568 PHENOMENA OF INDUCTION IN NON-LINEAR CONDUCTORS. 



The triangle ABB', gives also 



a- a sin 



or 



us'mO Usina 



a =a 



2C 



Substituting these values of h' and a! in the expressions of the 

 components, and neglecting quantities of the second order, we get 



~4' 2 U 



m R a 

 X= - s^r tan . 



4^ 2 U 2 



The force itself makes with the surface an angle /?, determined 

 by the conditions 



Z U-R a 



The induced currents act thus in opposition to the motion of 

 the pole, as might be foreseen ; but it is not directly opposed. 



If the motion of the pole is perpendicular to that of the 

 shell, we have = 0, a = 0, and U = R + ; we get then 



m 

 f-i = - 



The action is the same as that of a single mass equal to 

 m - -- , situate at each instant at the point B symmetrical with 

 the position of the pole, or of a mass - placed at the base 

 of the perpendicular let fall from the pole upon the plane. 



If the pole is displaced parallel to the plane, we have 



JS. 



