224 BELL SYSTEM TECHNICAL JOURNAL 



convection of electrons. The last two show that the plane polarized 

 ray whose electric vector is parallel to // will travel with the velocity 



—'while the one whose electric vector is at right angles to this direction 



and to the direction of propagation will travel at a dilTerent speed, 



c 



— . There is thus doiililc refraction. 

 Ml 



Bending of the rays. If m is the index of refraction, which is a 



function of the space variables, the curvature of the ray having this 



index is where s is taken perpendicular to the direction of the 



II ds 



ray. Since n is practically unity except at the critical frequency, 



this curvature is 1/2 d fr/ds. In order that the ray should follow 



the curvature of the earth it is clear that n must decrease at higher 



altitudes; that is, '-^ must be negative. 

 ds 



We shall workout the curvatures for the special cases considered. 



(The first case has been given above and was worked out in the papers 



cited). For the case of propagation along //, tlie two ciriii!arl\- 



polarized beams have indices given by 



Mr = ei + a = l + ^ j^. (0 



n" o}-\-\' 



(-=?)• 



We are interested in the \alues of 1/2—— in which .V and /; are fiinr- 



ds 



lions of distance s and also of the time. These conic out to be 



N dir 



(9) 



_ (T r <«'^ dX 0}-' i\ rf/;~j 



'"wLiii^ 'ds~ {u>-iyirdsj' 



^^ ~ 2n6'Lw+l ds ^ {oi+iyhdsS ^ ' 



.\ striking fact shown by tlicse formulae is that the curvatures of 

 tlie two rays are in general difTerent. A limited beam entering an 

 ionized medium along a magnetic meridian will be split into two 

 which will traverse different paths. Thus we should expect to find, 



