382 Bulletin American Museum of Natural History. [Vol. XXVIl, 



many similar cases Pyroiherium. has been derived from smaller forms with 

 ta])iroid molars (r/. Carolozittelia Ameghino), and such tapiroid molars in 

 several other cases (cf. Gregory, in Osborn, 1907, p. 171, footnote) have been 

 evolved from quadri tubercular molars with transversely ridged proto- and 

 metaconules, i. e., from a type nearly realized in the Patagonian protungu- 

 late genus Didohdus. The flat Amblypod-like astragalus of Pyrotherium 

 is more or less closely paralleled by that of Alheriogaudryia, Asmodeus and 

 several other Patagonian genera which the writer regards (p. 384) as belong- 

 ing in the suborder Astrapotheria. The peculiar form of the distal end of 

 the humerus is to some extent suggested in the more normal humerus of 

 Homalodotherium. (cf. Gaudry, 190G.1, p. 30, figs. 23, 24). 



TIic extinct 8out}i American Ungulate groups not related to the Rodentia, 



Artiodactyla, etc. 



The Condylarthra or Condylarthra + Taligrada appear, in short, to be 

 the only probable known source for the orders in ({uestion. Relationship 

 of the Protypotheres with the Rodents appears to be extremely remote 

 (Sinclair), notwithstanding the Hare-like adaptations of some of the "Pro- 

 typotheres" {e. g., Pachyrukho.s). Relationship even with the earliest 

 known Primates appears to be excluded by obvious differences in the skull, 

 dentition and limbs. While remote relationship with some of the Para- 

 theria (Edentates) is not definitely contradicted, derivation from that group 

 appears highly imjirobable. 



Finally, near relationship with the Artiodactyla appears to be negatived 

 by the following considerations: (1) ^J'he earliest known Typotheres 

 differ radically from the Artiodactyla in the characters and relations of the 

 astragalus. In the Litopterna the astragalus of the typical forms is, as 

 stated above, very widely separated from the cuboid; however the astragalus 

 ascribed to Thoafherium minusculum by Ameghino (U)OG, p. 342) has a 

 narrow facet in the position of the cuboid facet. 



Some at least of the Nesodonts, as figured by Gaudry (1906.1, p. 29), 

 developed a large cuboid facet on the astragalus, but since this character 

 appears late among the South American orders, it may be regarded as an 

 instance of convergent resemblance to the Artiodactyla and Rhinoceroses. 

 The Typotheres and Litopterns are likewise distinguished by the precocious 

 molarization of the premolars, in wide contrast to the very delayed and 

 imperfect molarization of the premolars in Artiodactyls. 



Assuming the correctness of the view that the extinct South x\merican 

 hoofed mammals are not directly related to the Perissodactyls, Hyracoids, 



