II] THE PRINCIPLE OF SIMILITUDE 31 



root of the peiidulum-length, or -^/ajy/'b. Therefore the velocity, 



, . , . 1 , amplitude .,, , , 



which IS measured by . , will also vary as the square- 

 time ■ ^ 



roots of the length of leg : that is to say, the average velocities of 



A and B are in the ratio of y'a : y/h. 



The smaller man, or smaller animal, is so far at a disadvantage 

 compared with the larger in speed, but only to the extent of the 

 ratio between the square roots of their linear dimensions : whereas, 

 if the rate of movement of the limb were identical, irrespective 

 of the size of the animal, — if the limbs of the mouse for instance 

 swung at the same rate as those of the horse, — then, as F. Plateau 

 said, the mouse would be as slow or slower in its gait than the 

 tortoise. M. Delisle* observed a "minute 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)^, or 1/216 

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

 high. 



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

 various exercise we shall obtain very different results. For 

 instance, by being careful to rise upon our instep, we considerably 

 increase the length or amplitude of our stride, and very considerably 

 increase our speed accordingly. On the other hand, 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 

 of the leg permits us to use it as the shortest possible pendulum 

 when it is swinging, and as the longest possible lever when it is 

 exerting its propulsive force. 



Apart from such modifications as that described in the last 

 paragraph, — apart, that is to say, 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 



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

 p. 443. 



t There is probably also another factor involved here : for in bending, and there- 

 fore 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. 



