286 Maxwell. 



from which equation it is evident that ^ represents the electro- 

 static potential. 



The principle which is peculiar to Maxwell's theory must 

 now be introduced. Currents of conduction are not the only 

 kind of currents ; even in the older theory of Faraday, Thomson, 

 and Mossotti, it had been assumed that electric charges 

 are set in motion in the particles of a dielectric when the 

 dielectric is subjected to an electric field ; and the prede- 

 cessors of Maxwell would not have refused to admit that the 

 motion of these charges is in some sense a current. Suppose, 

 then, that S denotes the total current which is capable of 

 generating a magnetic field : since the integral of the magnetic 

 force round any curve is proportional to the electric current 

 which flows through the gap enclosed by the curve, we have in 

 suitable units 



curl H = 4;rS. 



In order to determine S, we may consider the case of a con- 

 denser whose coatings are supplied with electricity by a 

 conduction-current i per unit-area of coating. If o- denote 

 the surface-density of electric charge on the coatings, we have 



i = d(r/dt t and o- = D, 



where D denotes the magnitude of the electric displacement D 

 in the dielectric between the coatings ; so i = D. But since the 

 total current is to be circuital, its value in the dielectric must 

 be the same as the value i which it has in the rest of the 

 circuit ; that is, the current in the dielectric has the value D. 

 We shall assume that the current in dielectrics always has this 

 value, so that in the general equations the total current must 

 be understood to be i + D. 



The above equations, together with those which express the 

 proportionality of E to D in insulators, and to i in conductors, 

 constituted Maxwell's system for a field formed by isotropic 

 bodies which are not in motion. When the magnetic field is 

 .due entirely to currents (including both conduction-currents 



