LECTURE IV. ' 105 



tliat the brains of tlie ass, the sheep, and the ox, all of which, 

 in fables, are the representatives of stupidity, are more convo- 

 luted than those of the beaver, the cat, and the dog, the axiom 

 connecting the convolutions with intelligence seems to have re- 

 ceived a hard blow. 



Happily, mathematics will assist us here. On compar- 

 ing two bodies of similar form but of different size, their 

 respective volumes vary as the cube of their diameters, whilst 

 the proportion of the surfaces is as the square of the diameters, 

 or, in other words, the volume of a body increases more rapidly 

 than the surface, and this more rapidly than the diameter. 

 Every artillerist knows well that a twelve-pounder, though 

 thrice as heavy as a four-pounder, does not nearly possess 

 a diameter thrice as large. 



In applying this principle to the head, and specially the cra- 

 nium of animals, it will be seen that in every natural group or 

 order of mammals the head, and especially the cranial capacity, 

 stands in a certain relation to the body, which is nearly constant 

 in the various species. The head of the tiger and the lion bears 

 the same proportion to the body as does that of the cat, 

 although the size of the animals is so different. It follows 

 hence that the volume of the cerebral mass of the tiger stands 

 in the same proportion to the body as does that of the cat ; 

 that the surface of the internal cranial capacity is proportion- 

 ately smaller in the larger animal, and that consequently in 

 order to secure a similar surface of grey matter, it must be 

 convoluted in the large animal, whilst it may remain smooth 

 in the small animal. We might, therefore, infer from the 

 above geometrical axiom, that if in two species of animals of 

 the same size and the same normal structure, the convolutions 

 are differently developed, this development is connected with 

 the development of intelligence, whilst animals of unequal size 

 are less capable of comparison with each other in proportion 

 as their respective sizes differ. When, therefore, man, 

 whose skull is, in proportion to the body, larger than that of 

 the largest animals, excels aU the rest in the richness and 

 variety of the cerebral convolutions, it is manifestly in har- 

 mony with his intelligence, in which he also far excels the rest. 



