of Unipolar Induction. 421 



M 



_ p riVri sin (fse) = Mpv sin (fse) . 



It is of course the same for the element of circuit dk, situated 

 between two planes, making the same angle with each other 

 and with the horizontal plane as those just mentioned passing- 

 through the pole, and the direction of motion of the points d 

 and k. 



The induction in this element of the circuit will conse- 

 quently be also Mpv sin (fse) , and its effect will be upwards 

 in the direction of the arrow. But, since these conditions 

 are applicable to all the positions which these planes can take, 

 it follows that the electromotive force produced in a part of 

 the closed circuit is equal to the force wdiich is produced in 

 the rest of the circuit. As these two forces neutralize each 

 other, there can be no current produced in this case. 



3. We will now suppose that the jacket is removed, and 

 that the ends of the metallic wire ahegb are in contact, one 

 with one of the poles, and the other with the centre of the 

 magnet. If now the wire is in rotation with the magnet 

 round the axis of the latter, it evidently follows from the pre- 

 ceding that in this case also no current can be produced. 

 When the magnet is in rotation round its axis it produces, 

 according to 4 of § 5, an electromotive force at each of the 

 points which receive a motion of translation, and in con- 

 formity with 4 of § 6, a like force is produced in the axis 

 itself, although it does not receive any motion of translation, 

 but simply one of rotation. The sum of these forces is equal 

 to that which would be produced in a jacket in rotation round 

 the magnet. As experiment shows, no current can therefore 

 be produced in a closed circuit. 



If, on the contrary, the magnet is at rest whilst the metallic 

 wire only is in rotation, no electromotive force will of course 

 be produced in the magnet, and consequently the electro- 

 motive forces produced in the metallic wire may in this case 

 give rise to a current. 



4. I have had occasion to verify, in the preceding w T ork, 

 formula 6, given above, by a great number of experiments on 

 unipolar induction, and I have always been able to observe 

 that it furnishes a true explanation. I therefore consider it 

 superfluous to submit it to new experiments of verification. 

 We are, moreover, entitled to affirm that the formula in 

 question ought to give a correct result, since it is an imme- 

 diate consequence of the mechanical theory of heat. 



