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THE AMERICAN NATURALIST [Vol. XLVI 



tions of the skull and of the teeth; these indices are ex- 

 tremely constant allometric specific characters, they are 

 independent of size. For example, the indices of a 

 diminutive pony and of a giant percheron would be the 

 same. Similarly the indices of a diminutive donkey and 

 of a very large ass would be the same. 



The index is the best and most exact form of express- 

 ing mathematically the profound differences between the 

 skull of the horse and that of the ass. Indices have the 

 value of specific characters ; they are of especial signifi- 

 cance in the present discussion in comparison with those 

 in the face, cranium and palate of man and of the titano- 

 theres above considered. 



Chief among the allometric differences are the follow- 

 ing: (1) In its proportions the ass has a relatively shorter 

 space between its grinding and its cutting teeth, the 

 bit-opening; this is correlated with the fact (2) that the 

 ass has a relatively broader and shorter skull than the 

 horse; also with (3) the fact that the ass has a relatively 

 longer cranium (postorbital space) and shorter face 

 (preorbital space) than the horse; (5) the ass also has 

 relatively broader grinding teeth correlated with the 

 broader skull; (6) correlated also with its less elongate 

 skull the ass has a relatively rounder orbit than the 

 horse, i. e., the vertical and horizontal diameters are more 

 nearly equal. (7) A very distinctive feature is the angle 

 which the occiput makes with the skull ; this is one of the 

 marked specific features of the ass. 



Ass 46.9-49.9 



