producing Arago's Rotation. 287 



In case (1) the increasing pole induces in the portion of the 

 sheet opposite to itself a circular current opposite in direction 

 to the currents representing the poles. Hence this portion of 

 the sheet is repelled by both poles. The repulsion from the 

 increasing pole is perpendicular to the sheet, and gives it no 

 tendency to move ; but the repulsion from the other pole tends 

 to move the sheet from the constant pole toward the one which 

 is increasing. 



In case (2) the diminishing pole induces in the portion of 

 the sheet opposite to it a circular current in the same direction 

 as those representing the poles ; so that this portion of the 

 disk is attracted by both poles, and the disk tends to move from 

 the diminishing pole toward the one which is constant. 



In cases (3) and (4) it can easily be shown that the results 

 are the opposite to those obtained in cases (1) and (2) respec- 

 tively. 



If one pole increases while the other diminishes, both ten- 

 dencies to move are in the same direction, and the resulting 

 tendency is the sum of the two. 



The pole of an electromagnet made or broken is the extreme 

 case of a pole increasing or diminishing. 



Now conceive an even number of vertical bar electromag- 

 nets arranged in a circle with their upper poles in one hori- 

 zontal plane, and a copper disk to be suspended above them ; 

 and the two magnets at the extremities of each diameter to be 

 coupled together, and with a battery, so that each such pair 

 of magnets forms a horseshoe electromagnet independent of 

 all the others. Let P, Q, B, S be pairs of magnets at the 

 ends of successive diameters. Make P, and then make Q so 

 that the north pole of Q is adjacent to the north pole of P, 

 and therefore the south pole of Q adjacent to the south pole 

 of P. Then by case (1) the portion of the disk opposite the 

 north pole of P is driven towards the north pole of Q ; and a 

 similar action takes place at the south poles. Now break P. 

 By case (2) the portion opposite the north pole of P is again 

 driven towards the north pole of Q, and so with the south 

 poles. Continuing the action by making R, and then break- 

 ing Q, making S and then breaking P, and so on, in each 

 case making the adjacent poles similar, we get a series of im- 

 pulses on the disk all tending to make it move in one direc- 

 tion round the axis of suspension. Hence the disk will rotate 

 as in Arago's experiment. 



In one extreme case, viz. when the number of electromag- 

 nets is infinite, we have the case of a uniform rotation of the 

 magnetic field, such as Ave obtain by rotating permanent- 

 magnets. 



