HERMANN VON HELMHOLTZ 



the previous history, reckoning from some chosen 

 instant, as epoch. If we take the simplest case of a 

 particle moving with constant velocity, and therefore 

 with constant kinetic energy in a straight line, the 

 Action is simply the kinetic energy multiplied by the 

 time, and increases at a steady rate. If the particle is 

 guided between two positions by any other than the 

 straight line connecting these positions, it must describe 

 a longer course and, since the speed is constant, take a 

 longer time. In this simplest of all cases the minimum 

 property is obviously fulfilled when the path pursued 

 is the natural path. 



As already indicated, the principle of least action, 

 taken in connection with the principle of the con- 

 stancy of the sum of the potential and kinetic energies, 

 leads to the equations of motion of the system under 

 consideration. But it is only in problems of abstract 

 dynamics that the sum of the potential and kinetic 

 energies is constant. With the recognition of the 

 true nature of heat came the great modern generalisa- 

 tion of the conservation of energy. Heat is a form 

 of molecular and ethereal energy ; and dynamically 

 this great doctrine of the conservation of energy is 

 the earlier principle of the constancy of the potential 

 and kinetic energies, if cognisance be taken of the 

 invisible motions of molecules and ether as well as of 

 the visible mass motions. 



The idea of Helmholtz was to apply the principle 

 of action to these wider problems. In the general 

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