558 



BELL SYSTEM TECHNICAL JOURNAL 



the heavy dots in Fig. 22, as might be expected, give sHghtly higher 

 values of variation for the non-restricted load values ^t gx -\- y = 36 

 and 52 trunks than for the restricted cases belonging to the second 

 division of the tests. The remarkable point here, however, is that 

 the phenomenon for the ranges studied exhibits practically a straight 



32 36 40 44 48 



NUMBER OF TRUNKS IN GRADED GROUP 



Fig. 22— Change in subgroup load variation with number of trunks in group. 



line relationship between variation of subgroup loads and the number 

 of trunks per subgroup, a difference of four in total trunks meaning 

 an increase of one in each subgroup. An added variation for the 

 larger number of trunks seems only natural, however, since as the 

 subgroup size is increased part of the fluctuations previously borne 

 by the commons is transferred to each subgroup itself. That this 

 natural increase in subgroup variability does not affect the grade of 

 service of the larger groups for busy hour measurements seems to be 

 amply demonstrated by the consistency of the "Half Gain" formula 

 in fitting the observed number of trunks in Fig. 16. We conclude, 

 then, that a formula based on the third assumption (equality of sub- 

 group loads), is considerably at variance with actual results; by 

 modifying this assumption, to approximate loading differences, the 

 graded loss formula appears to describe the observed losses quite 

 satisfactorily. 



Concerning the last assumption underlying the graded formula 

 derived here, that of "no-holes-in-the-multiple," somewhat less is 

 known. That the "holes" do exist is self-evident. It is suggested 

 by these Chicago half-hourly observations, however, that under or- 

 dinary conditions the reaction of holes-in-the-multiple upon the grade 



