(1) There was the same gradual increase in size from the earlier to the later geological stages. Not that all the phyla kept equal pace in this respect, and even within the same phylum it was the rule rather than the exception to find larger and smaller contemporary species. (2) In all of the early forms, up to the middle Miocene, the teeth were low-crowned; after that time there was a decided increase in the height of the teeth, though only in _†Elasmotherium_ was the fully hypsodont, cement-covered crown attained. In the existing African Broad-Lipped Rhinoceros (_Opsiceros simus_), which is a grazing animal, the high, cement-covered teeth may also fairly be called hypsodont. (3) In all of the lines, as in the other perissodactyl families, the premolars gradually took on the pattern of the molars; only in the †amynodonts were the premolars notably reduced in number and size. (4) The three different modes of development of the anterior teeth, exemplified by the true rhinoceroses, the †hyracodonts and †amynodonts respectively, need not be recapitulated here. It is sufficient to call attention to the fact that the three kinds of modification diverged from a common starting-point such as may be seen in the middle Eocene perissodactyls generally, and that in each series the transformation was gradual. (5) The modification of the skull followed several different courses, as designated by the major and minor subdivisions of families, subfamilies and phyla. The development of horns, whether single or double, in transverse or longitudinal pairs, was the most important single influence in transforming the skull, as determined by the mechanical adjustment necessary to make these weapons effective, but even in the hornless forms changes went on, and in all the phyla the skull departed more and more widely from the primitive Eocene type in each succeeding geological stage. The most aberrant form of skull was that of the hornless and presumably aquatic _†Metamynodon_, in which the greatly shortened face, high sagittal crest and extremely wide zygomatic arches were altogether exceptional. (6) When the history of any horned phylum is at all complete, the development of the horns may be followed step by step from the marks which they left upon the skull. As a rule, the story was one of gradual enlargement, but, in one case at least, an incipient horn apparently failed to enlarge and was eventually lost. (7) In the light, slender and cursorial †hyracodonts the mode of development resembled that of the horses, as appears in the elongation of the neck, limbs and feet, in the enlargement of the median toe and concomitant reduction of the lateral digits. Also, as in the horses, the elongation of the limbs began to be noteworthy while the body-weight was small and was consequently accompanied by great slenderness; as the body-weight increased, the limbs became stouter, to yield the necessary support.