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.
Therefore, when a force acts for a certain time on a mass that is free to move, however small the force and however small the time, that body will move. When a baby in a temper stamps upon the earth it makes the earth move—not much, it is true, but still it moves; nay, more, in theory, not a fly can jump into the air without moving the earth and the whole solar system. Only, as you may imagine they do not show it appreciably. Still, in theory the motion is there.
Hence then there are two different ways of considering and estimating forces, one suitable for observations on bodies at rest, the other suitable for observations of bodies that are free to move. The force of course always tends to produce motion. If, however, motion is impossible, then it develops pressures which we can measure, and calculate, and observe. If the body is free to move, then the force produces motions which we can also measure, calculate, and observe. And we can compare these two sets of effects. We can say, “A force which, acting on a ball of a mass of one pound, would produce such and such motions, would if it acted on a certain spring produce so much compression.”
The attraction of the earth on masses of matter that are not free to move gives rise to forces which are called weights. Thus the attraction of gravitation on a mass of one pound produces a pressure equal to a weight of one pound. Unfortunately the same word “pound” is used to express both the mass and the weight, and has come down to us from days when the nature of mass was not very well appreciated. But great care must be taken not to confuse these two meanings.