226 BELL SYSTEM TECHXICAL JOURNAL 



The bending of tlic plane polarized comixmriit lia\in,i; the index ixi 

 shows no selective effects, being simply 



In' as 



and is appreciable only for long waxes unless .V is \er\- large. For 

 the other component we find : 



wtiere, in onlcr lo simplify ilic furnuila, oiiK' liii' lerni cmitaining 



—;— has l)een iiirliifled. Tiiis api)lies to ions of one kind. 

 as 



I'or long wa\es those two curxatiires become 



2«o-v Wo^ / as 



These formulas show that the first curvature is alwa\s in the same 



(LX 

 direction for a given value of -^, while the second curxature, which is 

 lis 



that of the electric vector perpendicular to the magnetic field, is, for 

 very long waves, in the same direction as Ci but, as the wave length 

 is decreased or N increased, reverses in sign and becomes opposite 

 to Ci. As an example, if N= 10, for 6 kilometer waves the curva- 

 tures are opposite, so that if the first component tends to bend down- 

 ward the second will tend to bend upward; while if .V=100, for the 

 same wave length both cur\atures ha\e the same sign and the second 

 is five times as large as the first. 



For extremely short waves the two curvatures are equal as they 

 ob\iously should be, since the magnetic field can then ha\'e no effect. 



In transmitting from New 'S'ork to London, for example, waves 

 travel approximately at right angles to the magnetic field, which in 

 this latitude has a dip of about 70°. If we assume a plane polarized 

 ray starting out with its electric \ector \ertical, the component 

 parallel to the magnetic field will be the larger and will be subject 

 to the curvature C\ abo\e, while the smaller component will be affected 



