AN ESSAY ON QUANTITY
with some new faculty; for I know nothing of force but by its effects, and therefore can measure it only by its effects. Till force then is defined, and by that definition a measure of it assigned, we fight in the dark about a vague idea, which is not sufficiently determined to be admitted into any mathematical proposition. And when such a definition is given, the controversy will presently be ended.
Sec. 6. Of the Newtonian measure of force.
You say, the force of a body in motion is as its velocity; either you mean to lay this down as a definition as Newton himself has done; or you mean to affirm it as a proposition capable of proof. If you mean to lay it down as a definition, it is no more than if you should say, I call that a double force which gives a double velocity to the same body, a triple force which gives a triple velocity, and so on in proportion. This I entirely agree to; no mathematical definition of force can be given that is more clear and simple, none that is more agreeable to the common use of the word in language. For since all men agree, that the force of the body being the same, the velocity must also be the same; the force being increased or diminished, the velocity must be so also; what can be more natural or proper than to take the velocity for the measure of the force?
Several other things might be advanced to show, that this definition agrees best with the common popular notion of the word force. If two bodies meet directly with a shock, which mutually destroys their motion without producing any other sensible effect, the vulgar would pronounce, without hesitation, that they met with equal force; and so they do, according to the measure of force above laid down: for we find by experience, that in this case their velocities are reciprocally as their quantities of matter. In mechanics, where by a machine two powers or weights are kept in equilibrio, the vulgar would reckon, that these powers act with equal force; and so by this definition they do. The power of gravity being constant and uniform, any one would expect that it should give equal degrees of force to a body in equal times; and so by this definition it does. So that this definition is not only clear and simple, but it agrees best with the use of the word force in common language, and this, I think, is all that can be desired in a definition.
But if you are not satisfied with laying it down as a definition, that the force of a body is as its velocity, but will needs prove it by demonstration or experiment, I must beg of you, before you take one step in the proof, to let me know what you mean by force, and what by a double or a triple force. This you must do by a definition which contains a measure of force. Some primary measure of force must be taken for granted, or laid down by way of definition; otherwise we can never reason about its