40 



ON MAGNITUDE 



[CH. 



root of the pendulum-length, or Va/Vb. Therefore the velocity, 

 which is measured by amphtude/time, or a/b x Vb/Va, will also vary 



as the square root of the hnear dimen- 

 sions; which is Froude's law over again. 

 The smaller man, or smaller animal, 

 goes slower than the larger, but only in 

 the ratio of the square roots of their 

 linear dimensions ; whereas, if the limbs 

 moved alike, irrespective of the size of 

 the animal — if the limbs of the mouse 

 swung no faster than those of the horse 

 — then the mouse would be as slow in 

 its gait or slower than the tortoise. 

 M. DeHsle* saw a fly walk three inches 

 in half-a-second ; this was good steady 

 walking. When we walk five miles an 

 hour we go about 88 inches in a second, 

 or 88/6 =14-7 times the pace of M. DeHsle 's fly. We should walk 

 at just about the fly's pace if our stature were 1/(14-7)2, or 1/216 

 of our present height — say 72/216 inches, or one-third of an inch 

 high. Let us note in passing that the number of legs does not 

 matter, any more than the number of wheels to a coach; the 

 centipede runs none the faster for all his hundred legs. 



But the leg comprises a complicated system of levers, by whose 

 various exercise we obtain very different results. For instance, by 

 being careful to rise upon our instep we increase the length or 

 amplitude of our stride, and improve our speed very materially; 

 and it is curious to see how Nature lengthens this metatarsal joint, 

 or instep-lever, in horse f and hare and greyhound, in ostrich and 

 in kangaroo, and in every speedy animal. Furthermore, in running 

 we bend and so shorten the leg, in order to accommodate it to a 

 quicker rate of pendulum-swing J. In short the jointed structure 



* Quoted in Mr John Bishop's interesting article in Todd's Cyclopaedia, iii, 

 p. 443. 



t The "cannon-bones" are not only relatively longer but may even be actually 

 longer in a little racehorse than a great carthorse. 



t There is probably another factor involved here: for in bending and thus 

 shortening the leg, we bring its centre of gravity nearer to the pivot, that is to 

 say to the joint, and so the muscle tends to move it the ,more quickly. After all, 



