36 



BELL SYSTEM TECHNICAL JOURNAL 



means that the maximum available field is reduced. Too, the impedance 

 will depend on wire size. 



It thus seems desirable to compare in some manner an actual helix and the 

 helically conducting sheet. It would be very difiicult to solve the problem 

 of an actual helix. However, we can make an approximate comparison by 

 a method suggested by R. S. Julian. 



In doing this we will develoj) the lielix of wires just as the helically con- 



CASE n 



Fig. 3.9 — The wires of a developed helix with about two turns per wavelength (case I) 

 and about four turns per wavelength (case II). In the analysis used, the wires are not 

 quite round. 



BOTTOM 



I I I I 



III, 



/'n, >7>, /'^, ,'i; /'•', 



r I i 



Fig. 3.10 — Voltages on a developed hehcally conducting sheet for two turns per wave- 

 length. 



ducting sheet was developed, by slitting it along a helical line normal to the 

 wires. We will then consider two special cases, one in which the wires of the 

 developed helix are one half wavelength long and the other in which the 

 wires are one quarter wavelength long. 



The waves propagated on the developed helix are transverse electromag- 

 netic waves propagated in the direction of the wires, and the electric fields 

 normal to the direction of propagation can be obtained from a solution of 

 Laplace's equation in two dimensions (as in (3.15)-(3.17)). 



