﻿Theory of the Optical Properties of Metals. 665 



equation is fundamental, but in the opinion of the present 

 writer it is by no means complete as it stands. The following 

 deduction of the equation may perhaps make this point clear, 

 If SN denote, as before, the number of electrons per cubic 

 centimetre with their velocity component between (f, ??, £) 

 and (£ + ^f, Tj + drj, f + df) then the component of the 

 momentum of this group parallel to the #-axis is m£8N, and 

 if E acts in the same direction we have 



Now we know that 



"f-* E - 



whilst according to Wilson the change in SN in the time dt 

 is equal to the number of collisions which take place in this 

 group in the time dt with the sign changed, and this is 



(•dt _ T a t * 



so that 



= -rfN*, 



>>-& 



and thus using r m — — we have the above equation in the 

 form 



at Cm 



and on integration over all values of (f, rj, f ) we reproduce 

 the Jeans-Wilson equation given above. 



But the assumption that the change in £N is due entirely 

 to the collisions is not valid. In fact SN is itself a function 

 °f {&V> ?) an d therefore changes on account of the variations 

 in these quantities. In the present instance we ought therefore 

 to write the momentum equation in the form 



a-(*e8N)-«B(^+^(«N))- g , 



* This neglects the contribution to the momentum of the group by 



the electrons coming: into it. This does not, however, affect the tinal 

 result as on integration these terms go out by themselves. 



