VOL, XLV.] PHILOSOPHICAL TRANSACTIONS. 563 



shall we essay to measure virtue and merit by them. This is only to ring changes 

 on words, and to make a show of mathematical reasoning, without advancing 

 one step in real knowledge. 



Dr. M. apprehends that the account given o the nature of proper and improper 

 quantity, may also throw some light on the controversy about the force of mov- 

 ing bodies, which long exercised the pens of many mathematicians, and perhaps 

 is rather dropped than ended ; to the no small scandal of mathematics, which has 

 always boasted of a degree of evidence, inconsistent with debates that can be 

 brought to no issue. 



Though philosophers on both sides agree with each other, and with the vul- 

 gar in this, that the force of a moving body is the same, while its velocity is the 

 same, is increased when its velocity is increased, and diminished when that is 

 diminished. But this vague notion of force, in which both sides agree, though 

 perhaps sufficient for common discourse, yet is not sufficient to make it a sub- 

 ject of mathematical reasoning : in order to that, it must ba more accurately 

 defined, and so defined as to give us a measure of it, that we may understand 

 what is meant by a double or a triple force. The ratio of one force to another 

 cannot be perceived but by a measure ; and that measure must be settled, not 

 by mathematical reasoning, but by a definition. Let any one consider force 

 without relation to any other quantity, and see whether he can conceive one 

 force exactly double to another ; I am sure I cannot, says he, nor shall, till I 

 shall be endowed 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 de- 

 fined, 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 mathe- 

 matical proposition. And when such a definition is given, the controversy will 

 presently be ended. 



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 he entirely 

 agrees 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 lan- 

 guage. 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 ve- 

 locity must be so also, what can be more natural or proper than to take the ve- 

 locity for the measure of the force ? 



Several other things might be advanced to show that this definition agrees 



4 c 2 



