A somewhat simple problem is presented to us by the act of walking. It is obvious that there will be a great economy of work, if the leg swing at its normal _pendulum-rate_; and, though this rate is hard to calculate, owing to the shape and the jointing of the limb, we may easily convince ourselves, by counting our steps, that the leg does actually swing, or tend to swing, just as a pendulum does, at a certain definite rate[51]. When we walk quicker, we cause the leg-pendulum to describe a greater arc, but we do not appreciably cause it to swing, or vibrate, quicker, until we shorten the pendulum and begin to run. Now let two individuals, _A_ and _B_, walk in a similar fashion, that is to say, with a similar _angle_ of swing. The _arc_ through which the leg swings, or the _amplitude_ of each step, will therefore vary as the length of leg, or say as _a_/_b_; but the time of swing will vary as the square {31} root of the pendulum-length, or √_a_/√_b_. Therefore the velocity, which is measured by amplitude/time, will also vary as the square-roots of the length of leg: that is to say, the average velocities of _A_ and _B_ are in the ratio of √_a_ : √_b_. 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[52] 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. Delisle’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. 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[53]. 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.