245 _ 247] EQUATIONS OF ELECTROMAGNETIC FIELD. 511 



We shall in the future, as we have done in the past, consider only 

 isotropic bodies. 



247. Consequences of the Equations of the Field. 

 Propagation. If we differentiate the equations (A) respec- 

 tively by x, y, z and add, we obtain 



the consequences of which we have discussed in Chapter X. If the 

 medium is an insulator, the relaxation- time is infinite, and 



8? + 9 + 83 



dx dy dz 

 is independent of the time. 



Applying the same process to the equations (B), we obtain 



dx dy dz 



independent of the time, and the value of this divergence is zero, 

 except in intrinsic magnets ( 201). 



We shall now deduce the more important consequences of the 

 equations, proceeding from the simpler to the more complicated 

 cases. We shall first, therefore, consider the phenomena in insu- 

 lators, in which the equations (A) and (B) are exactly symmetrical. 

 On account of the dual nature of the relations of the two fields it 

 follows at once that every effect of electrodynamic induction in 

 producing electromotive forces has an analogous effect in the pro- 

 duction of magnetomotive forces by electric displacement currents. 

 For instance a closed iron ring placed in an electrostatic field 

 varying with the time would become magnetized. Effects of this 

 sort have not yet been observed, on account of the extreme small- 

 ness of the factor A, by which the displacement current is multi- 

 plied. For the same reason, electrostatic forces produced in 

 insulators by the variation of magnetic fields have not been 

 successfully observed, although the attempt has been made by 

 Lodge*. The justification of the equations (A) has been given 

 by other results. 



* Lodge. " On an Electrostatic Field produced by varying Magnetic Induction. " 

 Phil. Mag. (5) 27, p. 469, 1889. 



