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” (ze. 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. 
