by a Magnet in a Rotating Conductor, 513 



x -*{4;-t-f)-Kg4;)Kj 



-{■®-g)-<S?-g)}J 



Before proceeding to the establishment of the corresponding 

 expressions for the components of the electromotive forces pro- 

 duced by the given magnetic distribution, we shall examine a 

 few properties of the integrals a, /3, y, of which use will be sub- 

 sequently made. Employing the general notation 



it is manifest that, for every point within the conductor, 



A«=— 47rw, A/3= — 4iirv } Ay=— 47rw\ . . (5) 

 Further, 



~ 1 



if? + *i + 9* = CW-J+W-yHW-'ty dy , d2 t 



d^ a- 



r . r 





both of which last integrals vanish in consequence of the equa- 

 tions (1) and (2) ; so that 



|ff + M + |y =0 (6 ) 



d# oy B* v 



In consequence of this relation (6), the equations (5) assume the 

 forms 



B*\a y a«; 3*Va» By/ - ' 



2. In order to exhibit the differential equations of the motion 

 of electricity, we have now merely to determine the electromotive 

 forces originated by the given magnetic distribution outside the 



Phil. Mag. S. 4. No. 185. Suppl. Vol. 27. 2 L 



(7) 



