29$ .Prof. E. Edlund on Unipolar Induction. 



rotation about the axis of the magnet so that, viewed from 

 above, it moves in the opposite direction to the hands of a 

 watch, an induced current is obtained passing from the mer- 

 cury-cup, through the galvanometer, to the spring that slides 

 upon the metal cylinder. We will now calculate the intensity 

 of this induced current. 



An electric element dr, situated in t, at the distance r from 

 the magnet, has a velocity which may be designated by rv if 

 v signifies the angular velocity. Upon this element the two 

 poles exert equal actions, the one along the right line tu, the 

 other along tw. Taking the component of these forces in the 

 direction ab, we shall get (21 signifying the distance between 

 the poles, M the magnetic moment of the poles, and k a con- 

 stant) 



2M.vlrdr 



(P + r 2 )?' 



Integrating this expression between the limits r = and 

 r=r (this last denoting the distance between the magnet and 

 the cylinder ac), we get, for the total electromotive force in- 

 duced in the bar ao, 



2M.V- 2kMv \ (0) 



(P+t-)- 



The two poles tend to drive in opposite directions an elec- 

 tric element dz of the bar ac, situated at the distance z from 

 the point a ; but the action of the south pole is the more pow- 

 erful, because that pole is nearer to dz than the other. The 

 resultant of their action will be 



Integrating between the limits z=0 and z—l, we get, as 

 the expression of the total of the electromotive force induced 

 in the cylinder ac, 



2kMvl 2kMvl 



(*»+f»* (4J» + t#* ( } 



For the calculation of the electromotive force induced in 

 the bar cs, the north pole will be sufficient to take into consi- 

 deration, since the south pole, acting perpendicularly to the 

 length of this bar, does not contribute to the transfer of the 

 electric molecules. It is moreover evident that the electro- 

 motive force induced in cs acts in a direction opposite to 

 that of the forces induced in ao and ac. The expression 



