THE INTERCONNECTION OF TELEPHONE SYSTEMS 



551 



the corresponding number of trunks which would be provided on each 

 of the bases considered above. The actual number in service is also 

 shown as a straight line through the shaded points for comparison with 

 the various theoretical schedules. As noted on the figure the studies 

 having 28 to 40 trunks were made on the State to Dearborn group and 

 those having 40 to 56 trunks on the State to Wabash group. 



As may readily be seen either from Table III or Figure 16 the 

 "Half Gain" schedule coincides especially well with the observed 

 data, while the other engineering plans fall consistently too high or 

 too low on the scale. It may be remarked that the "Full Gain" 

 values approach the limiting full group figures very closely and that 

 it should prove of considerable interest to determine the cause of 

 divergence between the field observations and these large theoretically 

 possible graded loads. 



Critical Inspection of Assumptions in Graded Theory 

 It has been noted that the number of "Full Gain" trunks specified 

 is well below the number really required. This confirms the possible 

 suspicion that not all of the four assumptions fundamental to the 



<^ 0. 10 



S 0.06 



D 



a 



UJ 

 IT 

 "- 0.04 



4 5 6 7 8 



LENGTH OF CALLS IN MINUTES 



Fig. 17 — -Distribution of interoffice trunk holding times. 



graded multiple formula presented in this paper are entirely satisfied. 

 We shall therefore examine, in order, the accuracy of these assumptions. 

 We know indeed, without investigation, that calls are of widely 

 differing lengths, and in addition are not "held" in the manner 

 assumed. In Fig. 17 is shown a typical holding time distribution for 



