134 Dielectrics and Inductive Capacity [CH. v 



direction of the field relatively to the axes of the crystal. We shall find that 

 the conception of molecular action accounts for these peculiarities of crystalline 

 dielectrics. 



As in 146, we may regard the field near any point as the superposition 

 of two fields : 



(i) the field which arises from the doublets on the neighbouring 

 molecules, say a field of components of intensity X l , F 1} Z^\ 



(ii) the field caused by the doublets arising from the distant molecules 

 and from the charges outside the dielectric, say a field of components of 

 intensity Z 2 , F 2 , Z z . 



The intensity of the whole field is given by 



X = X l +X 2 , etc. 



To discuss the first part of the field, let us regard the whole field as 

 the superposition of three fields, having respectively components (X, 0, 0), 

 (0, F, 0) and (0, 0, Z). If the molecules are spherical, or if, not being 

 spherical, their orientations in space are distributed at random, then clearly 

 the field of components (X, 0, 0) will induce doublets which will produce 

 simply a field of components (K'X, 0, 0) where K' is a constant. But if the 

 molecules are neither spherical in shape nor arranged at random as regards 

 their orientations in space, it will be necessary to assume that the induced 

 doublets give rise to a field of components 



K n X, K 12 A, K. 13 A. 



On superposing the doublets induced by the three fields (X, 0, 0), 

 (0, F, 0) and (0, 0, Z), we obtain 



(76). 



Thus we have relations of the form 



r ~\r __ TT" 7 x 

 L 21 * ~r * 31 ^ \ 



...(77), 



.F+^33- 



expressing the relations between polarisation and intensity. 



These are the general equations for crystalline media. If the medium 

 is non-crystalline, so that the phenomena exhibited by it are the same for all 

 directions in space, then the two vectors, the intensity and the polarisation, 



