910 THE SHAPES OF TEETH [ch. 



of the skull's asymmetry" is accordingly explained. I should put 

 this differently, and suggest that this counter-spirality of the skull, 

 is the direct result of the spiral component in locomotion. It implies, 

 I take it, a lagging and incomplete response in the fore-part of the 

 body to the rotatory impulse of the pai ts behind : or, in the plain 

 words of the engineer, a torque of inertia. • 



This tendency, dimly seen in the dolphin's skullj is clearly demon- 

 strated in the narwhal's "horn," and gives a complete explanation 

 of its many singularities-. The narwhal and its horn are joined 

 together, and move together as one piece — nearly, but not quite! 

 Stiif, straight and heavy, the great tusk has its centre of inertia 

 well ahead of the animal, and far from the driving impulse of its 

 tail. At each powerful stroke of the tail the creature not only darts 

 forward, but twists or slews all of a sudden to one side; and the 

 heavy horn, held only by its root, responds (so to speak) with 

 difficulty. For at its slender base the "couple", by which it has 

 to follow the twisting of the body, works at no small disadvantage. 

 A "torque of inertia" is bound to manifest itself. The horn does 

 not twist round in perfect synchronism with the animal; but the 

 animal (so to speak) goes slowly, slowly, little by little, round its 

 own horn! The play of motion, the lag, between head and horn 

 is sUght indeed; but it is repeated with every stroke of the tail. 

 It is felt just at the growing root, the permanent pulp, of the tooth; 

 and it puts a strain, or exercises a torque, at the very seat, and during 

 the very process, of calcification. 



Suppose that at every sweep of the tail there be a lag of no more 

 than a fifth part of a second of arc* between the rotation of the 

 tusk and of the body, that small amount would amply suffice to 

 account, on a rough estimate of the age and of the activity of the 

 animal, for as many turns of the screw as a fair-sized tusk is found 

 to exhibit. 



According to this explanation, or hypothesis, the slow rotation 

 of the tusk corrects all tendency to flexure or curvature in one 

 direction or another ; the grooves and ridges which constitute th6 

 "thread" of the screw are the result of irregularities or inequalities 

 within the alveolus, which "rifle" the tusk as it grows; and the 



* Or say a hundred-thousandth part of the angle subtended by a minute on the 

 clock. 



