"Mammalia, with small cerebral hemispheres which leave the olfactory lobes and cerebellum exposed. The feet short and plantigrade, with numerous (in the known genera, five) digits, terminating in flat, hoof-bearing, ungual phalanges. The seven bones of the carpus distinct, the unciform articulating with both lunar and cuneiform. The astragalus flat, without trochlear surface, and attached to the tibia with very little freedom of movement; its distal extremity divided into two facets, one for the navicular, and the other more or less for the cuboid. Molars inserted with enamel, with wide crowns and transverse crests. A post-glenoid process." This order falls naturally into two sub-orders: "I. A third trochanter on the femur, and a fossa for the round ligament: no alisphenoid canal; superior incisors present _Pantodonta._ "II. No third trochanter, nor fossa for the round ligament; an alisphenoid canal; no superior incisors. _Dinocerata._" This sub-order, Dinocerata, includes at present three distinct genera, _Uintatherium_, Leidy, _Dinoceras_, Marsh, and _Loxolophodon_, Cope (also probably _Megacerops_, Leidy). These three genera, in addition to the characters above given, are marked by the possession of two or more osseous projections from the upper surface of the head; and of these the posterior pair, developed from the parietals, are the largest. Synopsis of genera of DINOCERATA. A. Cervical vertebra? long; median horn-like processes anterior to the orbit; nasal tuberosities do not overhang the nasal tips. (_a_) Last molar, with or without a tubercle, occupying the entrance of the valley between the lobes, and but one on posterior basal ridge. Temporal fossæ not continued beyond the base of the parietal processes. Occipital condyles projecting. _Uintatherium._ (_b_) Last molar never has a tubercle at entrance of valley, and has two on posterior basal ridge. Temporal fossæ continued very far back; condyles sessile. _Dinoceras._ B. Cervical vertebræ short; median horn-like processes directly over the orbit; nasal tuberosities overhang the entire tips. _Loxolophodon._ Synopsis of species of UINTATHERIUM. A. With a tubercle occupying the entrance of the valley between the lobes of the last upper molar. _U. robustum._ B. No tubercle at the entrance of the valley. (_a_) Nasals divided by a deep groove; slender zygomatic arch; dorsal vertebræ compressed. _U. Leidianum._ (_b_) No nasal groove; stout zygomatic arch; dorsal vertebræ sub-cylindrical _U. princeps._ UINTATHERIUM.