It is, however, impossible to make a tuning fork or a stretched piano spring alter the pitch of its note without altering the elastic force of the spring by altering its tension, or without putting weights on the arms of the tuning fork to make it go more slowly. And this is because the tuning fork and the piano spring, being elastic, obey Hooke’s law, “As the deflection, so the force”; and therefore the time of back spring is in each case invariable, and the pitch of the note produced therefore remains invariable, whatever the amplitude of the vibration may be. Upon this law depends the correct going of both clocks and watches. Wonderful nature, that causes the uniformity of sounds of a piano, or a violin, to depend on the same laws that govern the uniform going of a watch! Nay, more, all creation is vibrating. The surge of the sea upon the coast that swishes in at regular intervals, the colours of light, which consist of ripples made in an elastic ether, which springs back with a restitutional force proportioned to its displacement, all depend upon the same law. This grand law by which so many phenomena of nature are governed has a very beautiful name, which I hope you will remember. It is called “harmonic motion,” by which is meant that when the atoms of nature vibrate they vibrate, like piano strings, according to the laws of harmony. The ancient Pythagorean philosophers thought that all nature moved to music, and that dying souls could begin to hear the tones to which the stars moved in their orbits. They called it, as you know, the music of the spheres. But could they have seen what science has revealed to man’s patient efforts, they would have seen a vision of harmony in which not a ray of light, not a string of a musical instrument, not a pipe of an organ, not an undulation of all-pervading electricity, not a wing of a fly, but vibrates according to the law of harmony, the simple easy law of which a boy’s catapult is the type, and which, as we have seen, teaches us that when an elastic body is displaced the force of restitution, in other words, the force tending to restore it to its old position, is proportional to the displacement, and the time of vibration is uniform. The last is the important thing for us; we seem to get a gleam of a notion of how the clock and watch problem is going to be solved. But before we get to that we have yet to go back a little.