1893.] the Electric and Luminiferous Medium. 447 



the interface, but demands that the amount of this discontinuity shall 

 be the same all along the interface ; these are precisely the circum- 

 stances of the observed phenomena of voltaic potential differences. 

 The component, normal to the interface, of the electric displacement 

 is of course always continuous, from the nature of that vector as a 

 flux. 



It may present itself as a difficulty in this theory that, as the elec- 

 tric displacement is the rotational displacement of the medium, its 

 surface integral over any sheet should be equal to the line integral 

 of the linear displacement of the medium round the edge of the 

 sheet; therefore that for a closed sheet surrounding a conductor this 

 integral should be null, which would involve the consequence that the 

 electric charge on a conductor cannot be different from null. This 

 line of argument, however, implies that the linear displacement is a 

 perfectly continuous one, which is concomitant with and required by 

 the electric displacement. The legitimate inference is that the 

 electric displacement in the medium which corresponds to an actual 

 charge cannot be set up without some 'kind of discontinuity or slip in 

 the linear displacement of the medium ; in other words, that a con- 

 ductor cannot receive an electric charge without rupture of the 

 surrounding medium ; nor can it lose a charge once received without 

 a similar rupture. The part of the linear displacement that remains, 

 after this slip or rupture has been deducted from it, is of elastic 

 origin, and must satisfy the equations of equilibrium of the medium. 

 December 7, 1893.] 



We can produce in imagination a steady electric current, without 

 introducing the complication of galvanic batteries, in the following 

 manner, and thus examine in detail all that is involved, on the present 

 theory, in the notion of a current. Suppose we have two charged 

 condensers, with one pair of coatings connected by a narrow conduct- 

 ing channel, and the other pair connected by another such channel, 

 as in the annexed diagram, where the dark regions are dielectric and 

 the white regions conducting. If we steadily move towards each 

 other the two plates of the condenser A, a current will flow round the 

 circuit, in the form of a conduction current in the conductors and a 

 displacement current across the dielectric plates of the condensers. 

 Let us suppose the thicknesses of these dielectric plates to be exces- 

 sively small, so as to minimise the importance of the displacement 

 part of the current. There is then practically no electric force, and 

 therefore no electric displacement, in the surrounding dielectric field, 

 except between the plates of the condensers and close to the conduct- 

 ing wires. Consider a closed surface passing between the faces of 

 the condenser A, and intersecting the wire at a place P. A movement 

 of the faces of this condenser alters the electric force between them, 

 and therefore alters the electric displacement across the portion of 



VOL. LIV. 2 i 



