664 PHILOSOPHICAL TRANSACTIONS. [aNNO 1748. 



best with the common popular notion of the word force. If 1 bodies meet di- 

 rectly 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 vekx;ities are 

 reciprocally as their quantities of matter. In mechanics, where by a machine '2 

 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 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 ite velocity, but will needs prove it by demonstration or experi- 

 ment; 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 mea- 

 sure of force must be taken for granted, or laid down by way of definition ; 

 otherwise we can never reason about its 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 mathe- 

 matical reasoning or experiment, to prove that the force of a body is as its velo- 

 city, without taking for granted the thing you would prove, or something else 

 that is no more evident than the thing to be proved. 



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 Q times the force, that which gives 3 times the velo- 

 city, 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 fi-om 

 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 24 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 3 feet. 



But though I allow this measure of force to be distinct, and cannot charge it 



