298 BELL SYSTEM TECHNICAL JOURNAL 



The area of the other diagrams oscillates about 1/2 and approaches 

 it as a limit upon increasing the separation and keeping the phase 

 difference constant. The minimum area (for a diagram in which the 

 radius vector reaches its maximum of unity ^^) is 0.2986, obtained 



Fig. 4 — Cumulative amplitude diagrams for two antennae 



by the array (0.6098X, OT). The directive diagram for this case is 

 shown by Fig. 3. 



Cumulative amplitude diagrams are shown by Fig. 4 for six selected 

 arrays, including the unit circle, which is the cumulative diagram 

 for the array (OX, OT). In this figure, the angle corresponding to 

 any value of the radius vector is equal to the total angle of the direc- 

 tive diagram of the array throughout which the relative amplitude 



^^ A. Koerts, loc. cit., pages 104, 105. In those cases in which the radius vector 

 does not reach the unit circle, in order to obtain a measure of the reduction of the 

 energy ratio of random static to signal, the unit circle should be replaced by the 

 circle with a radius equal to the maximum radius vector. The absolute minimum 

 0.2986 is not changed upon including these cases but a relative minimum 1/3 occurs 

 for the array (aX, bT) upon letting a and b approach and 1,2 in such a manner 

 that a-{-2b = \. If the two antennae are loops, with planes parallel to the axis of 

 the array, the area approaches the relative minimum 3/14 upon letting a and b 

 approach the same limits and 1/2 but in such a manner that 3a+46=2. 



