58, 59] WORK AND ENERGY. Ill 



is a maximum or minimum, and a little consideration shows that 

 for stable equilibrium it is a minimum. 



Examples of non-conservative systems are found whenever the 

 forces depend upon the velocities as well as upon the coordinates ; 

 for example, bodies moving through the air or other resisting 

 medium or bodies whose motion is opposed by friction of any sort, 

 form non-conservative systems. Even if the friction be constant 

 in magnitude, its direction will depend on the direction of the 

 velocities, being in such a direction as always to oppose the 

 motion, and to diminish the total energy of the system. The 

 dynamical theory of heat accounts for the energy that apparently 

 disappears in non- conservative systems. 



Kinetic energy being defined as ^^mv 2 is of the dimensions 

 -- , the same as those of work. Potential energy is defined 

 as work. The unit of energy is, therefore, the erg. 



59. Particular case of Force-function. Newtonian 

 Forces. In the particular case in which the only forces acting 

 on the system are attractions or repulsions by the several particles 

 directed along the lines joining them and depending only on their 

 mutual distances, a force-function always exists. 



For let the force between two particles m r and m s at a distance 

 apart r rs be 



It will be convenient to consider 

 F positive if the force is a repulsion. 



Consider now the force F s (r) acting 

 on m s and acting in the direction FlG - 26> 



from m r to m s . Its direction cosines are those of the vector r rS) 



