COMMON FREQUENCY BROADCASTING 



591 



This probability of the sum of "w" vectors being less than any given 

 percentage of the absolute sum of "w" vectors has been computed by 

 means of these expressions for the cases corresponding to the distant 

 reception of 1, 2, 3, and 5 stations. The results of these computations 

 have been plotted in Fig. 9. 



20 



30 40 50 60 70 



PERCENTAGE OF TIME 



100 



pig_ 9 — Curves showing the probability that the instantaneous sum of the signals 

 from a number of distant stations will be less than any given percentage, X, of their 

 absolute sum. 



There are two aspects of these curves which are of especial interest 

 in connection with this problem. First it will be noticed that as the 

 number of stations is increased the percentage of time that the signal 

 fades below a small value such as 5 per cent of its maximum should be 

 decreased. Thus the percentage of time that bad quality will be re- 

 ceived due to the elimination of the carrier should be noticeably reduced 

 as the number of stations is increased. Also it will be noted that a 

 rapid reduction in the percentage of time that the signal approaches the 

 maximum should occur as the number of stations is increased. This 

 serves to emphasize the second aspect of the problem, i.e., the level of 

 the signal received should remain near the mean for a much larger per- 

 centage of the time as the number of stations is increased. Thus a 



