G38 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



/3^ = /3'^ + ja sgn p 



da 



where /3' is the propagation constant for the loss-free case. Thus 



j^ = j^ - :w 



2^'d\cT\ 



(44) 



and the last term on the right, (multiplied by our scaling variable 

 /So = co\/jLi.eo) is the attenuation in nepers per meter. The present con- 

 vention is that the waves propagate in the positive z direction, as exp 

 {—j^z). It follows that they will decrease in that direction only if 

 5(/3')V^I o- I < 0. Occasionally this is not the case, and presumably 

 indicates that the direction of the power flow opposes that of the phase 

 velocity. 



For small dielectric loss, too, it is possible to derive formulae for the 

 attenuation constant from those already obtained; obviously the latter 

 depend on e only through e = en — jei , and can therefore be expanded. 

 But it must now be remembered that /3 was defined as /Sactuai/wv/Mce. 

 and ro as ractuai wVTiIe so that the scaling parameter oi\^ix,e will make 

 contributions to the imaginarj^ part. It is then readily verified that 



/3a 



= /3 - i 



1 



26o/3'(9(ro') 



{r.Y 



(45) 



A few words may be said about the relation of Faraday rotation to 

 the ^~ — a curves. A linearly polarized plane wave travehng in the un- 

 bounded medium along the magnetizing field can be regarded as the 



Fig. 14 ■ — The course of the fully developed modes (solid lines) and of some of 

 the lower incipient modes (dotted lines) as a function of <r for ro = 5.75 and 

 I p i = 0.6. 



