HALL. — CONDUCTIVITY OF MILD STEEL. 



299 



and the difference of potential between the top and bottom of S2 is 

 E^ -\- rG. The mean of these two differences is \ (E^ + E^), the 

 same value as if there were no short circuit. 



If the element S.^, instead of being of the same size as Si had a 

 cross-section n times as great, it would have n times as much weight 

 as Si' in reckoning the mean difference of potential, which would 

 then be 



-4-, (^1 + « ^2) 



with open circuit, and 

 1 



« + 1 



Ei-rC]-\-n[E, 



n 



n + ] 



(Ei + n e\ 



with short circuit. This appears to show that the vertical components 

 of short-circuiting currents within the steel disk do not affect the 

 mean difference of potential between top and bottom. 



.Aug. 13 

 Sept. 2 



. Mean 

 ■-.Aug. 22 



Fig. 12. 



The non-effect of the horizontal components is shown by the con- 

 sideration that a horizontal current, maintained in the disk by exter- 



