222 BELL SYSTEM TECHNICAL JOURNAL 



_ V= r + 1- di V E = ^' {iaX + 6 , F) , (5) 



oy c- 



02 C- 



These ecjuatioiis for the propagation of light in magnetically active 

 substances have been given by \'oigt, Lorentz, Drude and others 

 and form the basis of the explanation of optical phenomena in such 

 substances. As applied to optics, they are worked out, for example, 

 in Drude's "Optics" (English translation), page 433. As applied 

 to this problem, they assume either that the motion of the ions is 

 unimpeded or that the resistance to the motion may be expressed as 

 a constant times the velocity, which, as explained later, may be done 

 in this case. We shall work out some comparatively simple cases 

 and point out the conclusions to be drawn from them. 



Consider first a plane polarized ray having its electric vector pardllf] 

 to the magnetic field and moving in the xy plane; for example parallel 

 to X. In this case the electric vector is a function of x and / only 

 of the form 



Z = Zo 



H'-t) 



in which - is the \'elocit\' of the wa\e. Sutistituting in the general 



M 

 equations (.')) wc find that 



M- = l-l^. (6) 



The \el(>cit\ of projiagation is thus a fiuution of tlie frequency and 

 of the density A'. This particular case corresponds to that treated 

 by Eccles and Larmor in the papers cited. It will be noted that the 

 velocitj' is greater for long waves than for short waves and that if A^ 

 is a fimction of distance from the surface of the earth, the velocity 

 will \ary in a vertical direction, causing a curvature of the rays as 

 worked out by the authors mentioned. In this particular case, how- 

 ever, which corresponds completely in practice to conditions obtaining 

 over only a limited area of the earth's surface, the greatest effect is 

 produced on the longer wa\-es. Since electromagnetic waves are in 

 general radiated from vertical antennas so that the electric vector 

 is vertical, this case would correspond to the condition of transmitting 

 across the north or south magnetic poles of the earth. 



The second ca.se to be considered is that of propagation along the 

 direction of the magnetic field. In this case X and Y are functions 



