FAILURE OF OHM's LAW AT HIGH CURRENT DENSITIES. 153 



We now discuss the various experimental checks which were made 

 of the adequacy of the apparatus and the correctness of the assump- 

 tions underlying the mathematical discussion. One may perhaps 

 feel that I have gone too much into detail here, but in view of the 

 importance of the result, and the feeling of disquiet which must be 

 produced by the fact that the final result has to be obtained by an 

 extrapolation I do not believe that multiplication of precaution is 

 superfluous. 



Various Experimental Checks and Precautions. 



Relative Magnitude of D.C. and A.C. A fundamental requirement 

 of the experiment has been that the A.C. be small compared with the 

 D.C. If it is not, the cos^ term in the heat input becomes appreciable, 

 and the steady temperature rise is different when the A.C. is flowing 

 than when it is absent. This is easy to check experimentally. If the 

 A.C. is sufficiently small, the D.C. setting should be the same whether 

 the A.C. is flowing or not. This condition was checked repeatedly. 

 Before the experiments were begun the constants of the oscillating 

 circuit were so chosen for the different frequencies that the condition 

 should be met. In general the accuracy of setting for D.C. zero was 

 much greater than for A.C. zero. The latter could not usuallj^ be 

 set much closer than 0.5 mm. of bridge wire, whereas the D.C. balance 

 could be determined to 0.1 mm. Sometimes at the lower frequencies 

 there was a displacement of the D.C. balancing point by an appreci- 

 able amount when the A.C. was turned on, but less than the error in 

 the A.C. reading. Error at low frequencies does not affect the extra- 

 polation. At the high frequencies, however, any shift of D.C. balance 

 in the presence of the A.C. was less than 0.1 mm. An error of 0.1 mm. 

 in the slider setting means on the average an error of 1/20000 in the 

 resistance. 



An additional check was afforded by the requirement that the 

 difference between A.C. and D.C. settings (that is AR') should be 

 independent of the A.C. intensity over a considerable range of A.C. 

 intensity in the neighborhood of that used in the measurements. 

 This requirement is shown at once by the formula on page 152. At 

 constant D.C, i.e. constant AR, AR' is independent of the alternating 

 current. This requirement obviously continues to be demanded if 

 part of the AR' is due to a departure from Ohm's law of the kind for 

 which we are searching, for this departure depends only on the D.C. 

 density and not on the small A.C. This again was checked over the 



