FUNDAMENTAL FORMULATIONS OF ELECTRODYNAMICS. 211 



expression for the rate of change of the magnetic force vector at any point of the 

 tield. The first of these has the usual form 



wherein C, is the density of the true conduction current, v m is the velocity of the material 

 medium at the typical field point, and 



D = ^- 



47T 



is the total dielectric displacement of MAXWELL'S theory which consists in part of the 

 dielectric polarisation P and in part of an sethereal constituent proportional to the 

 electric force. 



The time rate of change of the composite vector D requires careful specification ; it 

 consists in the main of the terms 



dP 



in dt dt ' 



but when the dielectric media are in motion there is in addition a term arising on 

 account of the convection of the polarisation. This term has been shown* to be 

 equal to 



Curl [Pa 

 so that 



dD 1 dE , dP , n , i-p -, 



r- = - -j- + i \- Curl rv m \. 

 dt 47T dt dt 



The equation expressing the rate of change of the magnetic force is analogously 



dH. cB dl. ^ , rr -i 

 -^- = -; -- 4ir -- 4 TT L/url Lv m \. 

 dt dt dt 



This latter equation must be specially emphasised as it has apparently never yet 

 been explicitly introduced in the theory, although it is necessary to secure greater 



consistency in the dynamical theory. The expression represents the rate of change 



etc 



of the magnetic polarisation at a fixed point in the field only when the magnetic 

 media as a whole are at rest. When these media are in motion there will be a 

 contribution to this rate due to convection just as in the electric case, and the 

 argument for its exact form may be developed on the same lines. The vectors B and 

 H are, so to speak, attached to the aether, just as were the vectors D and E,t whilst 



* Gf. my ' Theory of Electricity,' pp. 365-367, or LARMOR, ' ^Ether and Matter,' Chap. IV. 



t The vector H being the composite vector of the magnetic theory is analogous to the vector D of the 

 electric theory ; the aethereal vector B is analogous to the aethereal vector E. This is the reverse of the 

 usual convention, but see below 10. 



