3-SS Bulletin American Museum of Natural History. [Vol. XXVII, 



in some unknown region, whence a long series of forms were driven into 

 the locahties in Europe and North America where conditions for preserva- 

 tion and discovery have been most favorable. The numerous lower Tertiary 

 forms have been described chiefly by Cuvier, de Blainville, Owen, Leidy, 

 Cope, Marsh, Osborn and Wortman and form the basis of many important 

 evolutionary writings. The evolution of the Tapiridae has been treated by 

 Wortman (1893) and Hatcher (1890), of the Lophiodontidse by Stehlin 

 (1903-1906) and Deperet (1901) who have also revised the European Eocene 

 hippoids and Palffiotheres (Deperet, 1901) while Wortman (1896) and 

 Granger (1908) have revised the American Eocene hippoids. The evolution 

 and phylogeny of the Rhinoceroses (including the Amynodonts and Hyra- 

 codonts) have been treated in a series of studies by Osborn (e. g., 1898, 1900), 

 who also has long been engaged in monographic revision of the Titanotheres 

 and Horses. The interrelations of the families themselves have been treated 

 principally by Kowalevsky (1873), Schlosser (1886) and Osborn (1898) and 

 the superfamily classification adopted by the latter author has been widely 

 accepted {cf. Weber, 1904, pp. 614-615). 



All these researches have supplied abundant data for a reconsideration 

 of the genetic relations of the order as a whole. The published figures and 

 descriptions show that the Lower Eocene representatives of the Tapirs, 

 Horses, Paheotheres, Titanotheres, Lophiodonts and Rhinoceroses had not 

 gone very far in acquiring the special characteristics of their descendants. 

 At any rate, the differences, for example, between Systemodou, of the Tapi- 

 ridae, Heptodon of the Lophiodontidae, Lamhdotherium of the Titanotheriidte 

 and Eohippus of the Equidfe are relatively small and indicate that the vari- 

 ous Perissodactyl families could not have been distinguished in the Upper 

 Cretaceous. If then the chief characters of these unknown stem Perisso- 

 dactyls may be inferred from those of their Lower Eocene descendants, the 

 question of the genetic relations of the order will be greatly simplified. 



This problem has long engaged the attention of the writer who has had 

 the pleasure of assisting Professor Osborn in the investigation of the Titano- 

 theres, and in that connection has studied the authors cited above as well 

 as the described Perissodactyl material which is on exhibition in the iVmeri- 

 can Museum of Natural History. Special attention has been given to the 

 genera Eohippus, Palceotherium, Systemodon, LavMotherium, Eotitanops, 

 Isectolophus, Trilopus, Hyrachyus, Heptodon and Lophiodon, which are 

 all primitive in some characters and which are represented by fairly adequate 

 material. By projecting backward the known trends of evolution in the 

 different families from the vantage ground furnished by the above mentioned 

 genera, we can assign certain characters to the unknown stem Perissodactyls 

 with considerable assurance of probability, as follows: 



