169-171] Maxwell's Displacement Theory 151 



From formulae (89) and (90), we must have 



= n 

 from which 



- [K n X + i (K K + K) Y + i (K 13 + K 3l ) Z\. 

 We must also have 



(W_(yWd dW dg dWdf^ 



dx ~ df dx + dg Sx + dh dx 



n 2l 



Comparing these expressions, we see that we must have 



J\-12 = K 2l , K j 3 = K 3l , Kos = KSZ . 



The energy per unit volume is now 



...) .................. (92). 



MAXWELL'S DISPLACEMENT THEORY. 



171. Maxwell attempted to construct a picture of the phenomena 

 occurring in the electric field by means of his conception of "electric dis- 

 placement." Electric intensity, according to Maxwell, acting in any medium 

 whether this medium be a conductor, an insulator, or free ether produces 

 a motion of electricity through the medium. It is clear that Maxwell's 

 conception of electricity, as here used, must be wider than that which we 

 have up to the present been using, for electricity, as we have so far under- 

 stood it, is incapable of moving through insulators or free ether. Maxwell's 

 motion of electricity in conductors is that with which we are already familiar. 

 As we have seen, the motion will continue so long as the electric intensity 

 continues to exist. According to Maxwell, there is also a motion in an 

 insulator or in free ether, but with the difference that the electricity cannot 

 travel indefinitely through these media, but is simply displaced a small 

 distance within the medium in the direction of the electric intensity, the 

 extent of the displacement in isotropic media being exactly proportional 

 to the intensity, and in the same direction. 



The conception will perhaps be understood more clearly on comparing a conductor to 

 a liquid and an insulator to an elastic solid. A small particle immersed in a liquid will 

 continue to move through the liquid so long as there is a force acting on it, but a particle 

 immersed in an elastic solid, will be merely " displaced " by a force acting on it. The 

 amount of this displacement will be proportional to the force acting, and when the force 

 is removed, the particle will return to its original position. 



