﻿Theory of Dispersion. 475 



Writing 



L# 2 + m = X ~\ 



47T 47T 6> 2 „ | 



h^~k, 3 = ^ X f (34) 



4tt 2 j 



we get 



A-f)VA=«o/,&c (35) 



if the magnetic field is weak, and 



/•• + A-V 2 A 2 /=V 2 !^ from (18). . . (36) 



From (35) we deduce 



p +(/?o s + «uV = 0| ^ 37 ) 



£ = ^000 COS (??i£ + e) 

 equations will be 



9 4. If ^=0, or p is independent of coordinates, the 

 3a- 



A+p 2 A=<W "l (38) 



/ + A-V 2 A 2 /=0i 



For a plane wave (z= const.), A 2 /"= =^> &c. 



and the solution is 





which yield 



n 2 = l + S^- , (39) 



Po~-'Ph 



9, 



where n is the index of refraction and — = the periodic 



Po 

 time of vibrations of electrons unaffected by the field, while 

 S refers to the several groups of electrons that are set vibrating 

 on account of the impressed disturbance. 



25. Returning to equation (35), and introducing a viscous 

 term /> A we get 



A + 5 l+^ 2 A=a a /'. .... (40) 



