Theory of the Optical Properties of Metals. 443 



general theory indicates, the presence of the resonance 

 •electrons may considerably modify this statement *. 



4. The Emission of Energy and the Complete Radiation 

 Formula, 



Although I have no intention of entering into an analysis 

 of the radiation from a. metal on the basis of the present 

 form of the theory, as this side of the problem has already 

 been amply dealt with in the work of Jeans and Thomson, 

 I should, nevertheless, like to take this opportunity of 

 miking a few remarks bearing on this subject, with a view 

 to emphasizing some aspects of the theory which appear to 

 have been overlooked in the discussions of the more general 

 problem. 



In a previous paper on the subject of the emission of light 

 from a metal, I have ventured to give in full detail a dis- 

 cussion of Lorentz's theory, which regards the radiation from 

 a metal as arising from the motions of the free electrons 

 inside the metal, basing myself mainly on the general 

 assumptions of the simpler form of the theory, which regards 

 the electrons and atoms as elastic spheres. The final result 

 of this analysis is that if it is possible to assume that the 

 time of duration of an encounter of an electron with a 

 molecule is always negligibly small, then the emission is of 

 such a type that the Rayleigh-Jeans formula for the com- 

 plete radiation is generally applicable all along the spectrum. 

 This absurd conclusion arises, however, as before stated, 

 from the fact that the assumption on which the analysis is 

 based virtually implies that the total amount of energy 

 radiated from the moving electrons, depending essentially on 

 their accelerations, is of definite amount. It is therefore 

 suggested that the theory and the Kayleigh-Jeans formula 

 which is derived from it are considerably restricted in their 

 applicability to the actual state of affairs, and are valid only 

 so far as the general nature of the collisions between the 

 molecules and electrons are not of primary importance in 

 determining the radiation from the electrons. Ultimately, 

 of course, the complete radiation formula must contain some 

 account of the general dynamical nature of these collisions, 

 although it is to be expected that any very special character- 

 istics would be eliminated by the usual statistical methods of 

 analysis, and such a conclusion is amply borne out by the 

 researches of Thomson and Jeans. 



* Vide J. Larmor, " On the Ran<re of Freedom of Electrons in Metab," 

 Phil. Ma?. August 1907. 



