Maxwell's Electro-magnetic Theory of Liylit. 375 



In what follows, I have endeavoured to extend Maxwell's theory so 

 as to include dispersion and metallic reflection. The initial assump- 

 tion that both conducting and dielectric media consist of molecules, 

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

 is essentially that made by Helmholtz in his paper on the " Electro- 

 magnetic Theory of Dispersion."* The methods I have employed are 

 however different, and my final results, though bearing a general 

 resemblance to those obtained by HelmhoUz, differ from them in some 

 important particulars, besides being simpler and more directly related 

 to the results of investigations on other theories of the nature of light. 

 But besides the gain in simplicity and consequent physical definiteness, 

 I have had other reasons for not following Helmholtz's method. The 

 utility of employing the principle of least action in this case may be 

 questioned, since the only difficulty appears to lie in formulating the 

 reactions due to the charged atoms, and the nature of these reactions 

 is implied in the energy equations assumed. Moreover, the energy 

 equations obtained by Helmholtz are themselves open to criticism, 

 and some of the results obtained do not reduce to Maxwell's equations 

 when the terms involving the polarization of the dielectric are equated 

 to zero.f 



2. This paper contains (I) a simple explanation of the fundamental 

 phenomena observed in connection with a state of steady electrical 

 strain in a dielectric ; (2) a consideration of the law of propagation 

 of electrical disturbances in a polarizable medium ; equations are 

 obtained which explain dispersion, both ordinary and anomalous ; (3) 

 and a consideration of metallic reflection, especially in connection 

 with Kundt's experiments on the velocity of light in metals. 



State of Steady Electrical Strain in a Dielectric. 



3. It is here sought to explain Faraday's discovery, that the intro- 

 duction of a material dielectric between the plates of a charged 

 condenser, diminishes the potential difference between the plates. 



* H. von Helmholtz, 'Wied. Ann.,' 1893, vol. 48, pp. 389-405, 723725. 

 Translated by Dr. Howard in the 'Electrician,' vol. 37, pp. 404 408. 



t Helmholtz's Theory of Dispersion has been criticised by Kieff (' Wied. Ann.,' 

 1895, vol. 55, pp. 8294) and Heaviside ('Electrician,' vol. 37, Aug. 7, 1896). In 

 addition it would appear that the employment of a term expressing the dissipation 

 of energy (other than Eayleigh's " dissipation function ") is inadmissible in the 

 principle of least action (Larmor, * Brit. Assoc. .Report,' " On the Action of Mag- 

 netism on Light," 1893 (Nottingham)). The final equations obtained by Helmholtz, 

 when the terms relating to the polarization of the medium are equated to zero, are 

 of the nature 



B = curl E and 4?rD = curl H, 



where B, E, D, and H represent the (vector) magnetic induction, electromotive 

 intensity, displacement, and magnetic force respectively. They differ in sign from 

 Maxwell's equations. 



2 F 2 



