of Unipolar Induction. 403 



current will always be the same as if the jacket only were in 

 rotation. 



3. If the magnet is in rotation whilst the jacket is at rest, 

 no current is produced in the circuit. 



4. If, without undergoing any change in their relative 

 position, the jacket and the wire are in rotation round the 

 magnet no current results. If we remove the jacket and put 

 one end of the wire in contact with one of the poles, and the 

 other end in contact with the middle of the magnet, a current 

 is produced when the wire only is in rotation. On the other 

 hand, the current disappears if the magnet and the electrode are 

 in rotation in the same direction and with the same angular 

 velocity. (Experiments of Profs. F. Exner and Czermak.) 



It has been attempted to give the following explanations of 

 the results of these experiments in accordance w T ith the theory 

 in favour : — 



1. The current obtained in case No. 1 is produced by the 

 electromotive forces having their seat in the jacket in rotation. 



2. The current produced in No. 2, when the magnet and 

 the jacket are in rotation with the same angular velocity, 

 cannot, according to the old theory, be due to the electro- 

 motive forces having their seat in the jacket ; for it is admitted 

 as an axiom that a magnet is incapable of producing induc- 

 tion in a conductor with which it is fixedly united*. The 

 theory proves, in fact, that the electromotive force has its 

 origin in the wire at rest, bed a ; and that it is, in intensity 

 and direction, equal to the force which would be produced if 

 the wire were in rotation in the opposite direction with the 

 same angular velocity, whilst the jacket and the magnet 

 remained at rest. 



If the angular velocity of the magnet is different from that 

 of the jacket and is denoted by t?„ that of the jacket being 

 denoted by v 2 , and if both take place in the same direction, 

 their relative velocity would be v 2 — V\. Now the electro- 

 motive force produced in the jacket must be proportional to 

 this difference. But the rotation of the magnet will give rise 

 to an electromotive force in the wire at rest, bed a, propor- 

 tional to +i\. If we add these two expressions together, the 

 sum is v 2 ; that is to say, the same electromotive force as if 

 the jacket alone had been in rotation. 



3. The old theory explains the results given under No. 3, 

 by the supposition that the rotation of the magnet gives rise 

 in the jacket to an electromotive force equal to that which is 



* Wiedemann, Die Lehre von der Electricitat, t. iv. 1. §§ 67 &c. 

 (Braunschweig, 1885) ; Wiilmer, Lehrbuch der Exp. Physik, t. iv. p. 896 

 (Leipzig, 1875) ; and several other works. 



