558 PHENOMENA OF INDUCTION IN NON-LINEAR CONDUCTORS. 



On the contrary, the tangential component along a perpendicular 

 to the stream-lines is discontinuous, and on both sides of the 

 surface we have 



on on an 



The value of V may also be expressed (360) as a function of 

 the potential Q of a layer which covered the same surface, and 

 the density of which is equal at each point to the strength < of 

 the shell. 



575. CASE OF A PLANE SHELL. Let us consider, as a special 

 case, a plane conducting plate in the plane xy, and suppose that 

 the positive face of the currents is at the top ; the potential of 

 the corresponding magnetic shell at a point whose co-ordinates are 

 x, y y and z, is expressed by (362) 



The function Q which represents the potential of a layer whose 

 density at each point is equal to the magnetic strength of the shell, 

 is symmetrical in respect of the xy plane, and does not change 

 when z is replaced by -2. The function V, on the other hand, 

 changes its sign with z, and its absolute value is the same at two 

 points which are symmetrical in reference to the shell. We have 

 therefore, for corresponding points of the positive and of the 

 negative face, 



The components X and Y of the magnetic force parallel to 

 the axes on the positive face, and the values of these components 

 X' and Y' on the negative face, are given by the equations 



Y= _^__ 27r ^ 



JL. ^ / _ 



oy oy 



