125-128] Experimental Basis 117 



127. Equation (59) has been proved to be the appropriate generalisation 

 of equation (60) only in a very special case. Faraday, however, believed the 

 relation expressed by equation (59) to be universally true, and the results 

 obtained on this supposition are found to be in complete agreement with 

 experiment. Hence equation (59), or some equation of the same significance, 

 is universally taken as the basis of the mathematical theory of dielectrics. 

 We accordingly proceed by assuming the universal truth of equation (59), 

 an assumption for which a justification will be found when we come to study 

 the molecular constitution of dielectrics. 



It is convenient to have a single word to express the aggregate strength 

 of tubes per unit area of cross-section, the quantity which has been denoted 

 by P. We shall speak of this quantity as the " polarisation," a term due to 

 Faraday. Maxwell's explanation of the meaning of the term " polarisation " 

 is that " an elementary portion of a body may be said to be polarised when 

 it acquires equal and opposite properties on two opposite sides." Faraday 

 explained the properties of dielectrics by means of his conception that the 

 molecules of the dielectric were in a polarised state, and the quantity P 

 is found to measure the amount of the polarisation at any point in the 

 dielectric. We shall come to this physical interpretation of the quantity P 

 at a later stage : for the present we simply use the term " polarisation " as 

 a name for the mathematical quantity P. 



This same quantity is called the " displacement " by Maxwell, and under- 

 lying the use of this term also, there is a physical interpretation which we 

 shall come upon later. 



128. We now have as the basis of our mathematical theory the 

 following : 



DEFINITION. The strength of a tube of force is defined to be the charge 

 enclosed by the positive end of the tube. 



DEFINITION. The polarisation at any point is defined to be the aggregate 

 strength of tubes of force per unit area of cross-section. 



EXPERIMENTAL LAW. The intensity at any point is ^ir\K times the 

 polarisation, where K is the inductive capacity of the dielectric at the point. 



In this last relation, we measure the intensity along a line of force, while 

 the polarisation is measured by considering the flux of tubes of force across 

 a small area perpendicular to the lines of force. Suppose, however, that we 

 take some direction 00' making an angle 6 with that of the lines of force. 

 The aggregate strength of the tubes of force which cross an area dS 

 perpendicular to 00' will be PcosOdS, for these tubes are exactly those 

 which cross an area dScosO perpendicular to the lines of force. Thus, 

 consistently with the definition of polarisation, we may say that the polari- 

 sation in the direction 00' is equal to P cos 0. Since the polarisation in 



