Progress in studying sedimentary rocks in thin sections would be greatly facilitated if the rates of change in the size, roundness, and sphericity of various minerals in rotating drums were determined by measuring size in diameters, not by screening, and the frequency by (percent of) number, not by weight. These should be two dimensional measurements. A start was made by crushing specimens of four minerals (quartz, microcline, tourmaline and garnet), screened to sand size and rotated dry in glass bottles supplied with three ordinary marbles at 150 RPM, to a total of 180,000 revolutions, or 31.5 kilometers. Small samples, taken from these ball mills periodically via a microsplitter, were measured microscopically. These data were slightly modified by smoothing and replotted as frequency-distribution curves and as cumulative carves. The roundness and sphericity of the grains were determined by direct comparison with patterns slightly modified from those of Krumbein and Rittenhouse. The results are shown graphically. The plotting of the data of the initial samples results in symmetrical frequency-distribution curves (bell shaped) with one peak. After a short time in the rotating ball mills, a secondary peak is developed in the small size ranges, and the primary peak is reduced and shifted toward small sizes. This increases the sknewness and lowers the sorting. The originally angular grains become slightly rounded and the sphericity increases somewhat. Ultimately the primary peak is destroyed and the secondary peak becomes dominant. The skewness at the start is close to zero, rapidly increases, then slowly decreases. This characteristic is apparently a transitory condition and it seems reasonable to suppose that it may be applied in some cases to natural sediments. The quartz is reduced in size at the fastest rate, the microcline next, followed by tourmaline, and last by garnet. The Mobs hardness does not seem to be the dominant or controlling factor. The brittleness of the quartz, the cleavage of the microcline, and the toughness of the other two seem to be influential. Very small grains are rarely rounded, the larger grains more. The degree of roundness, without specifying the size, means very little; the two are interrelated. These results are the product of mechanical abrasion, not of solution. In nature, solution is an additional process in size reduction, roundness, etc.