Ho THE APPEARANCE OF JAWS v. 3- 



movement in this plane, and since they lie in front of the centre of 

 gravity they greatly increase the instability. The fish must be able to 

 alter direction in the vertical plane, and it has apparently sacrificed 

 static stability for controllability. The equilibrium in this plane is a 

 dynamic one, controlled by the movable pectoral fins, and it is so 

 unstable that only a small movement of these fins is necessary to 

 produce a deflecting force that restores the original direction of 

 motion. 



The pectoral fins, lying in front of the centre of gravity, tend to 

 produce a movement of positive pitch, that is to say, they force the 

 head upwards. This effect is normally compensated by a component 

 produced by the heterocercal tail. The upper lobe of this is rigid and 

 the lower more flexible, therefore the lateral motion given by the 

 swimming movements of the body produces a vertical lift force on the 

 tail, giving, of course, negative pitch. After amputation of the hypo- 

 caudal lobe and anal fin a dogfish swims continually along the bottom 

 of the tank : in order to compensate for the absence of negative pitch 

 the pectoral fins are held horizontally and hence there is no moment 

 to counteract the weight of the fish. If the pectoral fins are then also 

 removed the anterior end of the body is pointed upwards, often so 

 much so as to cause the fish to swim with its head out of the water. 

 This is the result of an over-strenuous attempt to compensate, by 

 raising the head, for the negative pitch produced by the tail. The 

 system is no longer suitable for making the continuous adjustments 

 necessary to ensure stability. 



This analysis makes it clear why a heterocercal tail is found in 

 almost all the primitive swimming chordates; it is almost a necessity 

 for an animal with a specific gravity in excess of the medium and little 

 flexibility in the vertical plane. The component of positive pitch 

 could be provided by the flattened head or by continuous lateral fin 

 folds, such as may have been present in early fishes, and adjusted 

 by the limited flexibility possible in the fin. The development of 

 movable pectoral fins confers much greater control. Since the useful 

 portions of a fin fold for this purpose would be those well in front of 

 and behind the centre of gravity, we can perhaps see the reason why 

 the intervening portion has become lost. In the modern sharks the 

 pelvic fins have little influence on the stability and are perhaps retained 

 only for their modification as claspers. 



It is not surprising that races of fishes with stability ensured by 

 systems of this sort should tend to adopt a bottom-living habit, with 

 dorso-ventral flattening, such as is found in the skates and rays. 



