70 On a new fundamental Law of Electrodynamics. 



Call the distance between the two particles r. Further, let ds 

 and ds' be two path-elements simultaneously passed through 

 by the particles, e the angle between them, and v and v' the 

 velocities. If then the components (falling in the coordinate- 

 directions) of the total electrostatic and electrodynamic force 

 suffered by the particle e from the particle e' are represented 

 by Xee f , ^ee f , and Zee!, the following equations, written first 

 in the most general form, hold good, in which k is a positive 

 constant referred to the quantitative ratio between the electro- 

 dynamic and electrostatic portions of the force, and n another 

 constant, of which we shall speak further on :— 



tv , *?-\ ni d/ldn\. 



I-V cose + n___ ivv +A-57I- -jt I » 

 \»- 3 did?/ dt\rdtj 



r 6 



From these equations all the forces and induction-actions 

 exerted on one another by galvanic currents can be deduced. 



The three components of the force exerted on a current- 

 element ds by a current-element ds! are represented generally 

 by the following expressions — 



1 * <f! 



Cll 



d- ^ d- 7U d?^ 



dsds '( _ 4- C ose+ JL d l + -I * - n — lA 

 \ r z ds'ds^dsds' dsds'P 



in which % and i* signify current-intensities, and c is a positive 

 constant dependent on the constant k and also on the unit 

 selected for the measure of the current-intensity. 



The question now is, what value is to be given to the con- 

 stant n? If the value 1 be chosen, the preceding expressions 

 will represent the components of the same force that was de- 



