[ 218 ] 



XXVI. On the Bearing of the Fundamental Law of Electrody- 

 namics toward the Principle of the Conservation of Energy, 

 and on a further Simplification of the former. By Professor 

 K. Clausius *. 



THE new fundamental law of electrodynamics recently 

 communicated by me f presents, in relation to its admissi- 

 bility and the still existing possibility of a simplification, occa- 

 sion for some very essential considerations, which I take leave 

 likewise to communicate. 



Let two particles of electricity in motion, e and ef, have at 

 the time t the rectangular coordinates x, y, z and a/ 9 y ( , z* ', and 

 for abbreviation put %=x—x f , 7)=y—y', ^—z—z'. Further, 

 let r denote the distance of the two particles one from the other, 

 ds and els' two path-elements simultaneously traversed by them, 

 e the angle between these, and v and v' the velocities. If then 

 the components, in the coordinate-directions, of the force which 

 the particle e' exerts upon the particle e is represented by 

 Xee', Yee r , Zee' ', equations are valid to which in my previous 

 communication I gave the more general form 



r* Vr 3 dsds') dt\rdtP 



Y=*-k(loos € +n^)vv>+k£(±%\ 



v* \r d dTds 7 / dt\rdtP 



d? K 



r z \r d dsds' J dt\rdtP 



where h is the constant which refers to the quantitative ratio 

 between the electrodynamic and the electrostatic force, and n 

 denotes a constant provisionally left undetermined. 



The question now arises, whether the law of force expressed 

 by these equations is compatible with the principle of the Con- 

 servation of Energy. 



If the electrodynamic action on each other of the two par- 

 ticles is effected through a material medium existing between 

 them, it is not absolutely necessary that the forces to which 

 the two individual particles are subjected shall by themselves 



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

 having been laid "before the Niederrheinische Gesellschaft fur Natur- und 

 Heilkunde on the the 7th Feb. 1876. 



t Phil. Mag. January 1876, pp. 69-71. 



