FAILURE OF OHM S LAW AT HIGH CURRENT DENSITIES. 



135 



found. The material used was constantan, of a diameter of 0.1 mm. 

 The maximum current density reached produced a potential gradient 

 in the wire of 400 volts per cm. With "Kruppin" wire, a gradient 

 of 1500 volts/cm. was reached, although with not so high a current 

 density. In spite of the very considerable error, these experiments 

 have pushed the boundary of the validity of Ohm's law considerably 

 farther back than the previous limit. With regard to the materials 

 used, it should be said that the maximum departure from the law is 

 to be expected in those materials which, other things being equal, have 

 a long free electronic path, and which are presumably the best con- 

 ductors. From this point of view the most promising place to look 

 for the effect is in silver, copper, and gold. Of course, on the other 

 hand, it is to be said that in poor conductors it is possible to reach 

 much higher potential gradients for the same current density, so that 

 this advantage may outweigh the disadvantage. 



Outline of Method. 



In the method which I have used, the specimen exposed to the high 

 current density is made one arm of a bridge, and its resistance is meas- 



FlGURE 1, 

 connections. 



Skeleton of the bridge 



ured simultaneously for a heavy 

 direct current and a small superposed 

 sinusoidal current of acoustical fre- 

 quency. If there is a deviation from 

 Ohm's law the resistances to the two 

 currents will not be the same. The 

 following considerations show why 

 thfs is. It must in the first place be 

 remembered that a bridge is an instrument for testing the equality 

 of potential of two points in a net work. In Figure 1, x denotes 

 the arm of the bridge which contains the fine wire in which the 



Figure 2. Hypothetical re- 

 lation between current (I) and 

 e.m.f. (E) not satisfying Ohm's 

 law. 



