DIELECTRIC PROPERTIES OF INSULATING MATERIALS 645 



but we can then increase the size of the cubes until p is the same for 

 each cube to a close enough approximation. The polarization in each 

 cube is then representative of that of the dielectric as a whole, ^ and by 

 dividing X! ^i Si for a typical cube by the volume of the cube we obtain 

 the polarization per unit volume, which for the present will be designated 

 as P. This quantity is a statistical mean value involving a summation 

 over a large number of particles; its value depends not only on the 

 structure of the material but upon the effect of thermal motions on the 

 mean positions and orientations of the molecules or other elementary 

 particles in the material. One of the most interesting points in dielec- 

 tric theory is the consideration — pointed out by Debye and at the 

 basis of his theory of polar molecules — that for some types of structure 

 the mean positions of the particles from which P is calculated are 

 unaffected by changes in the amplitude of thermal motions while for 

 another type of structure (consisting of polar molecules free to assume 

 many or at least several orientations) an increase of temperature de- 

 creases P, because the randomness of the orientations of the polar 

 molecules is increased. 



For many materials P is zero when no electric field is applied, and 

 assumes a finite value only when an electric field is applied, though as 

 has been indicated, some crystalline materials have a finite value of P 

 even in the absence of an applied electric field. In either case, how- 

 ever, the application of an electric field causes the bound charges 

 within the dielectric to be shifted in general to new equilibrium posi- 

 tions, corresponding to the slight change in the system of forces acting 

 upon them, and if the material did not have a polarization before the 

 application of the field, it assumes one; if it did, it assumes a different 

 value of P. The value of P when an electric field E is applied will be 

 designated as Pe, and that when no field is applied by Pq. Then 

 Pe — Po is the polarization per unit volume induced by an applied 

 field £. As the dielectric constant of a material depends upon the 

 magnitude of the polarization induced in it by an applied field, and we 

 are concerned here with dielectric constants, it will be desirable to 

 simplify the notation by setting Pe — Po = P- This gives P a 

 slightly different meaning than it had in the earlier part of the dis- 

 cussion, where it represented the total polarization per unit volume 

 whatever its origin. 



2 A detailed consideration of the method of dividing a dielectric up into ele- 

 mentary volumes in order to compute the mean polarization encounters complications 

 which need not be discussed here. A critical analysis of the method of computing 

 the volume density of polarization of a dielectric is given by Mason and Weaver, 

 "The Electromagnetic Field," Chicago (1929); Chapter III. 



