TRANSATLANTIC RADIO TELEPHONY 355 



By reference to Fig. 17, the impressed field may be identically 

 defined at each point along the antenna. 



The longitudinal electromotive force in each element of the wire is 



fw'dx = F'(x, d) cos d dx, 

 fjdx = F'(0)e-^''"'°^^ cos e dx. 



The impressed voltage at the point x along the antenna is 



V'{x) = h-E\x, 6), 



V'ix) = h-E'(0)e-''"^°''. *^^^^'* 



In (118) and (119) F'(0) and £'(0) represent the horizontal and vertical 

 components respectively of the impressed electric field at the end of 

 the antenna x = 0, and h represents the height of the antenna above 

 ground. For the purpose of this discussion, it will be assumed that 

 F' and E' are not dependent upon 6. The current produced at the 

 receiving end 5 by the horizontal component of the impressed field is 

 given by 



from which 



/.. = f— ^^— -%— , (120) 



2a (7 — 7 cos d)s 



The current produced at the receiving end 5 by the vertical com- 

 ponent of the impressed field is evaluated as follows: 



^' 2K 2K ^ ^ 



and by combination of (119) and (122) 



IK. 



Zenneck's theory of wave propagation ^- has been developed by 

 Breizig ^^ to show that the horizontal and vertical components of the 

 impressed field are related by the expression 



-^'=e^Hanr. (124) 



^^ J. Zenneck, "Ueber die Fortpflanzung ebener electromagnetischer Wellen langs 

 einer ebenen Leiterflache und ihre Beziehung zur drahtlosen Telegraphie," An7i. der 

 Phys., 23, 846; June, 1907. 



^^ Franz Breizig, "Theoretische Telegraphie," Braunschweig, 1924. 2d ed., pp. 

 482-487. 



