On the Definition of Force as the Cause of Motion. 343 



it does not actually do so because it is prevented by the 

 resistance. This has been virtually answered already. If force 

 is not the cause of motion it does not tend to produce it, in 

 any real and useful sense of the expression. But a further reply 

 now suggests itself. If we reflect upon our notions of cause and 

 effect we shall see that that which can exist without producing a 

 certain effect cannot be the cause of that effect when it is produced, 

 and therefore does not tend to produce it; it may be a factor of 

 the cause or a necessary condition of it ; but that is all, 



(8.) Another illustration of the tendency of which we are speak- 

 ing is the very frequent statement that " the " measure of force 

 is the quantity of momentum that it produces in unit of time. 

 Sometimes this is expressed even more strongl}^ and it is said 

 that this is the "proper" measure of force. But this is the 

 measure of impulse. Force, no doubt, ca'??, be measured kineticall}^, 

 and it so happens that, for certain practical reasons with which 

 we are not now concex'ned, the kinetic measure of force is the 

 most preferable. But to say that the kinetic is " the " measure, 

 or the "proper" measure, of force, and that the Gaussian, or 

 kinetic unit is its absolute unit, to the implied ignoring of the 

 static and energetic measures of it, is unduly emphasizing its 

 kinetic relations. It is calculated to make the learner think 

 that / in fs=^mv^ is impulse of unit of time. It is similar 

 to declaring arbitrarily that " the " measure of volume is the 

 weight of the quantity of matter of unit density which would 

 fill it. (In many cases, no doubt, this would be practically the 

 best.) 



Let us observe, finally, that the " vis " in Newton's Laws of 

 Motion which changes, i.e. causes, motion is impulse (see the 

 explanation of Law II. ; " gradatim" &c., excludes force proper, 

 " additur" &c., excludes rate, and posits amount, of change of 

 motion) ; though in the sentence from the Scholium to the Laws 

 brought into light by Thomson and Tait, Nam si oestimetur, 

 &LC., " vis " is force proper. 



