444: Electron Theory of the Optical Properties oj Metals. 



The calculations of Thomson and Jeans prove decisively 

 that the energy emission in a particular wave-length is a 

 function of that wave-length which falls off exponentially 

 as the wave-length is increased. The above calculations- 

 show that the absorption diminishes as a function of the 

 wave-length like 



X 

 a + A 2 ' 



The complete radiation formula determined by the ratio 

 of the emissivity to the absorption is therefore precisely of 

 the general form required by experience, although the 

 difficulties of the analysis preclude the deduction of any 

 simple relation. 



It must therefore be insisted that although the theory in 

 its present state may be too indefinite in its details to give 

 anything beyond a tentative account of the general phe- 

 nomena of the radiation from the metal, the general 

 conclusions which can be drawn from it are in themselves- 

 not materially inconsistent with the known facts as contained 

 in the experimental results ; and that therefore there seems- 

 to be no imperative need for resorting to a wholesale and 

 phantastical modification of the general basis of physical 

 theories, on the grounds that such a modification appears at. 

 first sight to be required in one aspect of the general 

 problem. 



In his attack on the theory McLaren comes to a conclusion 

 which is just the opposite of that just stated, and he attempts 

 to support his result by a general assertion that on all 

 dynamical principles the absorption is a function of the same- 

 type as the emission. There does not, however, appear to 

 be any legitimate ground for such an assertion, which, as 

 experience and theory prove, is only true so long as the 

 wave-length is long compared with the mean time of the 

 free molecular motions in matter. It is to be insisted that 

 the two phenomena of absorption and emission are essentially 

 different in their mean aspects, and this difference even extends 

 to the dynamical characteristics of the phenomena. Absorp- 

 tion is essentially a free path phenomenon, whilst the emission 

 must ultimately depend in its main features on the collisions 

 at the ends of the free paths, and must therefore contain a. 

 much more intimate account of these collisions than any 

 other phenomenon, which is, practically speaking, in no way 

 concerned with them, except, perhaps, in so far as they 

 temporarily remove the electrons concerned from con- 

 sideration in the treatment of the phenomenon. Whilst 



