

Relations of Dielectric and Magnetic Polarization. 163 



very generally reproduced and it has subsequently been 

 further developed and extended by Oohn *, Gansf, Sanot, 

 and others. 



It seems therefore desirable to examine in closer detail the 

 criticism of Larmor, applying it to the more general case 

 when the law of induction is no longer linear or isotropic, 

 but with the view rather to emphasising the underlying 

 physical principles than of adding anything original to the 

 criticism itself. To aid in the examination a short account 

 of Maxwell's theory based on a correct interpretation of the 

 energy method is added, and it is thus hoped to establish on 

 a firmer footing the only consistent specification of the 

 problem which has so far been put forward. 



The discussion is confined entirely to the case of dielectric 

 media, and the methods and notations of the vectorial calculus 

 will be employed throughout. 



2. According to the theory of Maxwell as elaborated and 

 extended in the theory of electrons, a body polarized to 

 intensity P in a field of force of intensity E requires on 

 account of the polarization induced in it an amount of 

 energy per unit volume at any place expressed by 



-(PE), 



which together with the energy of the free charges makes 

 up a total equivalent to a distribution throughout the whole 



field of density ^— E 2 at each place. 



This energy does not, however, arise as a result simply of 

 the action of mechanical forces applied to the media as a 

 whole, and is not therefore compensated by a reduction of 

 the available mechanical energy associated with these forces ; 

 for part of it has arisen from the store of internal elastic or 

 thermal energy in the medium, which may for the purposes 

 of the present argument be regarded as of effectively non- 

 electric nature. The separation of these two fundamentally 

 different parts is effected by the usual method, which consists 

 in imparting a small virtual variation to the general con- 

 figuration, both geometrical and electrical, of the medium 

 and calculating the work in each part separately. In this 

 way it is easily seen that the part 



W m P(PtfE) 



of the total electric energy per unit volume is associated 



* L. c. p. 512. f Ann. Phys. xiii. p. 631. 



X Phys. Zeitschr. iii. p. 401 (1902). See also the articles by Pockels 

 and Gans in the Encyclopadie der mathematischen Wissenschaften, Bd. v. 



M2 



