512 



TITANOTHERES OF ANCIENT WYOMING, DAKOTA, AND NEBRASKA 



beds and what each was like at the end, and thus to 

 compare the beginning and the end of each phylum in 

 respect to its several biocharacters. Measurements 

 were made of the elements shown in the accompany- 

 ing table, including (1) length of skull, (2) breadth of 

 skull, (3) cephalic index, (4) length of superior grind- 

 ing teeth, (5) length of horns, and each titano there 



phylum is seen to have its absolute increase, rep- 

 resented by the plus sign ( + ). In a sixth part 

 measured, the length of the nasals, there is an absolute 

 decrease, represented by the minus sign ( — ). It is 

 seen that not only are the absolute increments and 

 decrements different in each phylum but that the 

 relative increments and decrements are distinctive. 



Maximum increase or decrease {in males) of certain elements in -phyla distinguished hy di^erent rates in the genesis 

 and transformation of biocharacters during the deposition of the Titanotherium ieds 



[All figures approximate] 



Menodontine group Cshort-horned) 



Mesaticephalic to 

 brachycephalic 



Brontops Diploclonus 



Mesaticephalic to 

 dolicbocephalic 



Brontotheriine group (long- 

 horned) 



Mesaticephalic to 

 brachycephalic 



Megacerops Brontotherium 



Basilar length of skull: 



Percentage 



MilUmeters 



Zygomatic breadth of skull: 



Percentage 



Millimeters 



Primitive and progressive cephalic index (limits) 



Superior grinding teeth (premolar-molar series) : 



Percentage 



Millimeters 



Free length of horns : ' 



Percentage 



Millimeters 



Free length of nasals: 



Percentage 



Millimeters 



+ 31 



+ 185 



+ 39 



+ 187 

 72-87 



+ 34 

 + 96 



+ 143 

 + 122 



(?) 

 (?) 



(?) 

 (?) 

 85-91 



(?) 

 (?) 



(?) 

 (?) 



(?) 

 (?) 



+ 17 

 + 110 



+ 67 

 + 230 

 67-76 



+ 30 



+ 85 



+ 240 

 + 140 



-31 

 -33 



+ 36 

 + 222 



+ 15 



+ 73 



62-70,<' 79 



+ 75 

 + 200 



+ 300 

 + 220 



+ 33 

 + 43 



(?) 

 (?) 



(?) 



(?) to 84 



(?) 

 (?) 



(?) 

 (?) 



(?) 

 (?) 



+ 32 

 + 215 



+ 61 



+ 270 



66 to 80-87 



+ 25 



+ 75 



+ 260 

 + 283 



-66 

 -76 



DISTINCTION BETWEEN RECTIGEADATION BIOCHARAC- 

 TERS AND ALLOMETRON BIOCHARACTERS 



Apparently two kinds of biocharacters arise in the 

 hard parts of titanotheres and other mammals. The 

 difference is observed in their respective modes of 

 origin and evolution. Theoretically we may attribute 

 them to different complexes of causes. 



"Eectigradation"55 (Osborn, 1907.301, p. 228) is a 

 designation for the earliest discernible stage of an 

 absolutely new adaptive character of an orthogenetic 

 kind. Such rudiments of new characters were first 

 termed (Osborn, 1891.53) "definite variations" to 

 distinguish them from the theoretic "indefinite" or 

 "chance" variations of Darwin. When the shadowy 

 rudiment of a new dental cusp or of a new horn first 

 appears it is termed a rectigradation. It marks a 

 numerical change, the addition of the rudiment of a 

 new biocharacter that was not previously present, 

 which when observed in successive generations is 

 found to develop into an important adaptive character. 



Quite distinct is an " allometron" ^^ (Osborn, 1912.372, 

 p. 250). It is not a numerically new character but a 



" Rectigradation>rec('M, straight; gradus, step. 



M Allometron>dXXoIos, different, changed; liirpoy, the contents or thing meas- 

 ured; hence alloiometron or allometron, a changed quantity or measurement. 



' Height above narial opening. 



new proportion ^' in an old character, which may be 

 expressed in differences of measurement, in ratios and 

 indices. This evolution of new proportions in existing 

 characters is a quantitative change; although a highly 

 adaptive and important process it adds no new unit 

 to the organism. These changes of proportion in the 

 titanotheres were investigated very carefully by Osborn 

 and Gregory between 1902 and 1916. In the skull 

 there arise such contrasting proportions as brachy- 

 cephaly and dolichocephaly; in the feet, brachypody 

 and dolichopody. We learn from breeding that both 

 kinds of change, rectigradations and allometrons, are 

 germinal or become so; both become separable in 

 heredity. 



As certain differences of opinion and interpreta- 

 tion as to the distinctness of rectigradations and 

 allometrons have arisen between three observers (H. 

 F. Osborn, W. D. Matthew, W. K. Gregory) it is 

 important to state very clearly some of the resem- 

 blances and differences between these two kinds of 

 biocharacters. 



s' Proportion >j3ro, tor; portia, share, part; the relation ot one thing to another 

 in respect to size, quantity, magnitude of corresponding parts, capacity, or 



