HALL'S PHENOMENON, 623 



Explained in this manner, Hall's phenomenon would seem to be 

 in contradiction with the opinion generally adopted, that in electro- 

 magnetic phenomena the action is exerted on the supports of the 

 currents, and not on the current itself. But, however we may 

 explain the experiment, it follows that a magnetic field in the 

 stationary state develops an electromotive force which tends to move 

 electricity in the direction of the electromagnetic action that is, to 

 the left of an observer placed in the current, and who is Booking in 

 the direction of the magnetic force. 



As the effect in question is very small, the most natural hypo- 

 thesis, which moreover is approximately verified by Hall's experi- 

 ments, is to assume that it is proportional to the electromagnetic 

 force. 



641. GENERAL EQUATIONS. Let A, B, C be the components of 

 this new electromotive force, and suppose' that we are dealing with a 

 magnetic medium. The component A, which acts along the x axis, 

 is the algebraical sum of the two actions exerted on the components 

 v' and w' of the flow of electricity along the y axis, and along the 

 z axis ; the former is proportional to - Zz/ and the second to Yw'. 

 If y is the coefficient of proportionality we shall have 



(30) B=y(Z'-X/), 



C = y(Xz/-Y<). 



The components of the total electromotive force of the field 

 become then 



<3<> (> i 



^ = ~1J7 



Introducing the new electromotive forces, equations (15) give 



0, etc. 



