FL UCTUA TIONS IN MICROPHONES A ND OTHER RESISTA NCES 223 



B is the amplitude and F the frequency. From these two expressions 

 of the energy we get B ~ F~^ T^'^. The area of secondary electrical 

 conduction surrounding each hill in coincidence is proportional to B, 

 and since this area determines the number of elements of area through 

 which secondary conduction takes place, as assumed in the derivation 

 of Eq. (11), we arrive at the conclusion that 



7- = Const. F' r'\ (12) 



While the hypothesis leading to Eq. (12) is only intended as a sugges- 

 tion it does explain the inverse frequency relationship, and the temper- 

 ature relationship is not an impossible one judging from the past un- 

 satisfactory measurements. It may be possible, also, to explain the 

 departure of a in Eq. (1) from the value 2, for one would expect electro- 

 static forces to distort the contacting surfaces so that the secondary 

 conduction area would become smaller as the voltage increases. A 

 satisfactory experiment on the effect of temperature on noise will do 

 much to establish or disprove the tenability of this hypothesis. 



Brillouin ^^ has recently derived an expression for the noise in a 

 conductor carrying a current by using the statistical method to deduce 

 the most probable distribution of the electrons in such a system when 

 it is in equilibrium. This method of calculation gives a noise energy, 

 in addition to thermal noise, which is proportional to the square of the 

 current and inversely proportional to the volume of the conducting 

 material. We have made a calculation of the relative magnitudes of 

 the two terms in Brillouin's equation which correspond to our experi- 

 mental conditions. Assuming reasonable dimensions for a carbon 

 contact and a current density as high as any we used it turns out that 

 the magnitude of the term for contact noise is far below^ that for 

 thermal noise. Furthermore it seems to us that Brillouin's mecha- 

 nism would require a fiat frequency distribution of noise rather than the 

 distribution which we have observed. For these reasons we do not 

 i)elieve that the noise which we have studied is produced by the 

 mechanism postulated by Brillouin. 



In conclusion we wish to acknowledge our indebtedness to Dr. J. B. 

 Johnson and Dr. F. S. Goucher for the helpful criticism they have 

 given us during the course of this work. 



I'L. Brillouin, Helv. Phys. Acta, Supt. 2, 7, 47 (1934). This theory is intended 

 to explain the "Fluctuations de resistance dans un conducteur mt-tallique de faible 

 volume," reported by M. J. Rernamont, Comptes Rendus 198, 1755 (1934); ibid. 

 198, 2144 (1934). 



