of the Optical Properties of Metals. 841 



the heat H produced per c.c. per sec. is given by 



Hence 



<T = 



_ 4:7r^en m (g\ s,2 C co Ve-? V W 



as before. 



I£ i denotes the current carried by the c?N electrons which 

 have velocities between V and V + d V, then i = eu dN, which 

 with equation (1) gives 



m di mV __v 



+ 7 .SJAT 1 — ^' 



The theory of the propagation of light in the«metal follows 

 from this equation in Drude's manner*. If n denotes the 

 refractive index and k the coefficient of absorption, we get | 



reg (l-«.)=l-16^^f r ^- 3) 



and n 2 K = 2ir(TJp. 



If all the V's are taken to be equal these equations reduce 

 to the simpler form which applies when only one class of 

 electrons is supposed present. 



The emission of light by a metal has been discussed by 

 several writers. H. A. Lorentz has given a calculation of it 

 on the assumptions adopted in this paper but applicable to 

 very long waves only. J. J. Thomson f worked out the 

 emission for any wave-length on the assumptions that all the 

 free paths occupy equal times and that the velocities of the 

 electrons at the ends of each free path vary in a particular 

 way. 



Jeans (loc. cit.) gives two calculations. In the first he 

 assumes equal free path periods while in the second free 

 paths are not assumed at all, but the calculation is based on 

 the equation which seems to be exactly correct only when 

 all the electrons have the same velocity. The following 

 calculation is very similar to that given by H. A. Lorentz J, 

 but it is not restricted to very long waves. It is therefore 



* ' Theory of Optics,' p. 397. 



t * Corpuscular Theory of Matter/ pp. 89-97. 



% ' Theory of Electrons,' pp. 81-90. 



Phil. Mag. S. 6 Vol. 20. No. 119. JSov. 1910. 3 K 



