FAILURE OF OHM's LAW AT HIGH CURRENT DENSITIES. 133 



constancy, for it is obvious that the durations of the large and the 

 small currents must be absolutely constant. A platinum contact 

 dipping into a mercury cup and driven by a tuning fork was used, but 

 always gave trouble, and the limits of accuracy were set by this part 

 of the apparatus. 



The conclusion as usually quoted which was drawn from these 

 experiments was that any deviation from Ohm's law must be less 

 than one part in 10^^. This statement needs some expansion; it is 

 obvious that no measurements can be made directly to this degree of 

 accuracy. For one thing, changes of temperature of the surroundings 

 absolutely preclude the direct attainment of any such accuracy as this. 

 The meaning of the statement is as follows. Maxwell remarked that 

 any departure from Ohm's law must involve only even powers of the 

 current ; it is obvious that the first power cannot enter, for if so there 

 will be a dependence of resistance on the direction of the current, which 

 cannot be the case in an isotropic material. The initial departures 

 from the law may be supposed to be proportional to the square of the 

 current density. The maximum current density employed by Max- 

 well was 5.6 X lO"* amp/cm^. At this density the resistance was found 

 to have changed by not as much as 0.3%. Assuming the square law, 

 this means that at a current density of 1 amp/cm- the departure from 

 Ohm's law cannot be more than 1 part in 10^^. The original paper 

 contains the careful statement of the conclusion in this form. 



The metals used by Maxwell were cylindrical wires of platinum 

 (0.042 mm. diameter), German silver (0.051 mm.) and iron (0.14 mm.). 

 The maximum current densities were respectively 3.4, 1.2, and 5.6 X 

 10* amp/cm2. 



Recently Wenner ^ of the Bureau of Standards has objected to the 

 second form of Maxwell's experiment. He has repeated a modifica- 

 tion of the first method with very much higher accuracy, and finds no 

 deviation of as much as 3 parts in 10^. His objection to the second 

 experiment is that negative results might be obtained even if there is a 

 departure from Ohm's law. Thus if the potential difference across 

 each arm of the bridge is proportional to the square of the current 

 flowing through it, negative results will be obtained, because the 

 bridge will stay in balance for any current, large or small. More 

 generally, negative results will be found if the potential difference 

 across each arm is the same function of the current for each arm. It 

 is to be noticed, however, that this is not the manner of departure 

 from Ohm's law which is to be expected. The departure sought for is 

 not a function of the total current flowing through the resistance, but 



