Because of suggestions that at least some alum crystals may become ferroelectric at low temperatures, and that a ferroelectric crystal would show anomalies in the absorption of sound, the attenuation of 10, 30 and 50 M.c. sound waves has been measured in alum single crystals over the temperature range of 300°K to 4.2°K. Results are available for both longitudinal and transverse waves propagated in the [111] direction. In the temperature region between 160°K and 70°K we have obtained some very large attenuation peaks. For 10 M.c. these peaks have attained values up to 14 DB/CM, with a normal background attenuation of approximately 1 DB/CM. For the case of 30 M.c. and 50 M.c. the peaks are much higher than for 10 M.c. However,...