TRANSATLANTIC RADIO TELEPHONY 361 



are the relative directional receptivities of two arrays of vertical 

 antennas placed at the initial ends of the antennas comprising the 

 desired array. If, then, we designate the relationship between an- 

 tennas indicated by the expression 



J, = [/, + 7e_.€-^[2'^^/^'i<-°««€-^0 (219) 



as compensation " and recognize that this expression gives the direc- 

 tional characteristic of a compensated antenna, we may formulate the 

 rule that the directional characteristic of an array of similar parallel 

 unit antennas is equal to the product of the directional characteristic 

 of the unit antenna and the directional characteristic of an array of 

 unit vertical antennas placed at the initial ends of the unit antennas 

 forming the array, the product being taken point for point as the 

 angle of incidence increases. The relative directional receptivity of 

 each fundamental array of vertical antennas is termed the array 

 factor, so that similarly, the relative directional receptivity of an 

 array of similar parallel unit antennas is given by the product of the 

 relative directional receptivity of the unit antenna and the array 

 factor. This method may be extended to the solution of a complicated 

 array such as that shown in Fig. 19, by determining the relative direc- 

 tional receptivity for groups of unit antennas, then determining the 

 array factor for these groups taken as unit antennas. Expressed 

 literally for a complex array of this type: 



RDR^rv^y - [^1 X ^2 X • • • X ^»]i?i?i?unit antenna, (220) 



where Ai • • • , An are the array factors for the fundamental groups into 

 which the complete array may be divided. 



APPENDIX 3 



Wave Tilt and Ground Conductivity 



In Zenneck's '■'2 • •''■■' exposition of the relation between the horizontal 

 and vertical components of a plane electric wave propagated along a 

 horizontal surface between two media, it is demonstrated that these 

 two constituents of the wave in the upper medium (1) are related by 

 the expression 



19 X 10" , . 1 T 



where 



24 



P2 4i 



