ELECTRIC INDUCTION. 289 



conducting sheet will be identical with that of the electric currents which 

 actually exist in the sheet. 



Before proceeding to prove this statement, let us take notice of the form 

 which it assumes in certain cases. 



10. Let us suppose the real system to be an electro-magnet, and that its 

 intensity, originally zero, suddenly becomes /, and then remains constant. At 

 this instant a positive image is formed, which begins to travel along the 

 normal with velocity R. After an interval 8t another positive image is formed ; 

 but at the same instant a second negative image is formed at the same place, 

 which exactly neutralizes its effect. Hence the result is, that a single positive 

 image travels by itself along the normal with velocity R. The magnetic effect of 

 this image on the positive side of the sheet is equivalent to that of the currents 

 of induction actually existing in the sheet, and the diminution of this effect, as 

 the image moves away from the sheet, accurately represents the effect of the 

 currents of induction, which gradually decay on account of the resistance of the 

 sheet. After a sufficient time, the image is so distant that its effects are no 

 longer sensible on the positive side of the sheet. If the current of the electro- 

 magnet be now broken, there will be no more images ; but the last negative 

 image of the train will be left unneutralized, and will move away from the sheet 

 with velocity R. The currents in the sheet will therefore be of the same 

 magnitude as those which followed the excitement of the electro-magnet, but in 

 the opposite direction. 



11. It appears from this that, when the electro-magnet is increasing in 

 intensity, it will be acted on by a repulsive force from the sheet, and when 

 its intensity is diminishing, it will be attracted towards the sheet. 



It also appears that if any system of currents is produced in the sheet 

 and then left to itself, the effect of the decay of the currents, as observed at 

 a point on the positive side of the sheet, will be the same as if the sheet, with 

 its currents remaining constant, had been carried away in the negative direction 

 with velocity R. 



12. If a magnetic pole of strength m is brought from an infinite distance 

 along a normal to the sheet with a uniform velocity v towards the sheet, it 

 will be repelled with a force 



m* v 

 4z> R + v' 

 where z is the distance from the sheet at the given instant. 



VOL. ii. 37 



