( 730 ) 



§ 3. Tlie last equation of (4) shows, that there is no dielectric 

 displacement in the ::'-direction. Further it is evident from these 



equations, that S"!- has no share in the disturbance of the state of the 



aether at a distant point. Indeed, ^l' and S'y being zero, the equations 

 are satisfied by the solution 



At the distant point (T"!' is zero, therefore S-' is so likewise. Electro- 

 motive forces acting within a layer bounded by two parallel planes 

 and directed perpendicularly to these planes, do not therefore 

 produce any disturbance of equilibrium at a distant point. 



We eliminate S-- between the first and the third and between the 

 second and the third equation. 



This gives 



i>^=-?T- [(:■' - t;:) ''" +'''■'+ 1'" - ^j •'-■ + ^-'■)J 



Accoi'ding to what has already been said, these equations, if no 

 E. M. F. are acting, must have one solution in which €v is zero, 

 and another in which ^,y vanishes. This would follow from the 

 equations themselves, if we knew the above mentioned properties 

 of the quantities &, occurring in them. Conversely, we shall be able 

 to deduce these properties from the knowledge that the two solutions 

 must satisfy the equations. Indeed these solutions can only hold if 



^ = - ^. [(-—■)<-'"+ ^■'■' + (•■■- a <*'■ + ^'■>] • 



and 2 



where Fi» and V,/ are the velocities of the plane waves in the two 

 cases. By this the equations take the form 



-^= (€.' + e), -^= (e,'+ev) . (5) 



whereas the ^third equation of (4) gives €-' when 'S^' and (T^- are 

 known. We see from (5) that S^' depends only on @,f', and (5^' only 

 on fSy, further that both equations have the same form. We can 



