Time and Clocks: A Description of Ancient and Modern Methods of Measuring Time

by Sir Henry H. Cunynghame

Fig. 24.

This is a perfectly legitimate way of looking at the matter, just as the cook’s method of employing a spring balance to weigh masses of meat is a perfectly legitimate way of estimating the forces acting upon bodies at rest. But when you come to consider the laws of the pendulums of clocks, to which all that I am saying is a preparation, then you have to deal with bodies in motion. And for this purpose a new idea of force altogether is requisite. We shall no longer speak of forces as producing pressures. We shall treat them quite independently of their pressing power. The sun exerts a force of attraction on the earth, but it does not press upon it. It exerts its force at a distance. Hence then we want a new idea of “force.” This idea is to be the following. We will consider that when a force acts upon a body it endeavours to cause it to move; in fact, it tries to impart motion to the body. We may treat this motion as a sort of thing or property. The longer the force acts on the body, the more motion it imparts to it, provided the body is free to receive that motion. So that we may say that the test of the strength of the force is how much motion it can give to a body of a given mass in a given time. It does not matter how the force acts. It may act by means of a string and pull it; it may act by means of a stick and push it; it may act by attraction and draw it; it may act by repulsion and repel it; it may act as a sort of little spirit and fly away with it. In all these cases it acts. The more it acts, the more effect it has. In double the time it produces double the motion. If the mass is big, it takes more force to make the mass move; if the mass of the body is small, it is moved more easily. Therefore when we want to measure a force in this way we do not press it against springs to see how much it will press them in. What we do is to cause it to act on bodies that are free to move and see what motions it will produce in them. Of course we can only do this with things that are free to move. You cannot treat force in this way if you have only a pair of scales; in that case you would have to be content with simply measuring pressures. It is important clearly to grasp this idea. If a body has a certain mass, then the force acting on it is measured by the amount of motion that will in a given time be imparted to that mass, provided that the mass is free to move. This is to be our definition of force.

Therefore, by the action of an attraction or any other force on a body free to move; motion is continually being imparted to the body. Motion is, as it were, poured into it, and therefore the body continually moves faster and faster.

Here is a ball flying through the air. Let us suppose that forces are acting on it. How can we measure them? We cannot feel what pressures are being exerted on it. The only thing we can do is to watch its motions, and see how it flies. If it goes more and more quickly, we say, “There is propelling force acting on it”; if it begins to stop, we say again, “There is retarding force acting on it.” So long as it does not change its speed or direction, we say, “There is no force acting on it.” By this method, therefore, we tell whether a body is being acted on by force, simply by observing its speed or its change of speed. Merely to say a body is moving does not tell us that force is acting on it. All we know is that, if it is moving, force has acted on it. It is only when we see it changing its speed or direction, that is changing its motion, that we say force is acting. Every change of motion, either in direction or speed, must be the result of force, and must be proportional to that force. This is what we mean when we say motion is the test and measure of force.

This most interesting way of looking at the matter lies at the root of the whole theory of mechanics. It is the foundation of the system which the stupendous genius of Newton conceived in order to explain the motion of the sun, moon, and stars.

Forces were treated by him as proportional to the motions, and the motions proportional to the forces, and with this idea he solved a part of the riddle of the universe. Galileo had partly seen the same thing, but he never saw it so clearly as Newton. Great discoveries are only made by seeing things clearly. What required the force of a genius in one age to see in the next may be understood by a child.

Hence then we say a force is that which in a given time produces a given motion in a given mass which is free to move.

You must have time for a force to act in; for however great the force, in no time there can be no motion. You must have mass for a force to act on; no mass, no effect. You must have free space for the mass to move in; no freedom to move, no movement.

But what is this “mass”? We do not know; it is a mystery. We call it “quantity of matter.” In uniform substances it varies with size. Double the volume, double the mass. Cut a cake in half, each half has the same “mass.” But then is mass “weight”? No, it is not. Weight is the action of the earth’s attraction on matter. No earth to attract, and you would have no weight, but you would still have “mass.” What then is matter? Of that we have no idea. The greatest minds are now at work upon it. But mass is quantity of matter. Knock a brick against your head, and you will know what mass is. It is not the weight of the brick that gives you a bump; it is the mass. Try to throw a ball of lead, and you will know what mass is. Try to push a heavy waggon, and you will know what mass is. Weights, that is earth attractions on masses, are proportional to the masses at the same place. This, as we have seen, is known by experiment.