156 Mk WHEWELL, on the NATURE OF THE TRUTH 



the effect upon a body at rest? The answer to this is, that we here 

 take for the measure of the effect of the force, that motion which 

 must be compounded with the motion existing before the change, in or- 

 der to produce the motion which exists after the change: the rules for 

 the composition of motion being established on independent grounds 

 by the aid of definition alone. Thus if gravity act upon a body 

 which is falling vertically, the effect of gravity upon the body is 

 measured by the velocity added to that which the body already has : 

 if gravity act upon a body which is moving horizontally, its effect 

 is measured by the distance to which the body falls below the hori- 

 zontal line. 



The effect of the force which we consider in the second Law of 

 motion, is its effect upon velocity only : and it is proper to mark 

 this restriction by an appropriate term : we shall call this the accele- 

 rative effect of force; and the cause, as measured by this effect, may 

 be termed the accelerathe quantity of the force.* 



A law of motion which necessarily results from our second Axiom 

 is, that the accelerative quantity of a force is measured by the acce- 

 lerative effect. But whether the accelerative effect depends upon the 

 velocity and direction of the moving body, cannot be known indepen- 

 dently of experience. It is very conceivable, for instance, that the 

 force of gravity being every where the same, shall yet produce, upon 

 falling bodies, a smaller accelerative effect in proportion to the velocity 

 which they already have in a downward direction. Indeed if gravity 

 resembled in its operation the effect of any other mode of mechanical 

 agency, the result would be so. If a body moved downwards in 



* The accelerative quantity of a force (the quantitas acceleratrix vis cujusvis of Newton) 

 is often called the accelerating forces and we may thus have to speak of the accelerating 

 force of a certain force, which is at any rate an awkward phraseology. It would perhaps 

 have been fortunate if Newton, or some other writer of authority, at the time when the 

 principles of mechanics were first clearly developed, had invented an abstract term for 

 this quantity : it might for instance have been called acceleralivity. And the second law 

 of motion would then have been, that the acceleralivity of the same force is the same, 

 whatever be the motion of the body acted on. 



