INDUCTION OF A MOVABLE MAGNETIC SYSTEM. 



563 



point B. After an infinitely small time /, the pole comes to A' 

 (Fig. 121), at the distance ut ; it is as if we suddenly and simul- 

 taneously brought a pole - m to A, and a pole + m to A', producing 

 images of the same sign at B and B' ; but at this moment the first 

 image + m, which was at B, has come to C at the distance R8/. At 

 the period 28?, the mass +m is at A" (Fig. 122). There are then 

 two images equal to -m at C and B', and three positive images at 

 B", C' and D ; and so on. 



LA' 



Fig. 120. 



Fig. 121. 



Fig. 122. 



If the motion is continuous, it will be seen that the action which 

 the movable pole undergoes is that of two magnetic lines, one 



positive and the other negative. If U is the resultant Ju 2 + R 2 of 



the two velocities, the density of these two lines will be - and 



Uo/ 



their distance yr&/ t ^ ie P r duct of the density by the distance is 



Ru 

 then m . These two lines form an unlimited magnetised ribbon, 



which starts from the point symmetrical with the actual position of 

 the pole, is situate in a plane passing through the trajectory of the 



pole, and makes with the plane of the sheet an angle whose tangent 



R 



is equal to . 

 u 



582. If the pole + m, instead of describing a right line, rotates 

 uniformly about an axis perpendicular to the sheet, we may suppose 

 that the band which precedes, forms a helix on the right cylinder 

 which has the circumference described by this pole for its base. 



002 



