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BELL SYSTEM TECHNICAL JOURNAL 



The first column of vectors represents the phase of the induced volt- 

 ages, assumed to be lumped at points 1 to 5. The second column of 

 vectors indicates the phase of the directly propagated currents arriving 

 at R and due to each lumped voltage. The phase changes are due to 

 the varying intervals of time required to traverse the intervening path. 

 Likewise, the third column represents the current reaching R by way 

 of the open-end reflection where a 180-degree phase change occurs. 

 Summing up either column of current vectors, we trace a semicircum. 

 ference and the resultant is a diameter. Had the antenna wire been 

 slightly longer, the circumference would have been further closed and 

 the resultant smaller. Fig. 7 illustrates an extreme case where the cur- 



RMS 

 INDUCeO 

 VOLTAGE 



RMS. CURRENT 

 AT R-DIRECT 

 PROPAGATION 



R.M S. CURRENT 



AT R VIA END 



REFLECTION 



PERFECT GROUND 



RESULTANTS ♦ 



\ i 



Fig. 7 — Vector relations in a one-wave vertical antenna. 



rents in R are zero for the vertical antenna length of one wave-length. 

 Analyzing these vectors, we establish an important principle, as follows: 



The length of a straight antenna wire is an optimum value, for cur- 

 rents directly propagated to the load, when the elementary cur- 

 rents due to voltages induced in small lengths at the two wire 

 extremities are opposite in phase at the load, provided that this 

 does not also occur for intermediate points. 



This statement has been restricted to the directly propagated currents 

 since, in what follows, we shall, practically always, dissipate the cur- 



