Vol.. 7, 1921 
PHYSICS: P. W. BRIDGMAN 
299 
MEASUREMENTS OF THE DEVIATION FROM OHM'S LAW IN 
METALS AT HIGH CURRENT DENSITIES 
By P. W. Bridgman 
Jefferson Physical Laboratory, Harvard University 
Communicated August 10, 1921 
Any picture of the mechanism of current conduction in metals which takes 
account of the part played by the electrons would lead to the expecta- 
tion of departures from Ohm's law at high current densities. On the clas- 
sical free electron basis J. J. Thomson has shown that at currents of the 
order of 10 9 amp. /cm 2 , the current would be expected to increase as the 
square root of the applied E. M. F., and hence that the resistance will 
increase indefinitely. Many attempts have been made to detect the 
existence of this effect experimentally, but without success. The chief 
source of difficulty has been the necessity for separating the change of 
resistance due to the great temperature rise under the heavy current 
from the change due to a departure from Ohm's law. The best known 
attempt in this direction is perhaps that of Maxwell. 1 Assuming that the 
departure from Ohm's law must be proportional to the square of the cur- 
rent, which is plausible on grounds of symmetry, he showed that at a 
density of 1 amp. /cm 2 , the resistance of platinum, iron, and German silver 
does not differ by more than 1 part in 10 12 from the resistance at infinitely 
small currents. His maximum density was about 5 X 10 4 amp. /cm 2 . 
By the application of a new method I have been able to eliminate the 
source of error due to temperature rise, to detect the existence of the effect, 
and to measure it with a fair degree of accuracy. The specimen is made 
one of the arms of a bridge, and is 
traversed simultaneously by a heavy 
direct current and a small superposed 
alternating current of acoustical fre- 
quency. The resistance of the speci- 
men to the direct current is measured 
with an ordinary galvanometer, and f* 
the resistance to the alternating cur- ^ 
rent is measured at the same time 6 
with a telephone. If there is a de- 
parture from Ohm's law under the 
heavy current, that is if the relation 
between current and E. M. F. is 
not linear, the two resistances will 
not be equal, and from their differ- 
ence the departure from Ohm's law CURRENT 
may be calculated. The reason for fig. i 
