v. 2 SWIMMING OF FISHES 135 



is travelling along a figure 8 curve relative to a transverse line which is 

 moving forward at the average forward velocity of the whole fish. 

 The track of any point on the body (relative to the earth) is a sinu- 

 soidal curve whose pitch or wave length is less than that of a curve 

 which defines the body of the fish. There is therefore a definite angle 

 between the surface of the fish and its path of motion.' 



Each portion of the side of the fish can thus be considered as moving 

 like the blade of an oar used for sculling at the back of a boat. The 

 principle used, that of an inclined plane, is the same as in screw pro- 

 pulsion, the essential feature being that the moving surface is inclined 

 at an angle to its line of motion. The effect of the movement is greatly 

 increased by the fact that the amplitude of the oscillations grows 

 passing backwards, as is necessary to produce additive effects in any 

 coupled system of screws or turbines. The whole fish thus operates 

 as a single self-propelling system. 



The magnitude of the forward thrust thus generated depends 

 among other things on (a) the angle that the surface of the fish makes 

 with its own path of motion, (b) the angle between the surface of 

 the fish and the axis of forward movement of the whole fish, and 

 (c) the velocity of transverse movement of the body (Gray). These are 

 evidently factors that will vary with the shape of the body and the 

 action of its muscles. The body form of the faster-moving types of 

 bony fishes provides substantial advantages for swimming over that 

 of the more elongated types. The essential differences are that the 

 bony fishes have (1) large caudal fins, (2) a much smaller length of the 

 body relative to its depth, (3) less flexibility. 



The role of the large caudal fin is to resist transverse movements; 

 its effect is, again quoting Gray, 'to keep the leading surface of the 

 body directed obliquely backwards during both phases of its trans- 

 verse movements and thereby to exert a steady pressure on the water'. 

 Since, however, the tail does execute transverse movements, and at 

 the same time is being rotated towards and away from the axis of 

 motion, it exerts a very large propulsive effect, probably as much as 

 40 per cent, of the total thrust. 



The effect of the caudal fin, combined with the shortness of body 

 and reduced flexibility, is that the front part of a bony fish makes only 

 small transverse movements; the track of the head is therefore nearly 

 straight and the whole front of the body presents a streamlined 

 surface with little resistance. Further, the muscles just in front of the 

 tail exert their tension with very little change in length. 



No doubt the shape of the body also has an important influence on 



