II] OF LOCOMOTION 39 



But if the animal, with increasing size or stature, jump to a correspondingly 

 increasing height, the case becomes much more serious. For the final velocity 

 of descent varies as the square root of the altitude reached, and therefore as 

 the square root of tte linear dimensions of the animal. And since, as before, 



13 



cccmvcc j^ Vy 



c oc 75 . V ;, or c oc Z». 



If a creature's jump were in proportion to its height, the crushing strains 

 would so increase that its dimensions would be limited thereby in a much higher 

 degree than was indicated by statical considerations. An animal may grow 

 to a size where lit is unstable dynamically, though still on the safe side 

 statically — a size where it moves with difficulty though it rests secure. It is 

 by reason of dynamical rather than of statical relations that an elephant 

 is of graver deportment than a. mouse. 



An apparently simple problem, much less simple than it looks, lies 

 in the act of walking, where there will evidently be great economy of 

 work if the leg swing with the help of gravity, that is to say, at a 

 peTidulum-rate. The conical shape and jointing of the limb, the time 

 spent with the foot upon the ground, these and other mechanical 

 differences complicate the case, and make the rate hard to define or 

 calculate. Nevertheless, we may convince ourselves by counting our 

 steps, that the leg does actually tend to swing, as a pendulum does, 

 at a certain definite rate*. So on the same principle, but to the 

 slower beat of a longer pendulum, the scythe swings smoothly in 

 the mower's hands. 



To walk quicker, we "step out"; we cause the leg-pendulum to 

 describe a greater arc, but it does not swing or vibrate faster until 

 we shorten the pendulum and begin to run. Now let two similar 

 individuals, A and B, walk in a similar fashion, that is to say with 

 a similar an^le of swing (Fig. 1). The arc through which the leg 

 swings, or the amplitude of each step, will then vary as the length 

 of leg (say as a/6), and so as the height or other linear dimension (/) 

 of the manf. But the time of swing varies inversely as'the square 



* The assertion that the hmb tends to swing in pendulum-time was first made 

 by the brothers Weber {Mechanik der menschl. Gehwerkzeuge, Gottingen, 1836). 

 Some later writers have criticised the statement (e.g. Fischer, Die Kinematik dea 

 Beinschwingens etc., AhJi. math. phys. Kl. k. Sachs. Ges. xxv-xxvin, 1899-1903), 

 but for all that, with proper and large qualifications, it remains substantially true. 



t So the stride of a Brobdingnagian was 10 yards long, or just twelve times the 

 2 ft. 6 in., which make the average stride or half-pace of a man. 



