by a Magnet in a Rotating Conductor. 



515 



Hence if pdaf dy 1 dz ] denote the quantity of magnetic fluid con- 

 tained in the volume-element dx ] dy 1 dz 1 outside the conductor, 



and 



^$£&>ijf& 



(8) 



the potential of the given magnetic distribution, the required 

 components of the total electromotive action at the point #, y, z 

 will be 



A= 2 *{*g-*|?}, 



■4 P I- 



Since, by hypothesis, there is no magnetic matter within the 

 rotating conductor, we have, by a well-known theorem, 



AP=0. (9) 



3. If V be the potential of the free electricity existing on the 

 rotating conductor, and K the conductibility of the latter, the 

 components of the current-density at the point x, y, z will be 



Putting 



«= K {-s +x+A y 



"= K {-U +z+c }-J 



(10) 



bp 



»-»feM£-M)J 



(ii) 



we have 



X + A=bN~fa)Mn 



Y + B=foL-uN, I 



Z + C = uM-bL 3 J 



from which expressions we deduce immediately the relation 



u(X + A)H-b(Y+B)+fo(Z + C)=0, 



2L2 



(12) 



