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that many rectigradations occur in both vertebrates and 

 invertebrates which are not preceded by mechanical reac- 

 tions in the bodily tissues, the ornamental characteristics 

 of the shells of molluscs, for example. 



In brief, the mechanical reaction hypothesis of Lamarck 

 and Cope fails both as to the origin of certain new recti- 

 gradations and of certain new allometrons. For example, 

 the extremely elongated limbs of certain young quad- 

 rupeds, such as young horses and young guanocos, are 

 proportional characters which are certainly not due to the 

 inheritance of mechanical reactions in the adults because 

 they are entirely different from the adult proportions. 



For these various reasons I have reached the opinion 

 that, whatever the respective causes of rectigradations 

 and allometrons may be, they are different; that is, the 

 occasional origin of new numerical characters and the 

 . constant changes of proportion which are going on in all 

 organisms are due to a different series of direct causes. 



This divergence into matters of opinion is, however, 

 parenthetical. Let us now return to the observation of 

 facts which throw light upon the properties and qualities 

 of these least characters. 



5. Observed Differences in the Griffin and Inheritance of 

 Proportional and Numerical Characters 



Origin . The f un d a i n en ta 1 d i s t i n c t i on between the origin 

 of rectigradations and of allometrons is well illustrated 

 in the six phyla, I-V, of Eocene titanotheres (Fig. 5). 



It is seen that similar horn rudiments and similar cusp 

 rudiments arise independently at different geologic times 

 in every phylum, giving rise to a great number of new 

 homomorphic characters. On the other hand, each phylum 

 has its peculiar and distinctive allometrons both in the 

 bones of the skull and of the feet. These changes of pro- 

 portion are so universal and so profound that by a vast 

 system of comparative measurements it has been ascer- 

 tained that every bone of the skull, of the limbs and of 

 the feet has its differential rate of increase and decrease. 

 Since these characters of form and proportion are real 



