by a Magnet in a Rotating Conductor. 527 



one another indefinitely, and the current-curves degenerate to a 

 system of circles 



having the axis of f for a common tangent. This is the same 

 system of circles as that which Felici found in the case where 

 the pole was situated in the plane of an infinitely thin disc. It 

 must, however, be observed that this case is only admissible as 

 a limiting one, since the electromotive force, which is propor- 



tional to ^— , is equal to zero for all points of the disc, with the 



exception of the point f=0, 77 = 0, where it, together with the 

 potential V and the current-intensity, becomes infinite. 



The components of the action of a system of closed currents 

 on a magnetic pole m situated at a point x } y, z external to the 

 conductor are given by the known formulas 



W = m\ U - 



**=&£&=* M1iM % 



which are expressible thus : 



>HE-£> »-<&-S> "HB-» 



provided the integrals a, j3 3 7 have the same signification for an 

 external point as they previously had for an internal one. In 

 the case under consideration, of course 



y = 0. 

 If we assume 



and 



then, since vanishes at infinity, we have, by partial inte- 



gration, 



