47 cool giants have been made in a search for the onset of expansion in the Mg II h and k emission cores. It is found that, in a statistical sense, the longward emission peak becomes dominant above a velocity dividing line in the H-R diagram, which lies close to a temperature dividing line reported by Linsky and Haisch (1979). Also discussed are asymmetries in emission cores, collected asymmetry data including the evaluation of absolute visual magnitude by MK classification, Ca K emission width, and Mg k emission width, and evolutionary implications for the hypothesized supersonic transition locus (Mullan, 1978).