Of the three rhinoceros groups, whatever rank be assigned them, family or subfamily, much the most prolific in divergent forms was that of the true rhinoceroses (Rhinocerotidæ) of which seven or more phyla have been distinguished, three of them surviving to the present time. Only in this series were horns frequently present, the brief experiment, as it might be called, of the Bridger genus _†Colonoceras_, being the only known instances of horns among the †hyracodonts, and the †amynodonts were all hornless. In making the comparison as to degree of ramification among the three series, it should be borne in mind that the true rhinoceroses were the only long-lived group, the other two dying out before or at the end of the White River stage. Within the series or family of the true rhinoceroses, there was no great divergence of type, and all the members were much alike, heavy and slow animals, but with very great variety in the details of structure. Take, for instance, the matter of horns; we find both hornless and horned genera, the former preceding the latter in time, but, so far as North America is concerned, continuing in association with them till the end. Among the horned genera, the horn may be single, double in a transverse pair (_†Diceratherium_) or arranged one behind the other in the median line of the head (_Dicerorhinus_, _Opsiceros_, etc.). The single horn may be on the nose or the forehead; if on the nose, it may be on the upper side of the nasal bones (_Rhinoceros_) or on the extreme tip and pointing obliquely forward (_†Teleoceras_). The single frontal horn was much less common, but in the extraordinary _†Elasmotherium_, of the European and Siberian Pleistocene, the horn was of gigantic size and the surface for its attachment an enormous, dome-like boss on the forehead. All three of the series had their most ancient known representatives in North America, and it seems probable, though by no means certain, that they all originated here by divergence from a common stock, which was represented more or less closely by the genus _†Hyrachyus_ of the Bridger and Wind River stages of the Eocene. However that may be, true rhinoceroses flourished exceedingly in the Old World from the upper Oligocene to the Pleistocene, the events of the latter epoch restricting them to their present range. The significance of the American genera for the ancestry of the modern types can be found only in the most ancient forms, _†Trigonias_ and _†Cænopus_; the subsequent development which led up to the existing species of Asia and Africa went on entirely in the eastern hemisphere. The †hyracodont subfamily had no known representatives outside of North America, but the †amynodonts sent out emigrants, which appeared for a brief time in the Oligocene of Europe. In the varied history of the rhinoceroses, the principles of evolutionary change which may be deduced from the recorded development of the horses, tapirs and †titanotheres are found to be applicable.