818 



TITANOTHERES OF ANCIENT WYOMING, DAKOTA, AND NEBRASKA 



Mechanically correlated rectigradations and allometrons of the upper and lower premolar teeth oj titanotheres 



(Palaeosyops) 



Lower premolars 



Upper premolars 



1. The conical tooth or protoconid pi becomes elongate 

 anteroposteriorly; rudimentary anterior and posterior ridges 

 run down from summit to base, becoming more sharply marked 

 and deflected linguad at the base; concomitantly the single fang 

 tends to become divided. Total, one cusp. 



2. In p2 the posterior vertical cingulum ridge acquires a deep 

 notch about halfway up the crown of the protoconid, separating 

 off a posterior lobe (or hypolophid); the tooth broadens trans- 

 versely, and the anterior and posterior fangs become wholly 

 separate; a rudimentary paraconid is seen. Total, three cusps. 



.3. In p3 the paraconid becomes stronger; the hypolophid or 

 posterior lobe grows higher; the protoconid broadens at the top, 

 producing finally a well-marked oblique crest (or metalophid); 

 concomitantly the hypoconid lobe becomes broader than the pro- 

 toconid lobe,' concavities appear on the internal face of both 

 cusps; by the deepening of these concavities the anterior and 

 posterior crests or metalophid and hypolophid become sharply 

 defined. Total, three cusps, a rudimentary protolophid, a 

 metalophid, and a hypolophid. 



4. In pi the paraconid is slightly stronger; the transverse ridge 

 at the summit of the protoconid divides, by the insinking of an 

 anteroposterior nick, into the protoconid proper and the meta- 

 conid, thus completing the protolophid; the posterior face of the 

 hypoconid broadens into the hypolophid; the valley separating 

 the protolophid from the hypolophid becomes straighter and 

 more transverse, and thus these anterior and posterior crests 

 become more symmetrical. Total, four cusps and two crests. 



The molarization of p4 is now complete except that an ento- 

 conid is not developed until the tetartocone is developed above. 



1. The laterally compressed conical tooth p' exhibits ridges 

 on the anterior and posterior faces and a continuous internal 

 cingulum; the crown is a protocone. Total, one cusp. 



2. The triangular second premolar p- consists of the high 

 protocone; externally devoid of cingulum, internally the cingu- 

 lum gives rise to the well-developed deuterocone; while on the 

 posterior ridge of the protocone is a very slight swelling which 

 indicates the rudiment of the tritocone. Total, three cusps. 



3. The third premolar p' now has a true ectoloph, with the 

 rudiment of a parastyle, and an incomplete external cingulum; 

 the deuterocone is larger; it is embraced on the posterior as 

 well as the anterior side (but not lingually) by the cingulum; 

 it exhibits a faint anterior crest or protoloph; the tritocone nearly 

 equals the protocone in size. Total, four cusps, an ectoloph, 

 and a rudimentary protoloph. 



4. The fourth premolar p* exhibits a still more pronounced 

 external cingulum, a prominent parastyle, a subequal protocone 

 and tritocone, between which is the faintest rudiment of a meso- 

 style. The deuterocone is still larger and not yet surrounded 

 basally by the cingulum; it exhibits a slightly stronger anterior 

 crest or protoloph, on which is seen a small protooonule. Total, 

 six cusps, an ectoloph, and a protoloph. 



The molarization of p^ is now complete except that a tetarto- 

 cone is not formed until the entoconid is formed below (as in 

 Diplacodon) . 



Summarizing this numerical addition of rectigrada- 

 tion cusps we get the following results in the com- 

 parison of similar teeth from successive levels. 



Number of reciigradation cusps on lower premolars of EoceriC 

 titanotheres 



First premolar-. 

 Second premolar 

 Third premolar.. 

 Fourth premolar 



As stated above, this successive numerical addition 

 of cusps as rectigradations affords one means of 

 arbitrarily dividing the stages of evolution in each of 

 the phyla and of naming them species, in the Lin- 

 naean sense, and mutations, in the Waagen sense, in 



a manner simUar to that commonly employed for 

 other quadrupeds. 



EECTIGRADATIONS OF OSBORN CONTRASTED WITH 

 MUTATIONS OF WAAGEN 



Osborn's rectigradations, which are single char- 

 acters, differ from Waagen's mutations, which are 

 subunits of classification or taxonomy. One or more 

 of Osborn's rectigradations when followed through a 

 series of stages would constitute the subspecific stage 

 known as a "mutation of Waagen." The same 

 rectigradations (homomorphs) appear on the premolar 

 teeth of one or more independently evolving phyla, but 

 in the rectigradation cusps, as in the rectigradation 

 horns, each phylum exhibits its own rate of evolution 

 for each rectigradation, as well as its own phylogenetic 

 velocity or rate of change. 



The foUowiug table presents crudely the actual 

 modes of evolution in monophyletic, diphyletic, and 

 triphyletic series of titanotheres, terminating in three 

 "genera," A, B, C. 



