184 JAMES CLEUK MAXWELL 



displacement is equivalent in all respects to a current. 

 The current at any point in a dielectric is measured 

 by the rate of change of displacement at that point. 



Moreover, it is also an essential point that if we 

 consider any section of the dielectric between the two 

 plates, the rate of change of the total displacement 

 across this section is at each moment equal to the 

 total How of current across each section of the con- 

 ducting wire. 



Currents of electricity, therefore, including dis- 

 placement currents, always How in closed circuits, 

 and obey the laws of an incompressible fluid in 

 that the total flow across each section of the circuit 

 conducting or dielectric is at any moment the 

 same. 



It should be clearly remembered that this funda- 

 mental hypothesis of Maxwell's theory is an assump- 

 tion only to be justified by experiment. Von 

 Helmholtz, in his paper on "The Equations of 

 Motion of Electricity for Bodies at Rest/' formed 

 his equations in an entirely different manner from 

 Maxwell, and arrived at results of a more general 

 character, which do not require us to supjwisc that 

 currents flow always in closed circuits, but permit of 

 the condensation of electricity at points in the circuit 

 where the conductors end and the non-conducting 

 part of the circuit begins. We leave for the; present 

 the question which of the two theories, if either, 

 represents the facts. 



\Ve have obtained above three fundamental rela- 

 tions (i) that between electric force and electric 

 current in a conductor; (ii) that between electric 



