122 Mr. R. Moon on the Conservation of Force. 



considering it is not true, as asserted by Prof. Maxwell, that 

 the energy of the system consists of two parts — one depending 

 on the motion of the body represented by the kinetic energy, 

 the other depending on the work which the forces would do if 

 the bodies were to yield to their action, since during this por- 

 tion of the motion the body cannot yield to the action of the 

 forces, that action being controlled and overcome by the mo- 

 mentum for the time being inherent in each body. 



If the second of the two components of which the total 

 energy is assumed to consist is to be expressed in the language 

 of the ' Theory of Work,' it is evident that during one half 

 of the motion in the last case, Prof. Maxwell's account of the 

 composition of energy must be modified into some such terms 

 as the following. 



The energy of the system consists of two parts — (1) the kinetic 

 energy which bodies have by virtue of being in motion, (2) 

 an energy depending on the amount of work which the mo- 

 mentum in the system would do if the bodies were to yield to 

 its action, — a classification which, however exactly it meets the 

 case to which it is intended to apply, is entirely deficient in 

 that antithetical character which the epithets " kinetic " and 

 " potential " would assign to the two functions which are as- 

 sumed to represent the total energy, and which has gone so 

 far to seduce the judgment of those who have given in their 

 adhesion to the theory. 



IY. A more obvious and decisive contradiction of the theory 

 will be afforded by writing down the equation for the vis viva 

 in the foregoing case of motion. 



Taking unity for the mass of each body, the equations ap- 

 plicable to the motions of P will be of the form 



d?a; _ fix 

 ~d£~~~^' 



dt 2 ~ r 3 ' 



the coordinates being measured from G parallel and perpendi- 

 cular to Aa. Hence 



•2\dt\ + dt\J J,f>\? dt + *dtJ 



fji dr 

 ) t r 2 dt' 

 or 



I 



" - * -co, 



¥.- r + °' 



