THE SHAPES OF VERTEBRATE SKELETONS. 219 



caused by transverse strains. As already said, it must be 

 acted upon much in the same manner as a bow, though it is 

 bent by forces acting in a more indirect way; and like a bow, 

 it must, at each bend, have the substance of its convex side 

 extended and the substance of its concave side compressed. 

 So long as the vertebrate animal is small or inert, such a 

 cartilaginous rod may have sufficient strength to withstand 

 the muscular strains; but, other things equal, the evolution 

 of an animal that is large, or active, or both, implies mus 

 cular strains which must tend to cause modification in such a 

 cartilaginous rod. The results of greater bulk and of greater 

 vivacity may be best dealt with separately. As the 



animal increases in size, the rod will grow both longer and 

 thicker. On looking back at the diagrams of forces caused 

 by transverse strains, it will be seen that as the rod grows 

 thicker, its outer parts must be exposed to more severe ten 

 sions and pressures if the degree of bend is the same. It is 

 doubtless true that when the fish, advancing by lateral 

 undulations, becomes longer, the curvature assumed by the 

 body at each movement becomes less ; and that from this 

 cause the outer parts of the notochord are, other things 

 equal, less strained the two changes thus partially neutrali 

 zing one another. But other things are not equal. For 

 while, supposing the shape of the body to remain constant, 

 the force exerted in moving the body increases as the cubes 

 of its dimensions, the sectional area of the notochord, on 

 which fall the reactions of this exerted force, increases only 

 as the squares of the dimensions : whence results a greater 

 stress upon its substance. This, however, will not be very 

 decided where there is no considerable activity. It is clear 

 that augmenting bulk, taken alone, involves but a moderate 

 residuary increase of strain on each portion of the notochord ; 

 and this is probably the reason why it is possible for a large 

 sluggish fish like the Sturgeon, to retain the notochordal 

 structure. But now, passing to the effects of greater 



activity, a like dynamical inquiry at once shows us how rapid- 



