200, 201] DIELECTRICS AND MAGNETIZABLE BODIES. 389 



In like manner 



CK Tjl ^V 



F n = - Q cos (ny), w = - cos (nz). 



O7T O7T 



Here again the components of F n are equal to gF/8-Tr 

 multiplied by the direction cosines of n, or the force is normal to 

 its plane. Consequently any plane tangent to a line of force is a 

 principal plane of the stress, and the stress is symmetrical about 

 the line of force. The negative sign shows that the stress is a 

 pressure. The state of stress consisting of tension along the lines 

 of force combined with an equal pressure at right angles to them 

 was described by Faraday*, who expressed the matter in words that 

 state in effect that the lines of force tend to contract and to repel 

 each other. 



This may be illustrated by supposing the medium to be divided 

 into filaments along the lines of force, and 

 these again to be subdivided into short 

 filaments. Then each short filament is a I 4 'II* "*ll* '|E^3 



polarized body which acts like a doublet, and h 1 1. 1r^^ 



I* *ll* 'II* 'II* 'I 

 since unlike poles of successive elements are 



in juxtaposition, the filaments all attract each 



other endwise. For filaments lying side by side, however, since 



like poles are together, there is a sidewise repulsion. 



201. Permanent Magnets and Electrets. Intrinsic 

 Polarization. The fundamental laws of magnetic and electric 

 induction may be summed up in the statement that in soft iron 

 and in similarly acting bodies the force is lamellar, and //, times 

 the force is solenoidal. Or in brief 



(i) curl.F=0, 



(i') div(/^) = 0. 



Iron for which this statement is true is said to be perfectly 

 soft. When the external field affecting such iron is removed, the 

 polarization disappears. As a matter of fact, this is an ideal 

 condition not exactly realized by any sort of real iron, for when 

 the external field is removed, a part of the polarization persists. 

 This is called residual magnetization. The harder the iron or 

 steel, the greater is the fraction of the induced polarization which 



* Faraday, Exp. Res. (1297). 



