Prof. E. Edlund on Unipolar Induction. 297 



rest and the axis were revolving round it with the same an- 

 gular velocity. As regards the induction in the metallic disk, 

 it can be determined in the following manner : — 



Let a (fig. 4) be the point of the disk in which the axis 

 is fixed, m that in which the disk is traversed by the magnet, 

 and p the distance between these points. The rotation-velocity 

 may then be expressed by pv, v denoting the angular velocity, 

 and this being effected in the direction from m to b. Any 

 point, q, of the disk, at the distance r from the axis, will then 

 move with the rotation-velocity rv in the direction qs. In 

 order to determine the induction at the point q, we now give 

 to the magnet and to the point q the velocity pv, but in a di- 

 rection opposite to that previously impressed on the magnet. 

 This comes to rest, and the point q receives a velocity equal in 

 quantity and direction to the resultant of the two velocities pv 

 and rv, represented in the figure by the lines qt and qs. The 

 angle qsw being equal to the angle «, the value of that resultant 

 will be 



v n/ r 2 +p 2 — 2rp cos a. 



Now *S r 2 +p 2 — 2rpcosa. denotes the distance at which q lies 

 from m, the point at which the magnet is fixed in the disk. 

 Consequently the point q receives the same velocity as if it 

 moved round the fixed magnet. As this applies to any point 

 whatever, it follows that the induction produced in the disk 

 during its motion round the axis will be the same as if the 

 disk moved round the magnet with the same velocity of rota- 

 tion. 



The following case of induction permits the intensity of the 

 induced current to be compared with the result obtained by 

 calculation : — In fig. 5, sm represents a magnet having its 

 south pole in s and its north pole in m. At the centre of the 

 magnet and near the south pole are two brass bars of equal 

 length, ab and cd, fixed perpendicular to the axis of the mag- 

 net. The bar ab is insulated from the magnet, and furnished 

 at its lower side with a cylinder which is soldered to it, sur- 

 rounding the magnet without being in contact with it. Upon 

 this cylinder slides a metal spring connected to the galvano- 

 meter by the wire L The other bar, cd, is in metallic contact 

 with the magnet; it carries at its upper extremity a mercury- 

 cup, into which dips the second wire, /', coming from the gal- 

 vanometer. 



The two brass bars are joined together by the cylinders ac 

 and bd of the same metal. These cylinders can be placed at 

 different distances from the magnet, either one on each side 

 or both on the same side of it. If this apparatus be put in 



