A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 563 



where a, /8, y are the components of magnetic intensity or the force on a unit 

 magnetic pole, and p,a, p./3, p.y are the components of the quantity of magnetic 

 induction, or the number of lines of force in unit of area. 



In isotropic media the value of /a is the same in all directions, and we 

 may express the result more simply by saying that the intrinsic energy of any 

 part of the magnetic field arising from its magnetization is 



f-r 



Sir 

 per unit of volume, where / is the magnetic intensity. 



(72) Energy may be stored up in the field in a different way, namely, 

 by the action of electromotive force in producing electric displacement. The 

 work done by a variable electromotive force, P, in producing a variable dis- 

 placement, f, is got by integrating 



from P = to the given value of P. 



Since P = kf, equation (E), this quantity becomes 



Hence the intrinsic energy of any part of the field, as existing in the 

 form of electric displacement, is 



The total energy existing in the field is therefore 



W- 



The first term of this expression depends on the magnetization of the field, 

 and is explained on our theory by actual motion of some kind. The second 

 term depends on the electric polarization of the field, and is explained on our 

 theory by strain of some kind in an elastic medium. 



(73) I have on a former occasion * attempted to describe a particular kind 

 of motion and a particular kind of strain, so arranged as to account for the 

 phenomena. In the present paper I avoid any hypothesis of this kind ; and in 



* "On Physical Lines of Force," Philosophical Magazine, 186162. (In this vol. p. 451.) 



712 



