Prof. A. Schuster on Magnetic Precession. 317 



Hence we may divide the electric forces into two parts, 

 one of which may be derived from a potential. This latter 

 portion will produce electrification and ultimately be coun- 

 terbalanced by electric charges having a potential equal to 

 — ^/jLcoal cos (/> sin 26/t. The remaining portion of the electric 

 forces will be 



W E = /ucolcos sin <f> It. .... (3) 



^ s = ~ A tft)Icos^ (4) 



These electric forces will tend to produce currents which 

 .are of the same type as those assumed to exist, but turned 

 through a right angle in a direction opposed to that of the 

 angular velocity. This is seen by comparing equations (1) 

 and (2) with (3) and (4), and noting that the latter becomes 



proportional to the former when ( <f> + ^ I is substituted for <fi. 



Hence the effect of these forces will be to add a system of 

 currents which will have the same effect as a rotation of 

 the original system in a direction opposite to that of the 

 rotating sphere. 



4. To show that the whole system of currents will rotate 

 in the body and to determine the period of rotation some 

 further calculations are necessary. The system of currents 

 we are considering will produce a uniform magnetic field, M, 



Q 



within the sphere, which is equal to = irl. The energy of 

 ;the total magnetic field is easily found to be 



pi 2 a 3 =^77*IV. 

 2 9 



Now imagine such a system of currents as we have been con- 

 sidering, in which the current crossing an element ds x of the 

 arc QA (fig. 1) is I sin a. ds^ and let electric forces equal to 

 A sin a act at each point on the system of currents. If ds 2 

 is an element of the line along which the forces act, the rate 

 .of doing work in the surface element ds 1 ds 2 is AI sin 2 a ds l ds 2 . 

 Hence the rate of doing work over the whole sphere is 



\ Al sin 2 a ds 1 ds 2 = '2irXIa 2 \ sin 3 acta 



8tt a t 

 = ^-AL 



The currents will increase in intensity and the rate of doing 

 work must be equal to the rate of increase of energy. Hence, 



