Theory of the Optical Properties of Metals. 435 



complete specification of the effect of resonance electrons 

 which is omitted by all the above authors *. 



The results of the present investigation seem to require 

 special emphasis as completing in the present respect the 

 work of Thomson and Jeans in the general theory of radia- 

 tion. These two authors have examined in great detail the 

 emission of light from a metal of the type under considera- 

 tion t- They agree in the conclusion that the most probable 

 law of force is the inverse cube law, this alone leading 

 to results which are consistent with the special as well as 

 the general laws of radiation. Reference may also be made 

 to an elaborate investigation carried out by Prof. McLaren J, 

 who attempts to obtain absolute generality in the problem. 

 His main result is that the absorption of energy from 

 radiation in the metal must ultimately be determined by a 

 function of exactly the same type as that which deter- 

 mines the emission, i. e. it must fall off exponentially as the 

 wave-length decreases. It appears, however, that McLaren's 

 analysis, which is not so general as at first sight appears, 

 will not stand the test of application in particular cases and 

 must therefore ultimately involve some oversight. McLaren 

 states that his analysis involves no assumption whatever, 

 which is equivalent to neglecting the Doppler effect, pres- 

 sure of radiation or fche square of Hi.' velocity of an electron 

 to that of radiation (varying mass of an electron) ; but, as I 

 understand his analysis, it appears that lii> dynamical equa- 

 tions, which are the particular ones usually associated with 

 Hamilton's name, ;ind fche analysis he bases on them, do in 

 fact involve a neglect of all these factors. It is well known 

 that Hamilton's equations, in fche particular form in which 

 McLaren uses them, are restricted for application to systems 

 in which the kinetic energy is expressible as a homogeneous 

 quadratic function of fche generalised momenta, and this is 

 certainly not the case nnless fche velocity of fche electrons 

 is small compared with that of light." Secondly, tho 

 analysis of the emission of the lighi as given by McLaren 

 is appropriate only so far as the effect of the collision- 

 does not impress itself on the radiation formula: a con- 

 dition which necessarily restricts it for application to long 

 wave radiation only as in the simple case examined by 

 Lorentz. 



• Enskog: does attempt to include this effect, but only partially, as he 

 neglects entirely the action of the internal local field en' the conduction 

 electrons. 



t Thomson, Phil. Mag. Aug. 1907: Jeans, Phil. Mwr. June-July. 

 1909. 3f 



\ Phil. Mag. July, 1911. 



2 F 2 



