Relations of the Magnetic Field. 677 



such phenomena as the Hall effect or the various magneto- 

 optical .effects turn out to he always proportional nut to the 

 magnetic force but to the induction (or polarization, the two 

 are practically the same in such cases), we have concluded 

 that the behaviour of such media in this connexion is 

 anomalous when, as a matter of fact, it is perfectly regular 

 and provides one of the most powerful arguments in favour 

 of our present contention. 



Finally, we may notice the way in which the present 

 permeability coefficient /i enters into the fundamental 

 equation for wave propagation in the electromagnetic field. 

 The fundamental equations in such cases are : 



1 dB , x, 1 dB , „ 



j- = curl h, rr = curl .□ , 



c dt c dt 



wliere - H = ^B, D = eE. 



These lead in the usual way to the wave equation 



V 9 = — 2 -t£, 

 yjr at 



which is satisfied by each component of the two vectors 

 defining the field. The velocity of propagation is now 



s/l 



so that the magnetic permeability acts counter to the 

 dielectric capacity, an increase in the one being negatived 

 by a corresponding increase in the other. But we must 

 remember that the larger values of //, correspond to free 

 space or diamagnetic media and that a " strongly inao-_ 

 netic" medium in the ordinary sense has a small permeability 

 coefficient according to the present definition — or in other 

 words, in strongly magnetic media the mechanical effective- 

 ness of the complete force (the induction) is practically 

 destroyed by the induced polarization which produces a 

 counterbalancing local forcive. 



The University, Manchester, 

 Jan. 20th*, 1920. 



