Let a heavy ball (_A_) be suspended by a long string, so that the action of gravity sideways on the ball is very small and may be neglected, and to each side attach an indiarubber thread fastened at _B_ and _C_. Then when the ball is pulled aside a little, say to a position _D_, it will tend to fly back to _A_ with a force proportioned to the distance _A D_. What will be the time it will take to do this? If the distance _A D_ is small, the ball has only a small distance to go, but then, on the other hand, it has only small forces acting on it. If the distance _A D_ is bigger, then it has a longer distance to go, but larger forces to urge it. These counteract one another, so that the time in each case will be the same. [Illustration: FIG. 32.] The question is this:—Will you go a long distance with a powerful horse, or a small distance with a weak horse? If the distance in each case is proportioned to the power of the horse, then the amount of the distance does not matter. The powerful horse goes the long distance in the same time that the weak horse goes the short distance. And so it is here. However far you pull out the spring, the accelerative pull on the ball is proportioned to the distance. But the time of pulling the ball in depends on the distance. So that each neutralises the other. Whence then we have this most important fact, that springs are all isochronous; that is to say, any body attached to any spring whatever, whether it is big or small, straight or curly, long or short, has a time of vibration quite independent of the bigness of the vibration. The experiment is easy to try with a ball mounted on a long arm that can swing horizontally. It is attached on each side to an elastic thread. If pulled aside, it vibrates, but observe, the vibration is exactly the same whether the bigness of the vibration is great or small. If the pull aside is big, the force of restitution is big; if the pull is small, the force of restitution is small. In one case the ball has a longer distance to go, but then at all points of its path it has a proportionally stronger force to pull it; if the ball has a smaller distance to go, then at all the corresponding points of its path it has a proportionally weaker force to pull it. Thus the time remains the same whether you have the powerful horse for the long journey or the weaker horse for the smaller journey. [Illustration: FIG. 33.] Next take a short, stiff spring of steel. One of the kind known as tuning forks may be employed.