114 THEORY OF NEWTONIAN FORCES. [PT. I. CH. II. 



The factor -J is introduced because in the above summation 

 every term appears twice. But in V each pair of particles is to 

 appear only once. 



If no constant be added to U as defined above, both it and 

 the potential energy 



(33) F = i2A !^, ' 



will vanish when every r rs is infinite, that is when no two particles 

 are within a finite distance of each other. This furnishes a con- 

 venient zero configuration for the potential energy, and is the one 

 generally adopted. We may accordingly define the potential 

 energy of the system in any given configuration as the work that 

 must be done against the mutual repulsions of the particles in 

 order to bring them from a state of infinite dispersion to the given 

 configuration. 



