i ELECTRIC DfDUCTIOX. 



This formula will not apply to the caae of the pole moving away from the 

 beet, because in that caae we must take account of the currents which are 

 excited when the pole begins to move, wliich it does when near the sheet 



13. If the magnetic pole moves in a straight line parallel to the sheet, 

 with uniform velocity r, it will be acted on by a force in the opposite direct i 

 to its motion, and equal to 



Besides this retarding force, it is acted on by a force repelling it from the 

 sheet, equal to 



14. If the pole moves uniformly in a circle, the trail is in the form of a 

 helix, and the calculation of its effect is more difficult ; it is easy, however, to 

 see that, besides the retarding force and the repelling force, there is also a force 

 towards the centre of the circle. 



15. It is shewn, in my treatise On Electricity and Magnetism (Vol. n. 

 Art. 600), that the currents in any system are the same, whether the conducting 

 system or the inducing system be in motion, provided the relative motion is 

 the same. Hence the results already given are directly applicable to the case 

 of Arago's rotating disk, provided the induced currents are not sensibly affected 

 by the limitation arising from the edge of the disk. These will introduce other 

 seta of images, which we shall not now investigate. 



16. The greater the resistance of the sheet, whether from its thinness or 

 from the low conducting-power of its material, the greater is the velocity //. 

 Hence in most actual cases R is very great compared with v the velocity <)' 

 the external system, and the trail of images is nearly normal to the sheet, and 

 the induced currents differ little from those which arise from the direct action 

 of the external system (see 1). 



17. If the conductivity of the sheet were infinite, or its resistance zero, 

 R would be zero. The images, once formed, would remain stationary, and all 

 except the bat formed positive image would be neutralized. Hence the trail 



