CHANGES OF PROPORTION 265 



with the exception of the Proboscidea. Every known step in 

 this transformation is determinate and definite, every additional 

 character which has been observed arises according to a fixed 

 law and not according to any principle of chance. In the 

 eleven principal branches which radiate from the earliest known 

 forms {Eotltanops gregoryi) of this family exactly similar new 

 characters arise quite independently at different periods of 

 geologic time which are separated by the lapse of tens of thou- 

 sands of years. 



The titanotheres exhibit an absolutely independent but 

 definite origin and development in each branch; so far as ob- 

 served, every new character has its own rate of evolution 

 and its own peculiar kind of form change; for example, in cer- 

 tain branches of the family the horns will appear many thou- 

 sands of years later in the evolution history than in other 

 branches, and after their appearance in many instances they 

 may exhibit a singular inertia, or lack of momentum, over a 

 long period of time, which is exactly in accord with our gen- 

 eral principle (p. 149) that every character has its own rate 

 of velocity both in individual development and in racial de- 

 velopment. 



The Origin of New Proportional Characters Not 

 Predetermined by Ancestry 



The titanotheres exhibit another very important principle, 

 namely, that the linear proportions of the bones of the limbs 

 are exactly adapted to the weight they are destined to carry 

 and to the speed which they are destined to develop; in other 

 words, the speed and the weight of all these great herbivora 

 may be very precisely estimated by ratios and indices of the 

 proportionate lengths of the different segments of the limbs, 

 upper, middle, and lower. These proportionate lengths are 



