Prof. E. Edlund on Unipolar Induction. 293 



net is put in motion round them, seeing that the phenomenon 

 can only depend on the relative motion between the magnet 

 and those molecules. If, then, it is proved by the above- 

 mentioned experiments that the magnet acts on an electric 

 molecule in rotation about it, it must equally act on the mole- 

 cule if the latter is at rest while the magnet moves round it. 

 This certainly ought to be the case, and we shall see examples 

 of it in the sequel. 



Let us imagine the cylinder divided into vertical columns, 

 each presenting a section equal to unity. To determine quanti- 

 tatively the force of induction produced in the cylinder by 

 the magnet, it will be sufficient to take one of the columns 

 into consideration. Let us represent the magnet by ab 

 (Plate VIII. fig. 1), and name one of the columns dc, the dis- 

 tance of which from the magnet shall be indicated by r. Let 

 5 designate the south pole, and n the north pole, and 21 the 

 distance from the one to the other. Suppose that the cylinder, 

 viewed from above, revolves round the magnet in the opposite 

 direction to that of the hands of a watch. The excess of aether 

 (electropositive fluid) will then collect at the extremities of the 

 column, and the deficiency will make itself sensible in the 

 centre. If the angular velocity be designated by v, the velo- 

 city of the column will be equal to rv. The intensity of a 

 current can be expressed by qav, in which q denotes a constant, 

 a the section of the conductor, and v the velocity of the elec- 

 tric fluid. The intensity of the current produced by the rota- 

 tion in any element dz can then be designated by grvdz, in 

 which q is a constant, and rv, as we have seen, the velocity of 

 the before-mentioned element. If straight lines be drawn from 

 the two poles to the element dz situated in k at the distance z 

 from the line fe, and if leg and hh are perpendicular to the lines 

 mentioned, the south pole will drive the aether (electropositive 

 fluid) along kg, while the north pole will lead it along kh. 

 Designating by M the intensity of the magnetic poles, the 

 first force will be represented by 



and the second by 



+ Mqrvdz 



Mqrvdz 



(l+zf + r* 



The component of these forces along the column cd will then be 

 + Mgr 2 vdz Mqr 2 vdz 



