THEORY OF A SYSTEM OF ELECTRIFIED CONDUCTORS. 331 



magnetism, they are electric currents and the " electrotonic state" of circuits; 

 and in electrostatics, they are the potentials and the charges of conductors. 



Now, if a change takes place in the configuration of the system, by which 

 the energy (whether potential or kinetic) of the system is diminished, while the 

 momenta, the strains, the electrotonic states, or the charges remain constant, the 

 displacement will be aided by a force of such a magnitude that the work done 

 by the force during the displacement is equal to the diminution of the energy 

 of the system. 



For the momenta, the strains, the electrotonic states, and the charges do not 

 require for their maintenance the application of energy from without the system. 



The same change of configuration, if effected under the condition that the 

 velocities, stresses, potentials, or electric currents remain constant, would, by 

 equation (9), increase the energy of the system by exactly the same amount as 

 it was diminished in the former case. The work done by the system during 

 the displacement will be the same as before, so that energy must in this case be 

 supplied from without to an amount double of this work, in order to satisfy 

 these new conditions. 



For it is only by external compulsion that the velocities of the system can 

 be maintained constant when the configuration changes. Work must be done on 

 an elastic system to keep the stress constant while the strain varies. The 

 currents in a conducting circuit tend to vary when the electrotonic state of the 

 circuit varies, and can only be kept constant by battery power. The same 

 agency must be employed to maintain the potential of a conductor constant 

 during the displacement of the system of conductors. 



Hence, when momenta, strains, electrotonic states, or charges are maintained 

 constant, the internal forces of the system tend to produce displacements which 

 would diminish the energy of the system. 



If, on the other hand, the velocities, stresses, electric currents, or potentials 

 are maintained constant, the internal forces tend to produce displacements 

 which would increase the energy of the system. 



This distinction between the two sets of physical quantities is of great 

 importance in the theory of classification of such quantities. The characteristic 

 of the first set is inherent persistence. Any persistence which we may observe 

 in the second set is only apparent, and arises from the second set being 

 functions of the first set when the configuration of the system either does 

 not vary or is not such as to cause a variation of the coefficients A and a. 



422 



