176 Bulletin American Museum of Natural History. [Vol. XX^'II, 



molars but the protoconid-paraconid shear is not oblique. Peraspalax, 

 which Osborn originally suggested might go with Peralestes (1888, p. 206) 

 has the desired oblique protoconid-paraconid shear but the molar heels 

 appear to be too small. 



The foreffoinff considerations seem to indicate that Peralestes is related 

 to Peramus, Leptocladus and Peraspalax and is not a member of the Tri- 

 conodonta but of the Trituberculata as defined by Osborn (1907, pp. 22-23). 



To return to the cjuestion as to the probable characters of the upper 

 teeth of Spalacotherium, in view of the symmetrical relations of the upper 

 and lower cusps in Triconodon, and of the mechanical conditions implied 

 in Spalacotherium, it seems quite probable that the upper teeth of the latter 

 genus (and of Menacodon as well) consisted of a symmetrical triad of sharp 

 cusps and that the upper and lower teeth in opposition nearly fulfilled the 

 characters of "reversed cutting triangles" (Osborn). 



Relations of the Trituberculata to the Triconodonta. 



After the exclusion of Peralestes we have to enquire in what manner are 

 the Triconodonts related to the Trituberculatesf 



The dental formula of Aviphilestes, I.g, C.j, P. 5, M.,^ (Osborn), is like 

 that of typical Trituberculates. As far back as the Upper Triassic this 

 formula was closely approximated by that of the Cynodont Diademodon 

 mastacus (P. 5, M.g, Broom, 1905.4) so that it may well be a primitive 

 character inherited by Triconodonts and Trituberculates. Another char- 

 acter foreshadowed in Diademodon and seen in both Triconodonts and 

 Trituberculates is the sharp differentiation of the premolars from the molars. 

 In both orders also p^ to p^ increase rapidly in size, P4 being a high-pointed 

 tooth much higher than mj. 



These characters scarcely seem sufficient to point to anything more than 

 the remote common origin of the orders as here accepted. 



The Triconodonta retain some very ancient characters besides those 

 mentioned above under the dentition. The angle of the lower border of the 

 jaw is inflected as in recent Marsupials. In Triconodon also the fourth 

 deciduous premolars alone was replaced by a successor (Osborn). The 

 coronoid is very broad, the condyle sessile (Fig. 6, no. 7). The latter looks 

 backward rather than upward and implies a glenoid-squamosal region ex- 

 tending down below the level of the teeth as in Cynodonts. The groove on 

 the inner side of the jaw for the Meckelian cartilage (Bensley) is pronounced. 



