XIII] AND OF BEAK AND CLAW 633 



the elongated tooth or claw has the selfsame curvature that it had 

 when it was short, but the spiral curvature becomes more and more 

 manifest the longer it grows. A curious analogous case is that 

 of the New Zealand huia bird, in which the beak of the female 

 is described as being comparatively short and straight, while that 

 of the male is long and curved; it is easy to see that there is a 

 slight curvature also in the beak of the female, and that the beak 

 of the male shows nothing but the same curve produced. In the 

 case of the more curved beaks, such as those of an eagle or a parrot, 

 we may, if we please, determine the constant angle of the loga- 

 rithmic spiral, just as we have done in the case of the Nautilus 

 shell ; and here again, as the bird grows older or the beak longer, 

 the spiral nature of the curve becomes more and more apparent, 

 as in the hooked beak of an old eagle, or as in the great beak of 

 some large parrot such as a hyacinthine macaw. 



Let us glance at one or two instances to illustrate the spiral 

 curvature of teeth. 



A dentist knows that every tooth has a curvature of its own, 

 and that in pulling the tooth he must follow the direction of the 

 curve ; but in an ordinary tooth this curvature is scarcely visible, 

 and is least so when the diameter of the tooth is large compared 

 with its length. 



In the simply formed, more or less conical teeth, such as are 

 those of the dolphin, and in the more or less similarly shaped canines 

 and incisors of mammals in general, the curvature of the tooth 

 is particularly well seen. We see it in the little teeth of a hedge- 

 hog, and in the canines of a dog or a cat it is very obvious indeed. 

 When the great canine of the carnivore becomes still further 

 enlarged or elongated, as in Machairodus, it grows into the 

 strongly curved sabre-tooth of that great extinct tiger. In rodents, 

 it "is the incisors which undergo a great elongation; their rate of 

 growth differs, though but slightly, on the two sides, anterior and 

 posterior, of the axis, and by summation of these slight differences 

 in the rapid growth of the tooth an unmistakeable logarithmic 

 spiral is gradually built up. We see it admirably in the beaver, 

 or in the great ground-rat, Geomys. The elephant is a similar 

 case, save that the tooth, or tusk, remains, owing to comparative 

 lack of wear, in a more perfect condition. In the rodent (save 

 only in those abnormal cases mentioned on the last page) the 



