XIII] OF THE NARWHAL'S HORN 909 



straightness of the tusk, for the grooving or "rifling" of the surface 

 accompanied by no internal twist, for the extension of that rifling 

 to the alveolar portion of the tusk within the jaw, and for the fact 

 that the several associate grooves and ridges preserve their individual 

 character as they pass along and wind their way around. A very 

 slow rotation is all we need demand — say four or five complete 

 revolutions of the tusk in the whole course of a lifetime. 



The progress of a whale or dolphin through the water may be 

 explained as the reaction to a wave which is caused to run from 

 head to tail, the creature moving ' through the water somewhat 

 slower than the wave travels. The same is true, so far, of a fish; 

 but the w^ave tends to be in one plane in the fish, the dorsal and 

 ventral fins helping to keep it so; while in the dolphin it may be 

 said to be "circularly polarised," or resoluble into two oscillations in 

 planes normal to one another, and caused by tail and tail-end swishing 

 around in circular orbits which alter in phase from one transverse 

 section to another. Just as in the case of a screw-propeller, or as 

 in a torpedo (where it is specially corrected or compensated), this 

 mode of action entails a certain waste of energy; it comes of the 

 development of a "harmful moment," which tends to rotate the 

 body about its axis, and to screw the animal along its course. A 

 slight left-handed curvature of the dolphin's tail goes some little 

 way towards correcting this tendency. M. Shuleikin's study of the 

 kinematics of the dolphin * — a fine piece of work both on its experi- 

 mental and its theoretical side — shows the dolphin to be a better 

 swimmer than the fish, inasmuch as its speed of progression comes 

 nearer to the velocity of the wave which is propagated along its 

 body; the so-called "step," or fraction of the body-length travelled 

 in a single period, is found to be about 0-7 in the dolphin, against 

 0-57 in a fast-swimming fish (tunny or mackerel). 



Shuleikin makes the curious remark that the asymmetry of the 

 skull (discernible in all Cetacea), which in the dolphin shews a screw- 

 twist with a pitch about equal to the length of the body, acts as 

 a compensatory check to the screw-component in the creature's 

 movement of progression, and that "the till now obscure purpose 



* Wassilev Shuleikin, Kinematics of a dolphin (Russian), Bull. Acad. Sci. U.R.S.S. 

 {CI. sci. math, et phys.), 1935, pp. 651-671; also, Dynamics, external and internal, 

 of a fish, ibid. 1934, pp. 1151-1186. On the latter subject see James Gray, 

 Crobnian Lecture, 1940, and other papers. 



