156 HELMHOLTZ ON THE CONSERVATION OF FORCE. 



If a piece of unmagnetized steel be caused to approach the 

 influencing magnet, supposing it, when removed, to retain the 



magnetism imparted to it, — ^W will then be lost in mechanical 

 force, and for this the magnet thus created is in a condition to pro- 

 duce — -W more than the piece of unmagnetized steel. 



Electro-magnetism. — Electro-dynamic phaenomena have been 

 referred by Ampere to attractive and repulsive forces exerted by 

 the elements of a current, the intensity of which depends only 

 upon the direction and velocity of the current. His deduction 

 does not comprehend the phaenomena of induction ; the latter, 

 together with the electro-dynamic, have been referred by W. 

 Weber to the attractive and repulsive forces of the electric fluids 

 themselves, the intensity of which depends on the velocity of ap- 

 proximation or of removal, and the increase of this velocity. Up 

 to the present time no hypothesis has been established by which 

 these phaenomena could be refeiTed to constant central forces. 

 The laws of induced currents have been developed by Neumann*, 

 by extending the law of Lenz for entire currents to the ultimate 

 particles of the same, and these laws coincide in the case of 

 closed currents with the developments of M. Weber. In like 

 manner the laws of Ampere and Weber for the electro-dynamic 

 actions of closed currents coincide with Grassmann's deduction 

 of the same from rotatory forcesf. Experience gives us no 

 further intelligence ; because thus far experiment has been 

 resorted to only in the cases of closed or nearly closed currents. 

 We will therefore confine the application of our principle to 

 closed currents, and show that from it the same laws follow. 



It has been already shown by Ampere that the electro-dy- 

 namic actions of a closed current can be always represented by 

 a certain distribution of the magnetic fluids on a surface which 

 is bounded by the current. Neumann has therefore extended 

 the idea of the potential to closed currents, by setting for a 

 current the potential of such a surface. 



5. When a magnet moves under the influence of a current, 

 the vis viva gained thereby must be furnished by the tensions 

 consumed in the current. During the portion of time dt, 



* Poggendorff's Annalen, Ixvii. 31. f Ibid, Ixiv. 1. 



