Motion of Electrons in Solids. 779 



and the total current (12) becomes 



K' dX 



4ttC dt ' 



wW K' = K + , 4?r0 .... (14) 



V 



/l , m . \ 



The analysis for the propagation of light is now identical 

 in form with that for the propagation of light in a non-con- 

 ducting medium of inductive capacity K'. 



10. It will be seen that the equations arrived at in this 

 way are exactly identical with those given by Drude, although 

 reached in a different manner. Our original differential 

 equations (3) and (8) we found to be true only when the 

 infinitesimal interval dt could be supposed at least as great as 

 the time of a collision. Thus our equations will be true 

 only for light of period much greater than the time of a 

 collision. 



Number of Free Electrons per Unit Volume. 



11. As Thomson has noticed *, the experiments of Hagen 

 and Rubens |, combined with a formula expressing the 

 variation of conductivity with frequency, will give us in- 

 formation as to the value of N. The velocity of an electron 

 is about 10 7 , the radius of an atom about 10~ 8 cm. The 

 time of collision is therefore probably about 10 -15 sec. ; for 

 light of wave-length A, = 4/z, the time of vibration would be 

 about thirteen times the time of collision. It would there- 

 fore appear to be legitimate to use our formula for light of 

 wave-length 4//, and greater, but probably not for wave-length 

 much less than this. 



Rubens and Hagen denote by C A the product of (100 — R) 

 (where R is the reflecting power for wave-length X) and the 

 square root of ac, the conductivity for infinite wave-length. 



They denote by Q' k the quantity — y4 . According to a theory 



which neglects the variation of conductivity with frequency, 

 C^ ought to be equal to C A . According to our equations C A 

 ought to be equal to (100 — R)v/c, so that we ought to have 



W-«-i|*V ,tf (15, 



so long at least as X is not less than about 4/x. 



* ' The Corpuscular Theory of Matter,' p. 84. 

 t Phil, Mag. vii. p. 165 (1901). 



