XXIV 



2. The principle of the correlation of local physiographic 

 diversity with the adaptive radiation, local and continental, 

 of titanotheres and other ungulates. 



3. The principle of adaptive radiation as expressed in adap- 

 tations to aquatic, forest, savanna, and plains life at different 

 altitudes. 



4. The principle of multiple lines of descent in the same 

 regions, of polyphyly and of polyphyletic evolution as more 

 common among ungulates than monophyletic evolution. 



5. The principle of distinguishing phyla by contrasting pro- 

 portions of the head (dolichocephaly and brachycephaly) , of 

 the Umbs (dohchomely and brachj'mely) , of the feet (dolicho- 

 pody and brachypody), and of the teeth (hypsodonty and 

 brachyodonty) . 



6. The principles of the lengthening and shortening of the 

 limb segments in harmony, respectively, with adaptation to 

 speed and to weight. 



7. The principles of evolution by rectigradation (origination 

 of new characters) and by allometry (changes of proportion) 

 as effecting the chief changes in the hard parts. 



8. The principles of continuity and of orthogenesis — the 

 direct continuation of animal form estabUshed in adaptation 

 to environment and of the evolution of new types irrespective 

 of external influences. ' 



The theoretic causes underlying these principles of 

 evolution are briefly stated in Chapter I, and the con- 

 clusions reached are summarized in Chapter XI. 



