290 Maxwell. 



The equations of the electromagnetic field in the metal may 

 be written 



curl H = 47rS, 



- curl E = H, 



S = i + D = K E + 



where K denotes the ohmic conductivity ; whence it is seen that 

 the electric force satisfies the equation 



=c 2 V 2 E. 



This is of the same form as the corresponding equation in 

 the elastic-solid theory* ; and, like it, furnishes a satisfactory 

 general explanation of metallic reflexion. It is indeed correct 

 in all details, so long as the period of the disturbance is not too 

 short i.e., so long as the light- waves considered belong to the 

 extreme infra-red region of the spectrum ; but if we attempt to 

 apply the theory to the case of ordinary light, we are confronted 

 by the difficulty which Lord Eayleigh indicated in the elastic- 

 solid theory,f and which attends all attempts to explain the 

 peculiar properties of metals by inserting a viscous term in 

 the equation. The difficulty is that, in order to account for the 

 properties of ideal silver, we must suppose the coefficient of 

 E negative that is, the dielectric constant of the metal must 

 be negative, which would imply instability of electrical 

 equilibrium in the metal. The problem, as we have already 

 remarked,:}: was solved only when its relation to the theory of 

 dispersion was rightly understood. 



At this time important developments were in progress in 

 the last-named subject. Since the time of Fresnel, theories of 

 dispersion had proceeded! from the assumption that the radii 

 of action of the particles of luminiferous media are so large 

 as to be comparable with the wave-length of light. It was 

 generally supposed that the aether is loaded by the molecules 



* Cf. p. iso. 



t Cf. p. 181. Cf. also Rayleigh, Phil. Mag. (5) xii (1881), p. 81, and 

 H. A. Lorentz, Over de Theorie de Terugkaatsing, Arnhem, 1875. 

 + Cf. p. 181. Cf. p. 182. 



