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BELL SySTEXr TECHNICAL JOURNAL 



in the estimate of the average holding time, will serve to indicate the desir- 

 ability where possible of eliminating altogether this and other supple- 

 mentary errors by seeing that individual counts are taken very quickly, 

 and that the first and last switch counts coincide closely with the ends of 

 the observation period. 



c. Errors in Measuring Each Call 



Due to the method of counting the switches at finite intervals, an exact 

 measurement of the length / of any one call will seldom if ever be made. 

 We shall attempt in what follows to determine the magnitude and char- 



g. 11 — Typical field of switch counts 



acteristics of these errors in measuring individual calls. In any field of 

 switch counts, such as in Fig. 11, there will be calls of types j^ 1 and #2 

 which receive about one switch count for each i call seconds of length. 

 There will likewise be many others such as ^ 3 and ^ 4 which will be sub- 

 stantially undercounted, and about as many others, ^ 5 and ^ 6, which 

 will be overcounted. We shall proceed with certain special cases, and then 

 obtain the general result desired. 



Case 1. t lies between and i 



If the holding times / follow some law of fluctuation /(/), a certain pro- 

 portion of them will have lengths lying in the range / = to / = i. Such 

 a call will either cross one of the switch count points, or it will not. Upon 

 the assumption of a random instant of origination the probability of its 



