122 Dielectrics and Inductive Capacity [CH. v 



Also, if there is no charge on the boundary, the aggregate strength of 

 the tubes which meet the boundary in any small area on this boundary is 

 the same whether estimated in the one dielectric or the other, for the tubes 

 do not alter their strength in crossing the boundary, and none can begin or 

 end in the boundary. Thus the normal component of the polarisation is 

 continuous. 



136. If J^! is the intensity in the first medium of inductive capacity K^> 

 measured at a point close to the boundary, and if e : is the angle which the 

 lines of force make with the normal to the boundary at this point, then the 

 normal polarisation in the first medium is 



- JR l cos 6j . 

 Similarly, that in the second medium is 



x! 2 7 -, 



R 2 COS 2 , 



so that KiRi cos e : = K 2 R 2 cos e 2 ........................ (68). 



Since, in the notation already used, 



jRi cos e x = N-L = -^ , 



the equation just obtained may be put in either of the forms 



K.N^K.N, .............................. (69), 



K = K .............................. (70). 



In these equations, it is a matter of indifference whether the normal is 

 drawn from the first medium to the second or in the reverse direction ; it is 

 only necessary that the same normal should be taken on both sides of the 

 equation. Relation (70) is obtained at once on applying the generalised 

 form of Gauss' theorem to a small cylinder having parallel ends at infinitesimal 

 distance apart, one in each medium. 



137. To sum up, we have found that in passing from one dielectric to 

 another, the surface of separation being uncharged: 



(i) the tangential components of intensity have the same values on the 

 two sides of the boundary, 



(ii) the normal components of polarisation have the same values. 

 Or, in terms of the potential, 

 (i) V is continuous, 



(ii) K -x- is continuous. 



on 



