542 BELL SYSTEM TECHNICAL JOURNAL 



sional transmission line are 



dlly . „ 

 dx 



-—^ = - iweE:,, (30) 



dz 



dEx _ dEz _ _ . jT 



dz dx ^' 



If n is an odd integer, these possess the following solutions: 



. r„ . nvx 



Ex = A - — sin , 



iwe a 



Ez = A-. cos , (31) 



tojea a 



Hy = A sin ; 



and if n is an even integer, 



r„ n-rrx 



Ex = A -. — cos ■ , 



twe a 



E,= —A-. sin , (32) 



tcjea a 



mrx 



Hy = A COS 



a 



where 





and X is the wave-length corresponding to the frequency /. 



Let us now define the longitudinal impedance (Z^) as the ratio of 



Ex to Hy, 



Z.=^, (34) 



and the transverse impedance (the impedance in the x-direction) as 

 the ratio of E^ to Hy, 



^ nir mrx .. . ,, 



Zx = -■ cot , 11 w is odd, 



^o:ea a ^^^^ 



„ mr mrx .. 



Zi = — -: — - tan- ■ , 11 w IS even. 



twea a 



It will be observed that, depending on the frequency, the longitudinal 



