390 ELECTROSTATICS AND MAGNETISM. [PT. II. CH. IX. 



persists. A substance in which, when the external field is removed, 

 the whole induced polarization remains, is called perfectly hard, 

 and a body consisting of such substance is called a permanent 

 magnet. The inductivity of such a body is to be considered the 

 same as of air. Such bodies do not exist any more than perfectly 

 soft ones. We may however treat actual bodies as if they were 

 formed by the superposition of perfectly hard and perfectly soft 

 matter. The portion of the polarization which permanently 

 remains is called the intrinsic polarization*. In order to carry out 

 the analogy, Heaviside has proposed to call a dielectric per- 

 manently polarized body an electret, and its polarization electriza- 

 tion. Certain natural crystals when heated assume this condition. 

 The permanent or intrinsic polarization now forms a real 

 magnetic or electric charge, and if the intrinsic polarization be 

 denoted by / with components A Q , B , C 0> we have for the real 

 density 



dx dy dz 

 with a similar expression for a. 



Comparing this with the expression for p in 182 (15), we find 



,, 



47r \dx ty dz) ( dx dy dz 

 or the divergence of the induction is equal to 4?r times the 

 convergence of the intrinsic polarization. Comparing the expressions 

 for the apparent density, that is the sum of the real and induced, 

 in terms of the force F, 186 (33), and in terms of the total 

 polarization /, 120 (6), we find 



,_3Z dY dZ 

 p - 

 Accordingly 



(5) l(Z4 



or more briefly, 



(5) div(F+47r/)=0. 



The solenoidal vector-sum, F+^TT!, has been called in 121, 

 the induction. We shall call it the Maxwellian induction, and 

 denote it by $ M , since it corresponds to the definition of the 



* Thomson. Reprint of Papers on Electrostatics and Magnetism, p. 578. 



