AN ESSAY ON QUANTITY
quantity. And why, then, may you not take the velocity for the primary measure, as well as any other? You will find none that is more simple, more distinct, or more agreeable to the common use of the word force: and he that rejects one definition that has these properties, has equal right to reject any other. I say, then, that it is impossible, by mathematical reasoning or experiment, to prove that the force of a body is as its velocity, without taking for granted the thing you would prove, or something else that is no more evident than the thing to be proved.
Sec. 7. Of the Leibnitzian measure of force.
Let us next hear the Leibnitzian, who says, that the force of a body is as the square of its velocity. If he lays this down as a definition, I shall rather agree to it, than quarrel about words, and for the future shall understand him, by a quadruple force, to mean that which gives a double velocity, by nine times the force that which gives three times the velocity, and so on in duplicate proportion. While he keeps by his definition, it will not necessarily lead him into any error in mathematics or mechanics. For, however paradoxical his conclusions may appear, however different in words from theirs who measure force by the simple ratio of the velocity, they will, in their meaning, be the same: just as he who would call a foot twenty-four inches, without changing other measures of length, when he says a yard contains a foot and a-half, means the very same as you do, when you say a yard contains three feet.
But though I allow this measure of force to be distinct, and cannot charge it with falsehood, for no definition can be false, yet I say, in the first place, it is less simple than the other; for why should a duplicate ratio be used, where the simple ratio will do as well? In the next place, this measure of force is less agreeable to the common use of the word force, as hath been shown above: and this, indeed, is all that the many laboured arguments and experiments, brought to overturn it, do prove. This also is evident, from the paradoxes into which it has led its defenders.
We are next to consider the pretences of the Leibnitzian, who will undertake to prove, by demonstration or experiment, that force is as the square of the velocity. I ask him first, what he lays down for the first measure of force? The only measure I remember to have been given by the philosophers of that side, and which seems first of all to have led Leibnitz into his notion of force, is this: the height to which a body is impelled by any impressed force, is, says he, the whole effect of that force and therefore must be proportional to the cause; but this height is found to be as the square of the velocity, which the body had at the beginning of its motion.
In this argument, I apprehend that great man has been ex-