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The Colorado River in its course from central Texas to the Gulf of Mexico carries quartz, chert, and limestone pebbles which can be traced for distances of up to 270 miles from their source. Limestone is so soft that it reaches its limiting roundness in the first few miles and thereafter undergoes no further increase. Harder quartz rounds much more slowly but eventually attains the same high limiting roundness value as limestone. Chert, being brittle, tends to spall and only rounds slightly downstream. A new and more behavioristic measure of equidimensionality, "maximum projection sphericity," is introduced, and a triangular diagram is proposed for analysis of the equant versus disklike versus rodlike aspect of particles, here termed "form." It was hoped that, by limiting the study to pebbles 32-64 mm. in length, the effects of grain size might be eliminated; the data show, however, that, even within this narrow range, particle size has a greater effect on sphericity and form than 200 miles of fluvial transport-larger pebbles tend to have lower sphericity and a rodlike form, while smaller ones are more discoidal. Limestone pebbles remain at constant low sphericity because of their bedding and show no significant change with distance. For quartz, pebbles larger than 54 mm. become more rodlike downstream but show little numerical change in sphericity, hence apparently roll like a rolling pin and wear chiefly on the intermediate axis. Quartz pebbles smaller than 38 mm. show a significant downstream increase in sphericity, chiefly by wear on the long axis, and hence must be carried chiefly in saltation where they bounce randomly along the bottom. Surprisingly, chert pebbles larger than 38 mm. show a striking downstream decrease in sphericity and become more bladed by diminution of the short axis, apparently by preferential splitting parallel with the bedding; but chert pebbles smaller than 38 mm. increase in sphericity in the same manner as do small quartz pebbles. For both quartz and chert, pebbles near the source have similar sphericity and form regardless of size; since large and small sizes wear by opposite mechanisms, there is increasing divergence in sphericity andform between large and small pebbles as they are traced farther from their source. Detailed analysis of the polymodal sphericity frequency distributions reveals the apparent existence of remarkably constant discrete sphericity populations for each rock type. Furthermore, for all rock types the intermediate axis tends to measure very close to halfway between the long and short axes-hence there is a dominance of bladed forms; this is true even for limestone, in which discoidal forms are but slightly more abundant than rodlike forms. Analysis of mean form on the triangular diagram seems to be the most powerful weapon available to attack the problem of particle abrasion. This study shows that sphericity depends most importantly on the inherent abrasional properties of the different rock types, is strongly a function of size as well as distance, and is but little affected by selective sorting.