116 Dielectrics and Inductive Capacity [CH. v 



It is, however, obvious that if we were to calculate the intensity in the 

 second condenser from this law, then the value obtained would be K times 



V V 



that in the first condenser, and would therefore be K - { 1 . In point of 



d 



V V 



fact, the actual value of the intensity is known to be - ^ - . 



CL 



Thus Faraday's discovery shews that Coulomb's law of force is not of 

 universal validity : the law has only been proved experimentally for air, and 

 it is now found not to be true for dielectrics of which the inductive capacity 

 is different from unity. 



This discovery has far-reaching effects on the development of the mathe- 

 matical theory of electricity. In the present book, Coulomb's law was 

 introduced in 38, and formed the basis of all subsequent investigations. 

 Thus every theorem which has been proved in the present book from 38 

 onwards requires reconsideration. 



126. We shall follow Faraday in treating the whole subject from the 

 point of view of lines of force. The conceptions of potential, of intensity, and 

 of lines of force are entirely independent of Coulomb's law, and in the present 

 book have been discussed ( 30 37) before the law was introduced. The 

 conception of a tube of force follows at once from that of a line of force, 

 on imagining lines of force drawn through the different points on a small 

 closed curve. Let us extend to dielectrics one form of the definition of the 

 strength of a tube of force which has already been used for a tube in air, and 

 agree that the strength of a tube is to be measured by the charge enclosed 

 by its positive end, whether in air or dielectric. 



In the dielectric condenser, the surface density on the positive plate is 



V V 

 K \ j an d this, by definition, is also the aggregate strength of the 



tubes per unit area of cross-section. The intensity in the dielectric is 



V V 

 l j -, so that in the dielectric the intensity is no longer, as in air, equal 



to 4?r times the aggregate strength of tubes per unit area, but is equal to 

 4<7r/K times this amount. 



Thus if P is the aggregate strength of the tubes per unit area of cross- 

 section, the intensity R is related to P by the equation 



= f P ................................. (59) 



in the dielectric, instead of by the equation 



................................. (60) 



which was found to hold in air. 



