FAILURE OF OHM's LAW AT HIGH CURRENTT DENSITIES. 141 



If now the alternations are slow, so that at every moment the wire 

 is approximately in thermal equilibrium, the factor of proportionality 

 connecting ri with the alternating heat input is the same as that con- 

 nectin ^ tq with the steady heat input, so that we would have 



To = const h" R I 

 Ti = const 2/iii R ) 



which gives, substituting above in (10), 



AR' 



AR 



= 9 



That is, for slow alternations, the difference between A.C. and D.C. 

 settings due to the microphone action alone is twice the D.C. shift due 

 to temperature rise under the steady current, and this relation holds 

 no matter how feeble the alternating current. Since the steady rise of 

 temperature is high, because the current density has to be pushed to 

 the limit that the conductor will carr}^ without burning out, it is 

 obvious that at slow alternations the microphone action will entirely 

 mask anv sought for deviation from Ohm's law. The acoustical 

 frequencies used in these experiments were not low enough to reach 

 the extreme value 2 for the ratio AR' /AR. At the lowest frequency, 

 320 cycles, the ratio had reached about 1.2. 



At rapid rates of alternation, however, the conditions of heat 

 transfer change. Kt low frequencies the thermal conductivity of the 

 surroundings alone determines the equilibrium; at higher frequencies 

 part of the heat input is used in raising the temperature of the sur- 

 roundings and a term enters proportional to the specific heat, and at 

 still higher frequencies this term preponderates, and the factor of 

 proportionality between amplitude of rate of heat input and amplitude 

 of temperature alternation becomes proportional to the specific heat 

 and inversely proportional to the frequency. We shall later apply 

 a dimensional analysis to obtain more information about tq and ri, 

 but for the present we may write, for any frequency 



and as before 

 This now gives 



Ti = const /(co) 2/i/i R, 

 To — const /i" R. 

 AR' 



AR 



= 2/(c.). 



