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BELL SYSTEM TECHNICAL JOURNAL 



lative curves. The successive curves of this cumulative series have 

 been plotted in Fig. 9 at regular intervals apart, the intervals being 

 the same distance as the average monthly message use scale of Fig. 8. 

 The horizontal scale of Fig. 9 used in plotting these cumulative dis- 

 tributions must therefore be movable so as to apply in turn to each 



100 



90 



80 



5 60 

 o 



CO 



50 



40 



30 



20 



10 



600 800 1000 1200 1400 1600 1800 2000 2200 

 AVERAGE MONTHLY MESSAGE USE 



Fig. 8 — Preliminary Family of Cumulative Curves 



of the cumulative curves. With the cumulative curves plotted, 

 the family of curves on Fig. 8 have been drawn in on Fig. 9, the curves 

 representing the various message uses being exactly the same as 

 those of Fig. 8 except that the method of drawing the cumulative 

 curves has automatically shifted successive curves of Fig. 8 further 

 and further to the right. It follows from the methods which have 

 been used in constructing Fig. 9 that any given cumulative curve 

 must intersect each curve of the other family somewhere on the 

 vertical line corresponding to the message use (expressed as per 

 cent, of the average message use) represented by that curve. For 

 instance, the cumulative curve for 1000 average message use (indi- 

 cated by A) must intersect the curve representing 30 per cent, of 

 the average message use on the vertical line corresponding to a co- 



