NEW YORK 



SOTANJCAS, 



THE FAILURE OF OHM'S LAW IN GOLD AND SILVER AT 

 HIGH CURRENT DENSITIES. 



By p. W. Bridgman. 



Received October 7, 1921. Presented October 19, 1921. 



TABLE OF CONTENTS. 



Page. 



Introduction 1^1 



Historical Survey ]^^ 



Outline of Method 1^5 



Experimental Details |42 



Dimensional Discussion of the Cooling Process 149 



Various Experimental Checks and Precautions 153 



Experimental Procedure and Data 159 



Other Possible Explanations of the Effect 164 



Computation of the Departure from Ohm's Law 166 



Theoretical Discussion 168 



Summary ^'^ 



Introduction. 



It is to be expected that at high current densities the usual Hnear 

 relation between current and E.M.F. in a metal will break down, 

 that is, that Ohm's law will fail. J. J. Thomson,^ for instance, has 

 shown that on the basis of the classical free electron theory of metallic 

 conduction the current will eventually increase only as the square root 

 of the E.M.F. at very high values, which means that the resistance will 

 increase at high current densities. On the usual assumptions the 

 current densities at which this effect will become important are of the 

 order of 10'^ amp/cm^. Many attempts have been made to detect 

 the existence of this effect experimentally, but hitherto without suc- 

 cess. The chief obstacle to success is that the changes of resistance 

 due to heating by the heavy current are sufficient to mask the changes 

 of resistance due to a possible departure from Ohm's law. 



By the employment of a new method of attack, which avoids errors 

 due to temperature rise, I have, I believe, not only succeeded in 

 establishing the existence of the effect, but in measuring the departures 

 from Ohm's law with some exactness in gold and silver. These 

 results are described in the following paper. I find a departure from 

 Ohm's law in the direction of an increase of resistance at high current 

 densities, the maximum effect being of the order of 1% at a current 

 density of 5 X 10*' amp/cm-. 



