A SINGLE SIDEBAND MUSA RECEIVING SYSTEM 317 



in the various antennas by this wave front be computed with respect 

 to that of antenna 9. The wave front will arrive at antenna 9 at 



a time - {d cos b) later than at antenna 8. The voltage from antenna 8 



will require a time - to reach the receiving station over the transmission 

 line, making the net time delay between the two outputs equal to 



/9-s = ^ ( ^ - ^ cos 5 ) , (1) 



where d is the horizontal distance between antennas 

 c is the velocity of transmission in space 

 V is the velocity of transmission in the transmission line 

 Similarly the difference in time of arrival of the voltages from 

 antennas 9 and 7 will be: 



/9_7 = 2^ ( ^ - -^ COS 5 j . (2) 



The voltages from all three antennas could be made to add in phase 

 if a delay of 



u[\-\cosi) (3) 



were added to the output from antenna 9, and half as much to the 

 output of antenna 8. For a greater number of antennas these delays 

 would have to be correspondingly increased. 



Now consider the outputs of antenna 9, and those antennas which 

 lie behind it. It will immediately be seen that the time between the 

 arrival of the voltage caused by the wave front at antenna 9 and 

 antenna 10 will be the sum of the times of transmission of the wave 

 front from 9 to 10 in space and on the transmission line back from 10 

 to 9, which is similar to equation (1) except that the sign between the 

 space and transmission line components is reversed. Similarly the 

 equation for the delay between the outputs of antennas 9 and 11 is 

 similar to that between 7 and 9 with the same sign reversed, and like- 

 wise with the other antennas. 



Considering either the group of antennas ahead of the station or 

 the group of antennas behind the station, and considering antenna 9 

 as a part of whichever group is being considered, it will be seen that 

 the delay compensation which it is necessary to insert in the various 

 antenna outputs to make the signal voltages add up in phase at the re- 



