222 BELL SYSTEM TECHNICAL JOURNAL 



conduction area one can derive, in much the same manner as for Eq. 

 (6), the relationship 



72 = vJ'-{Rzyi(R + zy, (10) 



where i^ = i-^ = • • • ij^. Since v is proportional to ^^ we have by Eq. 

 (9a) the relationship v = Const, /e (2"+2)/(2«+.-)) Substitutinj^^ this into 

 Eq. (10) we get 



? = Const. .i^^2„ii)/(2,.(:o 2;7(/^ + Z)-', 



and if we make Z large compared with R this becomes 



7 = Const. i?(2,.+4)/(2«+3)_ (11) 



Comparing this with Eq. (2), the experimentally derived relationship 

 between noise and contact resistance, we get n = 0.5. Goucher ^ 

 found by elastic measurements the value oi n = 0.6." In view of the 

 fact that a slight change in the experimental value of the exponent /3 in 

 Eq. (2) causes a rather large change in the value of n thereby de- 

 termined from Eq. (11), we can say that the agreement between the 

 results obtained from elastic measurements and noise measurements is 

 surprisingly good, and that this agreement supports the hypothesis 

 regarding the nature of a contact. ^^ 



In discussing the hypothesis that there exists a region of secondary 

 conduction which is responsible for the noise, we have not made any 

 assumption as to the nature of the secondary conduction. Several 

 possibilities, however, have occurred to us, one of which it seems 

 desirable to mention at this time. 



If one assumes that the thermo-mechanical vibrations of a solid 

 extend to the outside surface, then it is possible that the wave crests 

 may be able to make periodic electrical contact across the secondary 

 conduction area assumed in our hypothesis. This would permit a 

 pulsating current to flow, the frequency of which, it is supposed, is 

 determined by the frequency of the oscillator. For oscillators of 

 audible frequencies the hiw of energy equipartition applies and each 

 oscillator will ha\e the usual 1/2 kT of energy per degree of freedom. 

 The energy of an elastic oscillator is also proportional to {B • FY, where 



" Goucher found a discrepancy between the measured resistance-displacement, 

 resistance-force, and force-displacement relationships. But for reasons stated in 

 his paper we are inclined to accept the distribution function found from the force- 

 displacement measurements. 



'^ If one assumes the existence of a film in the contact, which some older theories 

 of microphonic action do, and that the number of independent elements of area 

 throu^di which current is conducted is proportional to the area of this film then 

 one is led to the verv unsatisfactory conclusion that ;/ = — 3.5. 



