Transparent Bodies by the action of Magnetism. 489 



no great difficulties. The arrangement of my apparatus, how- 

 ever, did not allow me to apply it ; besides that, it would have 

 been less simple and convenient than the following, which I 

 ultimately employed. 



This method is founded on a remarkable consequence that can 

 be deduced from the laws of induction established by MM. Neu- 

 mann and W. Weber. In his first memoir on the mathematical 

 theory of induced currents*, M. Neumann has given a formula 

 which represents the electromotive power developed by a mag- 

 netic pole in a closed conductor when displaced in any manner 

 whatever. If the magnetic pole be regarded as the summit of a 

 cone having for its base the closed conductor, the electromotive 

 force developed by an infinitely small displacement of the cur- 

 rent is proportional to the infinitely small variation in the angular 

 opening of the cone, and consequently the sum of the electro- 

 motive forces developed by a finite displacement is proportional 

 to the difference between the initial and final values of this an- 

 gular opening-)-. I shall call this sum the total electromotive 

 force. From this theorem the following conclusion may be 

 deduced : — "If in a spiace inhere the magnetic action is constant in 

 magnitude and direction, a circular conductor is placed so that its 

 plane be parallel with the direction of the magnetic action, and if 

 it be made to turn 90 degrees round an axis perpendicular to this 

 direction, the total electromotive force developed is exactly propor- 

 tional to the magnitude of the magnetic action.' y 



This conclusion would be evident if the magnetic action were 

 simply due to one or two very distant poles. In order to de- 

 monstrate it on the general case, let us consider a plane con- 

 ductor C, fig. 2, and a magnetic pole M, and let us suppose that 

 the conductor suffers any displacement whatever which causes it 

 to pass from the position C to the position C. Let us call ft 

 the quantity of magnetism accumulated at the point M, d?a) the 

 area of an infinitely small element o of the plane space surrounded 

 by the conductor, r and >•' the two successive distances oM, 

 and o'M from this clement to the point M, </> and cp' the angles 

 made by the right lines oM and o'M with the normal to the con- 

 ductor ; the total electromotive force will be expressed by 



Aj~W cos ^ ~ / 7^ cos *') ' 



* Memoirs of the Academy of Berlin for the year 1845. 



t M. Neumann has not directly demonstrated by experiment the prin- 

 ciples of his theory ; he has deduced them from the law of Lenz. But \vc 

 may regard the experiments of M. Weber, of M. Kirchholl", and of M. ltic- 

 cardo Felici, as having established the exactitude of the formula; relative 

 to the case of closed conductors, the only case with which we have here to 

 occupy ourselves, 



