by a Magnet in a Rotating Conductor. 519 



coordinates, the equations assume the forms 



or dz 



(22) 



OS $r J 



Since P, as a potential function of masses extern al to the con 

 ductors, satisfies the equation 



»(-© 



d 2 P n 



or ' d* 2 

 we deduce the value 



V=2w/tf( 



r^-dr-r^-'^). . . (23) 

 OZ or J v ' 



The equations (21), differentiated respectively according to 



*, V> *> g^e 



AV=4^|^ = -47re, .... (24) 



which determines the density e of the free electricity at every 

 point within the conductor. In order to find the density e at 

 any point of the conductor's surface, we have to remember that 

 by the equation (23) the value of V is given for every point of 

 this surface, that throughout the external space AV=0, and 

 that at infinity V must vanish. These conditions determine the 

 value of V a throughout external space, and by a known relation 

 we have 



da-©,-*- * 



For a sphere rotating under the influence of a constant magnetic 

 force, whose direction coincides with the axis of rotation, 



BP 



^— =T= const.; 



oz 



whence 



V.=nkTr 2 + const. 



Consequently, R being the radius of the sphere, and $ the angle 

 which the radius forms with the Z-axis, we obtain for each point 

 of the spherical surface the value 



V = rc£TR 2 sin 2 S + C. 

 By well-known methods we find, further, that 



