Theory of Electromagnetic Action. 443 



regarding the intrinsic energy gives, as shown below, exactly 

 the amount of energy, per unit of volume of the medium, 

 spent in any change of magnetization, whether a complete 

 cycle or not, otherwise than in increasing the intrinsic energy, 

 and therefore gives at once the energy dissipated in carrying 

 the medium through a complete cycle from one given state 

 as to intrinsic energy back to the same state again. 



Everything seems to point to the conclusion that what we 

 are in the habit of regarding as potential energy is really 

 kinetic energy. Every increase of scientific knowledge of 

 matter furnishes additional proof that all its properties have 

 their explanation in motion, and the conviction is more and 

 more forced upon every physical student that the ordinary 

 division of energy into potential and kinetic results from our 

 incomplete knowledge of the material system considered. If 

 we had perfect knowledge of the coordinates of all the parts 

 of the system and their velocities at a given instant, and, 

 further, knew fully the conditions to which these coordinates 

 are subject, we should ipso facto be able to define the confi- 

 guration at any time of any portion of the system, and to 

 state how at that time the whole kinetic energy is divided 

 between that portion and the rest of the system. Thus the 

 ordinary transformation of potential into kinetic energy, and 

 vice versa, is only a process of redistribution of kinetic energy 

 between the different parts of the system. 



It can in fact be proved that if a dynamical system be 

 specified partly by a certain group of position coordinates ((/>) 

 and partly by velocities of other coordinates (^), so that the 

 kinetic energy is the sum of two corresponding parts T^, T^, 

 of which the first is expressed as a quadratic function of the 



velocities of the type c£, and the other as a quadratic function 

 of the momenta corresponding to the velocities -v/r, the altera- 

 tions of the position coordinates will take place precisely as if 

 the system had a quantity of kinetic energy T<p, and a quantity 

 of potential energy T^*. For there being no potential energy 

 we can in this case write the Lagrangian equation for a 

 (£- coordinate as follows f : — 



d Qf(Tg-T^) _ d(%-T+) =Q _ 



dt d$ # 



or, since dT x p/d(j) = 0, 



ddT 1 _dT 1 = _dT 1 ^ 

 dt rfX d<p d<j) ' 



* See J. J. Thomson's ' Applications of Dynamics to Phjsics and 

 Chemistry,' p. 13. 



t Routh, 'Stability of Motion,' p. 61 ; Thomson and Tait's 'Natural 

 Philosophy,' vol. i. part 1, p. 323. 



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