of the Optical Properties of Metals. 843 



If we take all the electrons to be moving with the same 

 velocity Y we get instead 



The coefficient of absorption A of a very thin plate is 

 shown by Lorentz to be equal to crA/c, where a denotes its 

 conductivity. Hence using the value found for a- when all 

 the V's are equal we get 



A 



N* 2 Z ?)l A 



cmY{l+ P niJT 2 ) ' 



Hence we get for the energy density E\ per unit range of 

 wave-length in full radiation, after putting raV 2 = 2aT and 

 P — 2ttc\\^ 



_ 8tt E WttxT 

 A ~ c A~ 3\ 4 ' 



wnich is the value found by H. A. Lorentz for very long 

 wave-lengths, and also by Jeans. 



If the formulae allowing for the distribution of V according 

 to Maxwell's law are used instead, we get 



3\ 4 r Ve-*v*dV ' 



Jo I" 



It appears, therefore, that the extension of the calculation 

 to shorter wave-lengths gives no indication of a diminution 

 of Ex. Both the emission and the absorption are diminished, 

 but the diminution of the one compensates for that of the 

 other. 



On the assumptions that the atoms are hard spheres which 

 do not move and that the electrons do not collide with each 

 other on which the above calculations are based, the electrons 

 only gain or lose energy from the radiation. Consequently, 

 those electrons which are moving with a greater velocity 

 than the average will gradually Jose energy, while those 

 which are moving with a less velocity than the average will 

 gradually acquire energy. After a time, therefore, all the 

 electrons will acquire the same velocity, and the energy 

 density will be given by 167raT/3A. 4 exactly. The assump- 

 tion of a velocity distribution given by Maxwell's law is 



3K 2 



