328 



or 



BELL SYSTEM TECHNICAL JOURNAL 



2K 



ie^ 



E' 



2K 



(13) 

 (14) 



In terms of antenna constants alone, it is shown in Appendix 1 

 that the current produced at the far end of the wave-antenna is: 



where 



I E'( 



1 S\'F 



E'd 



If, 



e'« tan T 2K 

 SX'F' 



(a-hjb), 



F'd 



2K 



(c+jd), 



also 



--Er,= e'^ tan T. 



(125) 

 (15) 



(16) 

 (301) 



In equations (15) and (16), {a -]- jh) and (c -\- jd) are abbreviations 

 defined as follows: 



(fl+i&)=^(i 



-[aS\'+j2TrS{m- cos 6) \\ ^-J2irs cos B 



and 



(c -f jd) = cos 



I _ ^-laS\'+j2TrS(.m-coae)] 



-J2irS cos e 



aS\' -\- j2irS{m — cos d) 

 If we equate expressions (14) and (125), and solve for tan T: 



tan T = 

 where 



ac + bd + -yliac + bdY - jc'^ + d^){a~ -j- h' - g^) 

 c- + d:' 





(17) 

 (18) 



(19) 

 (20) 



It is pointed out in Appendix 3 that the phase angle 5 may be 

 expressed as a function of the quasi-tilt angle T and the dielectric 

 constant k. For that reason, the determination of T must be made 

 in two steps. The procedure is as follows: first, it is assumed that the 

 component of the total received current due to the vertical component 

 of the impressed field is zero, i.e., 



{a+jb) ^0. 



