172 Mr Larmor, On a mechanical representation of a [May 4, 



in a conductor, they are of the type 



_^_V 2 ^ = — + — . 



47T/A dt dx 



In the former case we derive at once 



at 



which merely expresses the fact that there can be no accumulation 

 of volume density in the dielectric, on account of the assumed non- 

 condensational character of the phenomena. 

 In the latter case also 



V 2 F=0. 



Thus, when the dielectric has no initial charge, the charge is 

 throughout confined to the interfaces separating media of different 

 quality, such as the surfaces of conductors. 



It will form a sufficiently general case for our purpose if we 

 consider the reflexion of a train of plane polarised waves at a plane 

 metallic surface. The axis of z may be taken normal to the sur- 

 face and the axis of x along it in train with the waves. If the 

 vibration of the vector potential is in the plane of incidence, we 

 have 



dF dH A _ n 



ax dz 



so that the variables are reduced to dependence on a single 

 function % by the substitution 



dz ' dx 



The important case is when everything is periodic, and so 

 involves the factor exp (— ipt). We have then 



tp ax ip dz 



and % is determined by the equations 



1 TK.,**! 



in the dielectric, and 



in the conductor. 



^K^ X df 



4>1Tfl A dt 



