2 Prof. Pliicker on the Action of the Magnet 



77. The above gives, in the form of an integral, the expres- 

 sion for the total action of a magnet upon a current whose con- 

 ductor is a linear one of arbitrary form. It has, however, been 

 assumed here that this form remains continually unchauged. 

 We obtain a new point of view if we regard the conductor as 

 jjerfecfJij jlexihJe, and then inquire what would be the form of 

 such a conductor as current- bearer under the influence of the 

 magnet. From the simplest mechanical principles the following 

 laws are derived. 



78. I. If any magnetic forces act upon a perfectly flexible con- 

 ductor through ivhich an electric current passes, equilibrium can 

 only exist ichen each element of the conductor is so disposed that 

 the mai/netic action upon it disappears, that is, lohen the conductor 

 assumes the form of a magnetic curve. 



If this condition cannot be fulfilled, the smallest portions of 

 the conductor, unless held together by cohesion or other forces, 

 must necessarily be rent asunder in consequence of the magnetic 

 action. Nothing is altered in the above consideration, if, in 

 place of the perfectly flexible stream- conductor, we imagine an 

 electric current itself, whicii is not circumscribed to a conductor, 

 but which is free to seek its path through a space in which 

 ponderable matter occurs which serves for its conduction. Be- 

 fore the magiu't begins to act, such a stream will follow a more 

 or less variable path, but under the magnetic influence it will 

 adopt the course of a magnetic curve. If it is unable to do this, 

 the current cannot continue : the electricity must be lost with- 

 out the formation of such a stream. 



79. II. In order that the perfectly flexible conductor under the 

 injluence of the magnet may he in equilibrium over a given surface, 

 the direction of the force acting at every point of the conductor 

 must coincide with the normal to the surface at this point. 



In order that this condition may be fulfilled for every point 

 in the conductor, the element of the magnetic curve passing 

 through this point, as well as the element of the conductor 

 itself, must fall in the given plane; and hence again the in- 

 ference is easily drawn that in the case of equilibrium, the per- 

 fectlv flexible conductor is the geometrical locus of those points in 

 which the element of the magnetic curve passing through them falls 

 upon the given surface. This geometrical locus, which changes 

 in form and position by an altei'ation in the position of the 

 given surface towards the magnet, is therefore the only way 

 which the current can pursue upon the given surface, and it 

 only adopts this path if its terminal points, which we consider 

 fixed in position, both lie upon the geometrical locus just defined. 

 Such curves may be appropriately named " epipolar-magnetic." 

 Before and after an inversion, both of the magnetic polarity and 



