2 ( J4 Prof. E. Edlund on Unipolar Induction. 



Supposing the length of the cylinder equal to the distance 

 between the poles of the magnet, or 21, by integration we shall 

 obtain the force conducting the electric fluid of the cylinder 

 to its extremities, namely 



2Mqvl[ — j 1 r l . . . (A) 



This last expression constitutes the electromotive force pro- 

 duced. 



We will now see if this expression of the electromotive force 

 conforms to the exigences of the mechanical theory of heat. 

 If a current equal to unity be made to pass through the column 

 from / to d, the column begins to rotate in the opposite direc- 

 tion to that in which we considered it to move by the action 

 of the external mechanical force. From the law previously 

 given, it is easy to calculate the force with which the mag- 

 net acts upon the current. The squares of the distances of the 

 two poles from the element dz, situated at the distance z from 

 the line fe, are (l—z) 2 + r 2 and (I + z) 2 + r 2 ; and sin X is equal, 



in the two cases, to r and i respec- 



[(*-*)* + *'? [(l + z) 2 + r 2 Y* 



tively. The force with which the magnet acts upon the cur- 

 rent in the direction normal to the plane containing the poles 

 of the magnet and the element dz is therefore 



Wrdz Ylrdz 



[(l-zf + ff [(l + z) 2 + rrf 



the integral of which, between the limits indicated, is 



It has been demonstrated in my memoir* that, according to 

 the mechanical theory of heat, the electromotive force of in- 

 duction resulting from the rotation of the cylinder with a 

 velocity w = rv will be equal to a constant (the value of which 

 depends on the unit chosen to designate the intensity of the 

 current) multiplied by the product of the expression (B) and 

 rv. In fact, by multiplying rv into that expression we find 

 again the previously given expression (A). 



We obtain, then, the following result : — If it be admitted 

 that, in the case in question, unipolar induction is produced 

 by the action of the magnet on the currents due to the electric 

 molecules being carried along in the direction of the rotation 

 of the cylinder, we shall get for the electromotive force an ex- 

 * Wiedemann's Annalen, vol. ii. p. 347. 



