634 THE SHAPES OF TUSKS [ch. xiii 



anterior, 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 construct 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 pursued its steady growth, 

 unchanged otherwise in form, till it attained the dimensions 

 which we meet with in the mammoth. In a species such as 

 Mastodon angustidens, or M. arvernensis, the specific angle is 

 low and the tusk comparatively straight; but the American 

 mastodons and the existing species of elephant have tusks which 

 do not differ appreciably, except in size, from the great spiral 

 tusks of the mammoth, though from their comparative shortness 

 the spiral is little developed and only appears to the eye as a 

 gentle curve. Wherever the tooth is very long indeed, as in the 

 mammoth or the beaver, the efiect of some slight and all but 

 inevitable lateral asymmetry in the rate of growth begins to shew 

 itself: in other words, the spiral is seen to lie not absolutely in 

 a plane, but to be a curve of double curvature, like a twisted 

 horn. We see this condition very well in the huge canine tusks 

 of the Babirussa; it is a conspicuous feature in the mammoth, 

 and it is more or less perceptible in any large tusk of the ordinary 

 elephants. 



The form of a molar tooth, which is essentially a branching or 

 budding system, and in which such longitudinal growth as gives 

 rise to a spiral curve is but little manifest, constitutes an entirely 

 different problem with which I shall not at present attempt to deal. 



