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BELL SYSTEM TECHNICAL JOURNAL 



city of light in free space divided by the index of refraction (square 

 root of the dielectric constant). It is also dependent to a small extent 

 on the resistance and permeability of the conductors themselves. 

 The velocity of propagation in wave guides depends not only on these 

 properties but also on the dimensions of the guide as well. For a 

 cylindrical guide it is convenient to express the relation between 

 frequency and dimension as a ratio of wave-length in free space to 

 diameter (X/(i). Also the velocity in the guide may conveniently be 

 expressed as its ratio to the velocity of light {cjv = k). Designating 

 by X the wave-length in free space and by X^ the wave-length in the 

 guide k = X/Xp. Figures 4, 5 and 6 show in graphical form these 

 velocity ratios for three representative cases. The solid curves are 

 calculated. The points are experimental. 



Figure 4 covers the case of Eq waves in a dielectric having a constant 



3 4 5 6 7 8 



RATIO OF WAVELENGTH TO DIAMETER 



(}) 



Fig. 4 — Velocity ratio for the E,j type of wave in a dielectric wire {K = 81). 



of 81 when surrounded by air. It will be observed that at the highest 

 frequencies (lowest values of \/d) the velocity of propagation is one 

 ninth that of light in free space whereas at the lower frequencies 

 (near cut-off) the velocity is that of light in free space. If the di- 



