THE INTERCONNECTION OF TELEPHONE SYSTEMS 549 



This will account then for the rather decided non-uniformity of the 

 loads supplied to the two groups for various numbers of trunks. In 

 Table III are recorded in the left-hand division the nine different 

 trunking arrangements tested. All cases consisted of grades of five 

 subgroups (g = 5) in a multiple having "x" individual trunks in each 

 subgroup placed before ">»" common trunks such that the access 

 (x -(- 3') remained constant and equal to 20. The sizes of the result- 

 ing groups were then varied from 28 to 56 trunks. 



In the central division of Table III, designated "Observational 

 Data," are shown the various loads carried by these trunk arrange- 

 ments with the corresponding proportions of calls lost during the 

 period of each test. The supporting data of columns VIII, IX and X 

 give one an idea as to the fluctuations which may be expected in the 

 lost calls in a limited number of week-day busy hours. 



The last division of Table III, "Theory," shows in its four columns 

 the number of trunks that would theoretically be specified, on various 

 bases of engineering, to carry the load actually observed in each run 

 at a probability of loss equal to the observed proportion of calls lost. 

 Column XI gives the number of trunks which would be required in 

 each case could the trunks all be placed in a single straight group. 

 Since this is the most efticient arrangement possible, a minimum of 

 trunks need be supplied. At the other extreme we have in column XIV 

 the number of trunks which would be required if each trunk operated 

 at the el^ciency of a group of 20 (= x + v) trunks. This could ac- 

 tually be realized, of course, only when the total number of trunks 

 required was an exact multiple of 20. As shown, from 2 to 12 more 

 trunks are required with this decreased efticiency than when a full 

 group is being considered. 



The two other columns, XII and XIII, show the number of trunks 

 that w^ould be needed in a graded multiple of five subgroups having 

 an access of 20 trunks, upon two different assumptions. The column 

 headed "Full Gain" is obtained from curves similar to Figs. 8 to 15, 

 but appropriate to the observed probabilities of loss, to give the "per 

 cent gain over the efficiency of x + y trunks." Knowing the total 

 load to be carried and the enhanced efficiency oi x -[- y trunks in each 

 case the number of trunks required is readily determined. The "Half 

 Gain" column is arrived at in precisely the same way with the excep- 

 tion that only one-half of the indicated "per cent gain over the 

 efficiency oi x -\- y trunks" is utilized. 



To facilitate the interpretation of these results they have been 

 shown graphically in Fig. 16. Above each point on the abscissa at 

 which a run with a known number of trunks was made is recorded 



