Maxwell 9 8 Electro-magnetic Theory of Light. 



381 



Propagation of Electrical Disturbances. 



6. Only a very slight modification of Maxwell's equations appears 

 to be necessary in order to determine the law governing the pro- 

 pagation of electrical disturbances in a polarized medium such as 

 that previously considered. 



Let P, Q, R be the components of the electromotive intensity at a 

 point, F, Gr, H being the components of the vector potential there. 

 The electromotive intensity due to the displacement of the atoms 

 may, if the velocity of the atoms is small compared with the velocity 

 of light, be derived from a potential y^. 



Hence 



P= 77 - 



at 



_ 

 dt dy 



dt d>< 



Here it must be remembered that ^ will be a function of t. 

 We may define the vector potential so that 



(5). 



In that case 



dF dG dR 



T~ ~**~~T +^T~ = 0. 

 ax ay dz 



<__ 



dx ^d T <fa 



(6), 



since any element of volume, if taken so as to comprise a sufficient 

 number of molecules, will contain as many positively charged as 

 negatively charged atoms. 



Let a, 6, c represent the components of magnetic induction. 

 Then 



_^H__^G 

 a ~ dy dz ' 



with similar equations for b and c. 

 Hence, from (5), 



da __ dQ_dR^\ 

 dt ~ dz Ty | 



^____ 



dt ~~ dx ds 



dc 

 dt 



dy 



