v. 3 FUNCTION OF FINS 139 



suitable horizontal and vertical fin surfaces at the rear end, when the 

 airship becomes in effect a feathered arrow. The forces operating on 

 the fins tend to bring the body back into the original line of motion. 

 The fins of the fish operate in a similar manner. If the experiment 

 is performed with a model to which all the fins behind the centre of 

 gravity have been added, namely, the caudal, anal, and second dorsal 

 fins, it is found that the curve for the yawing moment now has a steep 

 negative slope (Fig. 94 b), that is to say, every deviation produces 

 forces that tend to give directional stability. With the first dorsal fin 

 also in position the model possesses a remarkable neutral equilibrium 

 (Fig. 94 c). Deviations by as much as io° produce no resultant yawing 

 moment about the centre of gravity. The form of the dorsal fins is 

 therefore definitely such as to maintain stable swimming and prevent 

 yawing. 



Turning of a fish is produced either by the propagation of a wave- 

 down one side only of the body or by asymmetrical braking with the 

 pectoral fins (see below). The former type of turn has been investi- 

 gated by Gray in the whiting, where there is a large caudal fin. This 

 gives great lateral resistance, so that the first part of the turn is 

 executed by bending the front part of the fish on the tail as a fulcrum. 

 This enables the animal to turn through 180 within a circle of the 

 diameter of its own length. After removal of the caudal fin the turns 

 are much less effective. 



In both elasmobranchs and teleosts the dorsal fins are well developed 

 in the active swimmers. In most elasmobranchs they are fixed, but in 

 many teleosts the dorsal fin can be folded up and down, and it is 

 observed that the fin is raised during turning. This would have the 

 effect of increasing the yawing moment produced by asymmetrical 

 action of the body muscles or by unilateral braking with the pectoral 

 fins. 



Since the body is so markedly flexible in the lateral plane and there 

 are powerful muscles available for turning it in this direction,. the part 

 played by the fins in determining the stability is important mainly 

 when the body is held straight. The fish thus has the double advantage 

 of great stability (by keeping the body straight) and great control- 

 lability (by bending it). In a body unable to change its shape in this 

 way, stability and controllability would be inversely related. This is 

 the case for the stability of the fish in the vertical plane, in which the 

 body is little flexible. Fig. 94 n shows the positive slope of the curve 

 for the pitching moment and clearly the equilibrium in this plane is 

 quite unstable. The pectoral fins contribute more than any others to 



