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XXXV. On the Employment of the Electrodynamic Potential 

 for the Determination of the Ponder omotive and Electromo- 

 tive Forces. By E. Clausius*. 



1 1. 



IN order to represent in a convenient manner the electro- 

 dynamic forces between moved particles of electricity 

 and the 'mechanical work performed by them it is well known 

 that the electrodynamic potential can be employed, which 

 facilitates the calculations for these forces in like manner as 

 the electrostatic potential does for the electrostatic forces. Its 

 signification is the same as that of the electrostatic potential ; 

 for as the latter is defined by the statement that the work 

 done during a movement of the particles of electricity by the 

 electrostatic forces is equal to the simultaneous diminution of 

 the electrostatic potential, so also the electrodynamic potential 

 is defined by saying that the work done by the electrodynamic 

 forces is equal to the diminution of the electrodynamic poten- 

 tial. In its form, however, the electrodynamic differs essen- 

 tially from the electrostatic potential by this — that it comprises 

 not only the coordinates, but also the components of the velo- 

 city of the electric particles; and with this is, at the same time, 

 connected a difference in the procedure by means of which the 

 force-components are to be derived from it. 



If, now, we wish to determine with the help of the electro- 

 dynamic potential the forces which a galvanic current (which 

 may be in motion and variable) exerts upon a moved particle 

 of electricity, we cannot in general construct the former by 

 simply combining, for each current-element, the two potential- 

 expressions referring to the positive and negative electricity 

 present in the respective element of the conductor in an alge- 

 braic sum and then treating the current-element as a whole, 

 but must rather consider each of the two quantities of elec- 

 tricity separately, since the question is not merely what state 

 of motion they have in the conductor-element which concerns 

 us, but also how the state of their motion changes on their 

 passing from this element into the adjacent one, which takes 

 place differently for the two electricities. Of course the for- 

 mulas are thereby somewhat complicated. In certain cases, 

 however, especially in that in which the current whose action 

 upon a moved particle of electricity we wish to determine is 



* Translated from a separate impression, communicated by the Author, 

 from the Verhandlungen des naturhistorischen Vereim der jjreussischen 

 Rheinlande und Westfalens, vol. xxxvii. 1880. Read at the meeting- of 

 the Niederrheinische Gesellschaft fiir Xatur- und Heilkunde on July ] 2, 

 1880. 



