MAXWELL'S THEORY OF DISPLACEMENT. 109 



outside towards the inside; the duration of the current is equal to 

 that of the Variation. 



The displacement through any surface is the quantity of electricity 

 which traverses it. Let o-^S be this quantity ; for an element */S of the 



R/S 



surface of a conductor the displacement is equal to , it is there- 



4?r 



fore equal to the corresponding flow of force divided by 477-. In 

 contact with a dielectric the quantity of electricity has the value 



- ; the displacement is accordingly equal to the quotient of the 

 4 71 " 

 flow of induction by 477-. 



Generally, the displacement ', at any point of a dielectric, is equal to 

 the quotient of the induction by 477-, and is parallel to this force. 



A conductor opposes no obstacle to displacement. In a dielec- 

 tric the displacement is restricted by the action of antagonistic forces 

 which the displacement itself develops in other words, by a kind 

 of elasticity, which may be called the electrical elasticity of the 

 medium. If, by analogy, we denote the ratio of the force to the 

 displacement which it produces, by the term coefficient of -electrical 

 elasticity, and suppose the medium to be perfectly elastic, it will be 



seen that the coefficient of electricity is equal to , and that 



therefore the specific inductive capacity is inversely proportional to 

 the coefficient of elasticity of the medium. 



The displacement produced by induction across the entire mass 

 of the dielectric determines the polarization of the medium and the 

 apparent electrification of the conductors. 



Consider a tube of induction between two conductors. Through- 

 out the whole extent of the tube the displacement is constant ; every 

 orthogonal section is traversed by the same quantity of electricity. 

 At one end, the displacement is from the conductor towards the 

 dielectric, the corresponding element ^/S of the conductor is then 

 said to be charged with positive electricity of density a- at the other 

 end the displacement is from the dielectric towards the conductor, 

 and the corresponding element dS is charged with a density a-'. 

 Throughout the whole extent of the tube, if the dielectric is 

 the same, there is no apparent electricity; but this medium is 

 polarized ; for, conceive for a moment a portion of a tube comprised 

 between two orthogonal sections : the displacement has taken place in 

 the contrary direction for the two sections, and they would appear 

 oppositely electrified if their electrification were not neutralised by 

 the equal and opposite electrification of the portions of the tube in 



