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THE AMERICAN NATURALIST [Vol. XLIX 



chocephals or pure brachycephals. Characters of pro- 

 portion are thus " single characters" in the hereditary 

 sense. 



In the comparison, for example, of certain broad-heads 

 with other broad-heads such characters are termed 

 analogous because due to similarity of structure arising 

 from similarity of function. Thus brachypody (abbrevia- 

 tion of the digits) is analogous in the rhinoceroses and 

 the titanotheres. The broadening of the shell of one mol- 

 lusc is analogous to the broadening of the shell of another 

 mollusc. The broadening is none the less the heritable 

 characteristic of the skull or of the shell. 



Quite different are certain of the new numerical charac- 

 ters to which I have applied the term rectigradations, 12 

 such as new cuspules on the teeth and new rudiments of 

 horns, for these give rise to characters which are regarded 

 as homologous although not directly descended from each 

 other. Thus the horns in all the titanotheres are consid- 

 ered homologous, although they arise independently at 

 different times in different phyla. The larger number 

 of cusps in the teeth of mammals are termed homologous, 

 although they also have arisen quite independently of 

 each other. It is obvious that unless all similar new char- 

 acters have originated in the offspring of a single pair, 

 which we know is not the case, that the vast majority of 

 similar new numerical characters both in vertebrates and 

 invertebrates are related through s'nuilaritg of ancestry, 

 through the similarity of the tissues from which they 

 arise, and through the similarity of their relations, form- 

 ing a special kind of homology which Fiirbringer has 

 termed homomorphy. 



While different in these respects of analogy and 

 homology there are many properties which allometrons 

 and rectigradations as heritable characters have in com- 

 mon, such as the laws of growth, correlation with sex, 

 mechanical correlation, differential ontogenetic move- 

 ment, differential phyletic movement, or differential rates 

 of evolution, continuity of origin, increasing intensity of 



