358 ELECTROSTATICS AND MAGNETISM. [FT. II. CH. IX. 



electric case, /JL does not differ widely for different media, seldom 

 reaching ten times the value for air or empty space, and never 

 being less than for empty space, while in the magnetic case, /A 

 may be, for iron, several thousand times as great as for air, and in 

 some cases is slightly less than for air. Consequently lines of 

 force emerging from iron into air are generally nearly normal to 

 the surface in the air unless very nearly tangential in the iron. 

 This is exemplified in Fig. 7 la, showing the distribution of lines 

 of force between the pole-pieces of the field magnet of a dynamo 

 with the armature removed. In virtue of the analogy to electric 

 conductivity, it is evident that the lines of force exhibit a tendency 

 to crowd together into parts of the field where p is large. 



182. Relation of Charge to Induction. Since the force 

 no longer possesses the solenoidal property, except in homogeneous 

 media, while the induction does, it is more logical to speak of 

 tubes of induction than of tubes of force, although geometrically 

 the two coincide. The flux of force through various cross-sections 

 of a tube, however, varies, while the flux of induction is constant 

 for the tube. 



The volume density is no longer determined by the divergence 

 of the force, but of the induction, being equal to 1/4-Tr times the 

 divergence of the induction, 180 (8), 





dz 



while the surface density is l/4?r times the discontinuity of its 

 normal component, 180 (9), 



(16) <T = ^{8, +.} 



Accordingly the charge of any portion of space T, 



(17) -JII.*- 



JJj f 4> 



= _ JL jj { cos (nx) + g) cos (ny) + 3 cos (nz)} dS, 



is equal to l/4?r times the excess of the number of unit tubes 

 issuing from the space over the number entering. We shall call 

 the densities thus defined, for a reason to be presently explained, 

 the densities of true electricity or magnetism. 



