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BELL SYSTEM TECHNICAL JOURNAL 



such as in Fig. 13. Such a distribution would probably occur but rarely, 

 if ever, in practice. However, if the intervals i are short compared to the 

 average holding time /, such an assumption may not introduce any serious 

 discrepancy in whatever form is simulated.' 



3L 4L 5L 



t =HOLDING TIME 



Fig. 13 — A varying holding time with a number of equall>' likel\- ranges 



X=ERROR IN MEASUREMENT 



Fig. 14 — Distribution of call measurement errors for "equally likely" holding time 



distributions 



In this case it is obvious upon inspection that the sum of the terms in 

 the brackets in equation (14) is a constant for all values of x, and likewise 

 in equation (15), and that they equal each other. Hence 



px^n{x) = K 



, i 4- :v 



(20) 



and 



/>x>f)(a:) = K 



I — X 



(21) 



' The analytics of the allied case in which the errors at the ends of a call were assumed 

 to fall equally likely between ±J/2, were discussed by E. C. Molina in an unpublished 

 memorandum dated September 7, 1920. 



