218 BELL SYSTEM TECHNICAL JOURNAL 



realized when the dimensions of a granular aggregate or conducting 

 film are altered, and is not valid for cases where the resistance is 

 altered by changing the contact compressions. In this latter case Eq. 

 (2) applies. 



Another interesting property of an assemblage is obtained if we 

 express e^ by means of Eq. (1) in terms of the battery voltage V. Thus 

 for the parallel assemblage, e"^ = Const. F", and for the series assem- 



- / VY 



blage, e^ — Const. I — 1 . Thus Eqs. (6a) and (7a) can be written, 

 respectively, as follows: 



TTa C onst. V 



l^c parallel = (OC) 



and 



r^ _ Const. F° 



Vc aeries — ^„_i • {iC) 



If we now accept as an approximation a = 2 then Eqs. (6c) and (7c) 

 are equivalent, and we can say that for any assemblage of contacts, 

 where the value of e'^ for each contact element is equal to that of every 

 other contact element in the assemblage, the contact noise of the 

 assemblage is inversely proportional to the number of contact elements 

 in the assemblage. This principle we have established experimentally 

 by building "square" assemblages — Vw parallel paths with Vw ele- 

 ments in series in each path — and measuring the noise as a function 

 of n. The "square" assemblage is particularly interesting for it allows 

 a control of the noise of an assemblage without altering its overall 

 resistance. This suggests a principle which may be followed in de- 

 signing grid leaks and carbon transmitters with low contact noise 

 characteristics. 



Discussion 



It seems to us that the most logical hypothesis consistent with the 

 foregoing experimental data is, as before indicated, that the noise 

 mechanism lies in a fluctuating contact or boundary resistance. 

 Assuming this we are led to the following considerations concerning the 

 nature of the noise mechanism. 



Careful measurement has established that the conduction through a 

 carbon contact, as near as can be observed, is entirely ohmic. We have 

 shown that when a carbon contact through which direct current is 

 flowing is cyclically compressed, as in the acoustic modulation of a 

 carbon transmitter, the generated a.-c. power is proportional to the 

 square of the d.-c. voltage. This leads to the conclusion that the 



