NOVEL EXPRESSIOXS FOR PROPAGATION CONSTANT 157 



The expression iii (4) for tan 6 may be written: 



tan e = Vl - LCV"^ (6) 



where V = the phase velocity. 



Now LC = 1/ vl 

 where Vo = the transient velocity. 



Hence 



tan 6 = Vl - VyVl (7) 



and 



p = /3(\/i - Fvn + i) (8) 



Now it can also be shown that for a progressive wave: 



hLP 





(9) 



So that the real part of the propagation constant is equal to the square 

 root of the difference between the electrostatic energy per mile and the 

 electromagnetic energ}- per mile divided by the sum of the energies (multi- 

 plied by /3). 



This gives the attenuation constant in terms of the most fundamental 

 entity that we know, namely energ>^ 



Also multiplying each side of equation (8) by x the geographical length 

 of the line between the origin and the point under consideration: 



Px = (3iVl - T-IVl X + i-v) (10) 



Now |S.v is the number of radians (i.e. total phase shift along the length 

 X) and using relativity conceptions, 



l/i-fi 



is the apparent length of the wave structure in the length x (the waves 

 moving at velocity V) as observed from a li.xed point with signals moving 

 at velocity Y^- 



Also ^xy/\ - V^/Vl is the number of radians in the apparent length 



xVi - vyvi 



The characteristic impedance may be stated in terms of the phase velocity 

 as follows: 



z. = J,-if-^ (11) 



CV /CO 



