Extension of Maxwell? & Electro-magnetic Theory of T^iglit. 91 



<% An Extension of Maxwell's Electro-magnetic Theory of 

 Light to include Dispersion, Metallic Reflection, and Allied 

 Phenomena," By EDWIN EDSER, A.R.C.S. Communicated 

 by Captain W. *DE W. ABNEY, C.B., F.E.S. Received 

 February 18, Read March 10, 1898. 



(Abstract.) 



A dielectric, like an electrolyte, is assumed to consist of molecules, 

 each comprising, in the simplest case, two oppositely charged atoms 

 at a definite distance apart. In a homogeneous medium, when not 

 subjected to electric strain, these molecules will be arranged in such 

 a manner that any elerrfent of volume will possess no resultant 

 electric moment. If a definite potential difference be maintained 

 between any two parallel planes in the medium, the positively 

 charged atoms will move to points of lower, and the negatively 

 charged atoms to points of higher, potential. Thus two kinds of 

 molecular strain are produced: firstly, a molecular rotation; and 

 secondly, a separation in the molecule of the constituent atoms. 

 Let P be the actual electromotive intensity at any point in the 

 medium, and D be the electric displacement other than that pro- 

 duced by the atomic charges. Then 



where M is a constant depending on the nature of the medium. The 

 quantity ] +4?rM represents the specific inductive capacity of the 

 medium. The actual linear displacement of the atoms is shown to be 

 small when compared with molecular magnitudes. 



Maxwell's equation, expressing that the line integral of the electro- 

 motive intensity round a closed circuit is equal to the rate of 

 decrease of the magnetic induction through the circuit, needs no 

 modification when the propagation of disturbances through the 

 above medium is considered. Maxwell's second equation is modi- 

 fied by adding to the total displacement current at any point the 

 expression 2.qv x , where q is the atomic charge, v x is the velocity of 

 that charge in the direction considered, and 2 denotes summation 

 for unit volume. 



Subsidiary equations for the atomic vibrations (rotational and 

 separational) are given, and the refractive index is finally deter- 

 mined in the form 



cV c'V 



which is the most general form of Ketteler's dispersion formula. 



