of the Hall Effect and Allied Phenomena. 537 



special cases examined by Hall, Nernsfc, von Ettingshausen, 

 Righi, and Lednc we obtain at once a detailed account of 

 their respective results. We now proceed at once to this 

 examination. 



5. The Hall Effect. 



In Hall's experiments the induced potential gradient in a 

 direction perpendicular to the magnetic force and current 

 flux which is necessary to maintain the current in its un- 

 disturbed path is determined by a statical measurement. 

 If the magnetic field is in the direction of the A'-axis and the 

 current is flowing along the y-axis, then the conditions 

 parallel to the £-axis are to be such that there is no electric 

 flux in that direction. There are of course no temperature 

 effects to be reckoned with in this case, and the slight 

 accumulation of charge necessary to ensure the steady 

 conditions is entirely at the surface of the metal, so that in 

 the interior 



grad A = grad.ry = 0. 



The condition that there is no current along the r-axis is 

 then 





., ^ £L_'HE, 



mc 



If wo use J y to denote the component of the main current 

 in the direction of the y-axis, then 



J y = o-E y , 



where a is as above. AVe thus have 



(ffl«)(r(»+J)) 



This is exactly the form of the law which is usually adopted 

 to express the magnitude of this effect : the constant in this 

 equation which is defined to be the constant of the Hall 

 effect thus turns out to be 



El: 





