192 BELL SYSTEM TECHNICAL JOURNAL 



l/r of the contact formed by compressing, by an amount D, a single 

 smooth conducting sphere against a flat conducting plate, 



- = const. D'i\ (6) 



It appears reasonable to assume that the hills which come into contact 

 with compression act independently of each other as regards con- 

 duction. The conductances may therefore be added and we may 

 write for the total conductance (l/i?) produced by a compression D 

 involving many hills: 



(7) 



Using the value of n consistent with equation (5) through the measured 

 value of TV", viz., n = 0.6, we get N = 0.68. The measured value 

 of A^ (0.47) is, as we have surmised, too small though it is of the right 

 order of magnitude. 



We are, of course, investigating the factors which give rise to this 

 discrepancy as they will play an important part in any complete 

 theory of microphonic action, and we are extending our study to the 

 behavior of granular aggregates in simple cells and microphone 

 structures. We have shown that the value of iV in a simple cell com- 

 posed of parallel electrodes is quite consistent with our simple theory 

 for single contacts, which therefore indicates that the behavior of an 

 aggregate of contacts is determined by the behavior of the individual 

 contact. Furthermore, we have shown, through static measurements 

 on the handset instrument, that the granular aggregate within this 

 irregularly shaped structure behaves like the aggregate in a simple 

 cell. We are therefore confident that the behavior of the microphone 

 will be explained in terms of the behavior of the single contact. 



The behavior of the two dimensional model of the handset micro- 

 phone (Fig. 26) is most convincing in this connection. Although this 

 model was set up originally to study the distribution of stresses in 

 this type of structure it has proved most useful in other phases of our 

 work. Quarter inch rubber balls represent the granular particles of 



