898 THE SHAPES OF TEETH [ch. 



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

 and that in pulHng 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 simple, more or less conical teeth, such as 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 hedgehog, 

 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 extinct tiger; and- the boar's canine grows into 

 the spiral tusk of wart-hog or babirussa. In rodents, it is the incisors 

 which undergo elongation ; their rate of growth differs, though but 

 slightly, on the two sides of the axis, and by summation of these 

 slight differences in the rapid growth of the tooth an unmistakable 

 logarithmic spiral is gradually built up; we see it admirably in 

 the beaver, or in the great ground-rat Geornys. The elephant is a 

 similar case, save that the tooth or tusk remains, owing to com- 

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

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

 the tip, or first-formed part of the tooth wears away as fast as it is 

 added to from behind; and in the grown animal, all those portions 

 of the tooth near to the pole of the logarithmic spiral have long 

 disappeared. In the elephant, on the other hand, we see, practically 

 speaking, the whole unworn tooth, from point to root; . and its 

 actual tip nearly coincides with the pole of the spiral. If we 

 assume (as with no great inaccuracy we may do) that the tip 

 actually coincides with the pole, then we may very easily con- 

 struct the continuous spiral of which the existing tusk constitutes 

 a part; and by so doing, we see the short, gently curved tusk 

 of our ordinary elephant growing gradually into the spiral tusk 

 of the mammoth. No doubt, just as in the case of our molluscan 

 shells, we have a tendency to variation, both individual and specific, 

 in the constant angle of the spiral ; some elephants, and some species 

 of elephant, undoubtedly have a higher spiral angle than others. 

 But in most cases, the angle would seem to be such that a spiral 

 configuration would become very manifest indeed if only the tusk 



