50 ON MAGNITUDE [ch. 



for a few moments, then close their wings and shoot along*. The 

 flying-fishes do much the same, save that they keep their wings 

 outspread. The best of them "taxi" along with only their tails in 

 the water, the tail vibrating with great rapidity, and the speed 

 attained lasts the fish on its long glide through the airf. 



Flying may have begun, as in Man's case it did, with short spells 

 of gUding flight, helped by gravity, and far short of sustained or 

 continuous locomotion. The short wings and long tail of Archae- 

 opteryx would be efficient as a slow-speed ghder; and we may still 

 see a Touraco glide down from his perch looking not much unlike 

 Archaeopteryx in the proportions of his wings and tail. The small 

 bodies, scanty muscles and narrow but vastly elongated wings of 

 a Pterodactyl go far beyond the hmits of mechanical efficiency for 

 ordinary flapping flight; but for ghding they approach perfection J. 

 Sooner or later Nature does everything which is physically possible ; 

 and to glide with skill and safety through the air is a possibihty 

 which she did not overlook. 



Apart from all differences in the action of the limbs — apart from 

 differences in mechanical construction or in the manner in which 

 the mechanism is used — we have now arrived at a curiously simple 

 and uniform result. For in all the three forms of locomotion which 

 we have attempted to study, alike in swimming and in walking, and 

 even in the more, complex problem of flight, the general result, 

 obtained under very different conditions and arrived at by different 

 modes of reasoning, shews in every case that speed tends to vary as 

 the square root of the linear dimensions of the animal. 



While the rate of progress tends to increase slowly with increasing 

 size (according to Froude's law), and the rhythm or pendulum-rate 

 of the limbs to increase rapidly with decreasing size (according to 

 Galileo's law), some such increase of velocity with decreasing 



* Why large birds cannot do the same is discussed by Lanchester, op. cit. 

 Appendix iv., 



t Cf. Carl L. Hubbs, On the flight of. . .the Cypselurinae, and remarks on the 

 evolution of the flight of fishes. Papers of the Michigan Acad, of Sci. xvii, pp. 575- 

 611, 1933. See also E. H. Hankin, P.Z.S. 1920, pp. 467-474; and C. M. Breeder, 

 On the structural specialisation of flying fishes from the standpoint of aero- 

 dynamics, Copeia, 1930, pp. 114-121. 



X The old conjecture that their flight was helped or rendered possible by a denser 

 atmosphere than ours is thus no longer called for. 



