6 FISHES IN GENERAL 



marine motion. A study of the " lines " of typical fishes by 

 naval engineers * has led to some most interesting results 

 as to the uniformity of their mathematical "normals." It 

 is found, for example, that the "entering angles " of many 

 and very different fishes are surprisingly similar (Figs. 6 

 and 8) : they thus terminate regularly (at the plane of the 

 greatest cross-section of the body) at 36 per cent of the 

 fish's total length; and the curves of the "run" (i.e. of 

 the hinder part of the trunk, from the plane of the great- 

 est cross-section to the body'terminal), similar for all, are 

 smooth hollow curves, which in the forward motion of the 

 fish permit the passage of the displaced water. 



It would be unreasonable to doubt that the fish form is 

 adapted to the mechanical needs of its environment, even 

 if there existed no further evidence than that of the meta- 

 morphoses of aquatic mammals. Many of these have 

 shown so complete an adaptation to water-living that it is 

 scarcely remarkable that they were early included among 

 fishes. And it is of further interest that there exist 

 transitional forms between the land-living mammals on 

 the one hand and the cetaceans on the other. In the 

 Seal it is but the initial step in the transformation that 

 has taken place ; the head and body have become bluntly 

 tapering, the hind legs displaced backward, the foot and 

 hand webbed, the hair adapted to submerged locomotion. 

 A further stage in the acquisition of the fish-like form is 

 shown in the Dugong and Manatee. And finally in the 

 Dolphin and Whale (Figs. 5 and 7) have been actually 

 attained the numerical lines of fishes (cf. Figs. 6 and 8). 

 In these cases, the mechanical conditions of aquatic living 

 have produced their result only at the greatest cost, 



* '88. Parsons, Displacement and Area Curves of Fishes, Trans. Am. Soc. 

 Mech. Engineers. 



