762 



THE THEORY OF TRANSFORMATIONS 



CH. 



subject to a vertical expansion, or to growth in somewhat greater 

 proportion than the lower parts. Precisely the same changes, 

 on a somewhat greater scale, give us the skull of an existing 

 rhinoceros. 



Among the species of Aceratherium, the posterior, or occipital, 

 view of the skull presents specific differences which are perhaps 

 more conspicuous than those furnished by the side view; and 

 these differences are very strikingly brought out by the series of 

 conformal transformations which P" have represented in Fig. 396. 



Fig. 396. Occipital view of the skuUs of various extinct rhinoceroses 

 {Aceratherium spp.). (After Osborn.) 



In this case it will perhaps be noticed that the correspondence 

 is not always quite accurate in small details. It could easily 

 have been made much more accurate by giving a slightly sinuous 

 curvature to certain of the co-ordinates. But as tliey stand, 

 the correspondence indicated is very close, and the simplicity of 

 the figures illustrates all the better the general character of the 

 transformation. 



By similar and not more violent changes w^e pass easily to such 

 alHed forms as the Titanotheres (Fig. 397); and the well-known 

 series of species of Titanotherium, by which Professor Osborn has 



