Electron Theory of the Optical Properties of Metals. 835 



dielectric sphere whose coefficient is large. They do not 

 agree with the results deduced from a consideration of steady 

 motions, without redistribution, but must apparently be re- 

 garded, with the corresponding values for a conductor, as the 

 only values which have received a complete proof. 



Meanwhile, as stated in the preface, it may well be of service, 

 in any attempt to treat the electron as not subject to defor- 

 mation, to endow it with dielectric rather than conducting 

 properties. The analysis of this hypothesis presents no diffi- 

 culty which does not appear to be shared by the other, and 

 in a consideration of initial motions, it gives rise to great 

 simplicity in the possible case of no Newtonian mass. 



XCI. The Electron Theory of the Optical Properties of 

 Metals. By Prof. Harold A. Wilson, F.R.S., McGill 

 University, Montreal*. 



THE electron theory of the optical properties of metals 

 has been developed by Drude, J. J. Thomson, H. A. 

 Lorentz, J. H. Jeans, and others. 



Let N denote the number of free electrons per c.c. in the 

 metal, and let dN be the number in the group with velocities 

 between V and Y + dV. The number dN remains nearly 

 constant, although particular electrons are continually enter- 

 ing and leaving the group. Each such group may therefore 

 be regarded as having a permanent existence. Since the 

 mass of an atom is large compared with the mass of an 

 electron, the velocity of an electron will not be much altered 

 by collisions with atoms, and collisions with atoms must be 

 much more numerous than collisions with electrons. Con- 

 sequently the electrons in a particular group may be regarded 

 as making many colli sons, and still remaining in the same 

 group or in a set of groups covering a small range of 

 velocities. 



When an electric force acts in the metal the electrons in 

 each group will acquire an average velocity which will not 

 be the same for the different groups. The motion of a group 

 will be determined by a differential equation which will be 

 of the same form for all the groups, but with different values 

 of the constants for the different groups. It will therefore 

 not be possible to represent the average velocity of all the N 

 electrons by a single differential equation, unless we make 

 the assumption that all the electrons have the same velocity 

 of agitation. 



* Communicated bv the Author. 



