_Synopsis of Species._ I. Long diastema between lower canines and molars. A. Lower jaw with six molars _H. nanus_. B. Lower jaw with seven molars. _a a._ Upper molars with complete cingulum. Enamel wrinkled. _a._ The last molar with two external lobes on nearly the same transverse line _H. intermedius_. _b._ Last molar with the external lobes on the same longitudinal line _H. modestus_. _b b._ Upper molars with cingulum incomplete externally. _a._ With anterior conical buttress larger than anterior lobe. α. Buttress separate, and no fold from anterior lobe _H. princeps_. β. Buttress united, and quite large fold from anterior lobe _H. imperialis_. _b._ With anterior conical buttress smaller than anterior lobe. α. Tooth large _H. eximius_. β. Tooth smaller _H. agrarius_. _c c._ Cingulum only on outer side of first molar, buttress separated by a ridge from anterior lobe, fold from this lobe very prominent. _H. implicatus_. II. Short diastema between lower canines and molars. A. Descending ridge from antero-external point of lower molar extends entirely across the crown of the tooth anteriorly _H. crassidens_. Hyrachyus imperialis, _sp. nov._ Established on the second and third molars of each upper jaw, and three premolars, and one lower molar, portions of the skull and vertebræ.