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XVII. On Lorentz 3 s Theory of Long Wave Radiation. 

 By G. H. Livens *. 



f I^HE Lorentz form of the theory of radiation, which 

 JL regards the radiation from a thin metallic plate as 

 arising from the motion of the electrons inside the plate, 

 will probably always remain as a deciding factor in the 

 general theory of this subject, since it involves no principles 

 which cannot certainly be regarded as well established by 

 independent theory and experiment. The final formula to 

 which this theory leads and the extent to which it depends 

 on the assumptions made must therefore be matters of the 

 first importance in the general theory. Basing mainly 

 on the two assumptions that the period of the radiation 

 considered is long compared with the interval of time 

 between two consecutive collisions of an electron with an 

 atom and that this latter interval is also long compared 

 with the time of duration of a collision, Lorentz derives 

 a formula, identical with the Rayleigh-Jeans formula, 

 which is apparently correct in the long wave part of the 

 spectrum but fails hopelessly for obvious reasons in the 

 visible and ultraviolet regions. These two assumptions of 

 course naturally restrict the analysis to long waves, but it is 

 the expressed opinion of Prof. Lorentz f that the same 

 Rayleigh-Jeans formula would be obtained as the general 

 result for the other parts of the spectrum if only the 

 difficulties of the analysis could be overcome. The main 

 object of the present paper is the discussion of a partial 

 generalization of Lorentz's analysis, in which one of the two 

 above-mentioned restrictions is removed. A formula, which 

 is concluded to be practically identical with the Kayleigh- 

 Jeans formula, and applicable to all parts of the spectrum, is 

 obtained on the single assumption that the duration of the 

 impact of an electron with an atom is always negligibly 

 small ; and the conclusion carries with it a partial confir- 

 mation and possible limitation of a certain well-known result 

 in the optical theory of metals. 



The method to be followed is identical with that given by 

 Lorentz with the single exception that it will not be found 

 necessary to assume the relation between the period of 

 oscillation and time interval between successive collisions 

 which is implied in his theory. It is, however, necessary to 

 retain the assumption he makes regarding the smallness of 

 duration of a collision in order to avoid making arbitrary 



* Communicated by the Author. 



t See *' Discussion on Radiation/' B.A. Report, 1912. 



