171-174] Maxwell's Displacement Theory 153 



If the element of volume is taken in a dielectric of inductive capacity K, 



Kit? K 



the energy is - , so that c = , and the displacement is 



KR 



47T ' 



173. It is now evident that Maxwell's "displacement" is identical in 

 magnitude and direction with Faraday's "polarisation" introduced in 

 Chap. V. 



Denoting either quantity by P, we had the relation 



(93), 



expressing that the normal component of P integrated over any closed 

 surface is equal to the total charge inside. On Maxwell's interpretation of 



the quantity P, the surface integral 1 1 PcosedS simply measures the total 



quantity of electricity which has crossed the surface from inside to outside. 

 Thus equation (93) expresses that the total outward displacement across any 

 closed surface is equal to the total charge inside. 



It follows that if a new conductor with a charge e is introduced at any 

 point in space, then a quantity of electricity equal to e flows outwards across 

 every surface surrounding the point. In other words, the total quantity of 

 electricity inside the surface remains unaltered. This total quantity consists 

 of two kinds of electricity (i) the kind of electricity which appears as a 

 charge on an electrified body, and (ii) the kind which Maxwell imagines to 

 occupy the whole of space, and to undergo displacement under the action of 

 electric forces. On introducing a new positively charged conductor into any 

 space, the total amount of electricity of the first kind inside the space is 

 increased, but that of the second kind experiences an exactly equal decrease, 

 so that the total of the two kinds is left unaltered. 



174. This result at once suggests the analogy between electricity and 

 an incompressible fluid. We can picture the motion of electric charges 

 through free ether as causing a displacement of the electricity in the ether, 

 in just the same way as the motion of solid bodies through an incompressible 

 liquid would cause a displacement of the liquid. 



REFERENCES. 



On the stresses in the medium : 



FARADAY. Experimental Researches, 1215 1231. 

 On Maxwell's displacement theory : 



MAXWELL. Electricity and Magnetism, 5962. 



