This species is, with the exception of _H. princeps_, (Marsh), the largest species of the genus as yet known. It differs from _H. princeps_ in the greater proportionate length of the molars, in their larger size, compared with the bulk of the animal, and in the less separation of the anterior external conical buttress. The third molar is the largest; the fold extending from the antero-external lobe into the valley is very conspicuous. The basal ridge (which is very strongly marked on the posterior edge), is very feebly indicated on the exterior. The transverse crests are more oblique in the second than in the third, but in the latter the valley is deeper and the crests slightly longer. The anterior conical buttress is of great size, being larger than the anterior lobe. The premolars have, as usual, one internal cone; the anterior and posterior external lobes approach close together, while the accessory fold from the anterior lobe becomes very prominent, reaching the internal cone and enclosing a valley between itself and the transverse crest. The basal ridge does not extend around the inner part of the crown as in _H. agrarius_. The only lower molar we have, seems to be a penultimate molar of the right side. The basal ridge is large anteriorly, very short posteriorly, but does not appear at all upon the sides, as in _H. agrarius_. The remaining bones of the skeleton indicate a rather small animal, the teeth are therefore proportionately very large. The occipital condyles are small and sessile; they are much extended laterally, and the external angles are pointed. In other respects they resemble the condyles of _Palæosyops_. The zygomatic arch is slender and does not curve outward strongly. We cannot tell how far the malar encroaches upon the face. After leaving the maxillary it becomes much compressed; it has no postorbital process. The maxillary is of unusual breadth, extends far backwards, and it forms the floor of the large orbit. The mandible is slender and compressed, with a large dental canal. The atlas is small, and has narrow transverse processes, which are perforated by a large vertebraterial canal. The dorsals have considerably depressed centra, and the ribs are slender. _Measurements._ M. Length of last molar ·025 Breadth of last molar ·030 Length of second molar ·024 Width of second molar ·0305 Length of last (?) premolar .018 Width of last premolar ·0245 Length of second lower molar ·025 Width of second lower molar ·018 From Henry's Fork Divide. Hyrachyus intermedius, _Sp. nov._ Established on the upper true molar series of the right side.