64.] FORCE. 37 



Like the sensations of light, sound, heat, etc., the sensation of exerting 

 force is capable, in a rough way, of measurement.^ But the physiological 

 and psychological phenomena attending the exertion of muscular force 

 when analysed more carefully are very complicated. 



In ordinary language the term " force " is applied in a great variety of 

 meanings. For scientific purposes it is of course necessary to attach a 

 single definite meaning to it. 



63. In physics it is customary to speak of force as producing or 

 generating velocity, and to define force as the cause of acceleration. 

 Thus observation shows that the velocity of a falling body increases 

 during the fall ; the cause of the observed change in the velocity, i.e. 

 of the acceleration, is called the force of attraction, and is supposed to 

 be exerted by the earth. Again, a body falling in the air, or in some 

 other medium, is observed to increase its velocity less rapidly than 

 a body falling in vacuo ; a force of resistance is therefore ascribed to 

 the medium as the cause of this change. In a similar way we speak 

 of the expansive force of steam, of electric and magnetic forces, etc., 

 because all these agencies produce changes of velocity. 



Now, any change in the velocity v of a body of given mass m implies 

 a change in its momentum mv ; and it is this change of momentum, or 

 rather the rate at which the momentum changes with the time, which 

 is of prime importance in all the applications of mechanics. It is there- 

 fore convenient to have a special name for this rate of change, and that 

 is what is called force. 



It is, however, well to remember that in using this term "force," it is not 

 intended to assert anything as to the objective reality or actual nature 

 of force and matter in the ordinary acceptation of these terms. Our 

 knowledge comes to us through our sense-impressions, and these would 

 all seem to reduce finally to changes of motion and changes of momen- 

 tum : these alone we can perceive directly. 



64. The definition of force (Art. 60) as the product of mass 

 and acceleration gives the dimensions of force as 



The unit of force is therefore the force of a particle of unit 

 mass moving with unit acceleration. 



Hence, in the C.G.S. system, it is the force of a particle of 



