Ponder omotive and Electromotive Forces. 269 



and (8) the following equations: — 



Precisely corresponding expressions to those here derived 

 for the x component of the force of course holds good also for 

 y and z components. 



The three force-components referring to the three direc- 

 tions of coordinates can now, in the manner discussed in § 1, 

 be traced back to one quantity, from which they can be derived 

 by differentiation. This is the electrodynamic potential of the 

 closed current or system of currents upon the moved unit of 

 electricity existing in the point x, y, z. Now, as w r ith the 

 forces which are independent of the motion that potential of a 

 given agent which has reference to a unit of the same agent 

 supposed to be concentrated in a point is by Green named the 

 potential function, we will here also introduce the same distinc- 

 tion, and call the electrodynamic potential of a closed current 

 or current- system, so far as it refers to a unit of electricity 

 supposed concentrated in a point, the electrodynamic 'potential 

 function. 



This electrodynamic potential function is distinguished (as 

 was mentioned in § 1), even externally, from Green's potential 

 function, which refers to forces that are independent of the 

 motion. It contains, namely, not merely the coordinates 

 x, y, z of the unit of electricity, but also their velocity-compo- 

 nents y ? -f>-r* Further, the operation by means of which 

 at at at 



the force-components are to be derived from the electrody- 

 namic potential function is the same operation as that to which, 

 according to Lagrange, the vis viva, expressed in universal 

 coordinates, is to be submitted in the derivation of the compo- 

 nents of the force. For if the electrodynamic potential func- 

 tion be denoted by n, and the x component of the force by £ ; 

 then the following equation can be formed: — 



*~BJ dtYZd^) (13) 



d 'di 



We have now to construct the forms of the potential fnnc- 



