The Followers of Maxwell. 369 



as a rotation of conduction-currents under the influence of a 

 magnetic field ; and if it be assumed that displacement-currents 

 in dielectrics are rotated in the same way, the Faraday effect 

 may evidently be explained. Considering the matter from the 

 analytical point of view, the Hall effect may be represented by 

 the addition of a term k [K . S] to the electromotive force, 

 where K denotes the impressed magnetic force, and S denotes 

 the current : so Kowland assumed that in dielectrics there is an 

 additional term in the electric force, proportional to [K . D], i.e. 

 proportional to the rate of increase of [K . D]. Now it is 

 universally true that the total electric force round a circuit is 

 proportional to the rate of decrease of the total magnetic 

 induction through the circuit : so the total magnetic induction 

 through the circuit must contain a term proportional to the 

 integral of [K . D] taken round the circuit : and therefore the 

 magnetic induction at any point must contain a term proportional 

 to curl [K . D]. We may therefore write 



B = H + a curl [K . D], 



where <r denotes a constant. But if this be combined with the 

 customary electromagnetic equations 



curl H = 47rD, curl E = - B, D = eE/47rc 3 , 



and all the vectors except B be eliminated (K being treated 

 as a constant), we obtain the equation 



B - (c 7 /0 V 2 B + O/47r) curl 



where 3/80 stands for (K x d/fa + K y d/dy + K z d/dz) ; and this is 

 identical with the equation which Maxwell had given* for the 

 motion of the aether in magnetized media. It follows that the 

 assumptions of Maxwell and of Eowland, different though they 

 are physically, lead to the same analytical equations at any 

 rate so far as concerns propagation through a homogeneous 

 medium. 



The connexions of Hall's phenomenon with the magnetic 

 rotation of light, and with the reflexion of light from magnetized 



* Cf. p. 308. 



2 B 



