210 ME. G. H. LIVENS ON THE 



In the dynamical theory, however, this vector B appears as the complete aethereal 

 magnetic force,* the part H being merely the mechanically effective part of this 

 force in the material media. This new conception of the magnetic force, which is 

 supported by such phenomena as the Hall effect, &c., where the deviations in ferro- 

 magnetic media are proportional to the induction,! is not really inconsistent with the 

 previous definition given under (c) above. As there explained, although the vector H 

 is defined as the force on unit magnetic pole, there is still the possibility that there 

 may exist in addition a force (iirl) not directly detectable in a mechanical 

 experiment. 



(e) In addition to these fundamental field vectors there are certain others of a 

 subsidiary nature determining the electric and magnetic conditions in the media. One 

 of these, the magnetic polarisation intensity I, has already been introduced, and there 

 is an electric analogue in P, the dielectric polarisation intensity ; these two vectors 

 define respectively the effective resultant magnetic and electric bi-polar moments per 

 unit volume of the media. 



3. MAXWELL'S theory may now be expressed in the statement that in the most 

 general case of interaction between the magnetic and electric fields the four 

 fundamental vectors defining these fields are subject to the two differential vector 

 equations 



CurlE= -~, 

 c at 



together with the scalar relation defining the electric charge density p 



div E = 47T/J. 



The second vectorial equation practically implies that 



div B = 0, 



so that it is hardly necessary to add this as an additional equation. 



For the further development of the theory air that is now necessary} is the 

 kinematical specification of the current C in terms of the material vectors and an 



* 



" This was first clearly recognised by LARMOR. Of. his papers "On a Dynamical Theory of the 

 Electric and Luminiferous Medium," 'Phil. Trans.,' 1894-1897, or < ^Ether and Matter' (Cambridge, 

 1900). 



t The results are interpreted usually as implying that the deviations are proportional to the polarisation 

 intensity in such cases, but this is equivalent to the statement given. 



J We are not here concerned with the constitutional equations giving the laws of induction and 

 conduction. These form a separate branch of the subject, whose results are irrelevant to the present 

 discussion. 



