On Potentials and their A2:)plication. 159 



the system. This quantity^ thus shown to be a function 



of both force and space, is the Potential Function. The 



integral 



dx', dy', dz' 



y=JL 



I> 



is its analytical ex|Dression, and means what we have just 

 indicated. The Physical idea it represents is, therefore, 

 wo?'k, or energy. 



It is a quantity representing not the actual energy of 

 work heing done, but the jpossible energy due to work 

 already done. It is a consequence of the inertia of matter 

 and the indestructibility of force. Energy exerted is not 

 energy lost, but energy stored or transformed. Potential 

 energy is energy stored. The Potential energy of Elasti- 

 city is, according to Rankine's definition, the worh which 

 a body, in a state of strain, is capable of performing in 

 returning to the free state. The Potential energy of Heat 

 is, according to Clausius, the work which the moving 

 molecules are capahle of performing in being brought to 

 a state of less energetic motion, or to rest ; and Mohr has 

 apparently shown that the Potential energy of Chemical 

 Afiiuity is due to atomic motions within the molecule, 

 which, on being lessened or destroyed, must be changed 

 to Heat, Light, Electricity, or Mechanical work. In all 

 these cases, the Potential Energy is a function of force 

 and space, or its correlative, time. When expressed 

 mathematically, it is the famous Potential Function^ 

 and its value is determined by the special circumstances 

 of each particular case. 



We will give an easy example of its application, in a 

 manner which all students of Analytical Geometry and 

 Elementary Mechanics will readily understand. 



It is well known that if a material point whose co-ordi- 

 nates are f, g, h, be acted on by forces whose resultant P 

 may be regarded as emanating from 0, a point whose 



