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X. On a new fundamental Law of Electrodynamics. 

 By Professor E. Clausius *. 



IN order to explain electrodynamic phenomena, W. Weber, 

 as is well known, advanced a law on the force exerted on 

 each other by two moving particles of electricity. Let e and 

 ef be the two particles, each of which may be either positive or 

 negative, and let r be their distance from each other, which is 

 to be regarded as a function of the time t ; according to Weber 

 these particles exert a repulsion upon one another which is re- 

 presented by the formula 



&Y't 1 f dr \ 2 2 f/2 n 



in which c is a constant. 



Against this formula objections have been raised by Helm- 

 holtz ; and from reasons quite independent of Helmholtz's, the 

 conviction has forced itself upon me that it does not correspond 

 to the reality. On the other hand, my considerations have led 

 me to another dynamic law, which I take leave to communi- 

 cate provisionally, reserving for a subsequent occasion the 

 complete exposition of the reasons which have induced me to 

 advance it. Two remarks only, serving for elucidation, I must 

 premise before introducing the formulae. 



If we start from the conception that the electrodynamic 

 action upon each other of two moving particles of electricity 

 takes place through an intervening substance, we need not 

 assume that it is dependent only on the relative motion of the 

 particles, but we can also ascribe an influence upon it to the 

 absolute motions of the two individual particles. If, for in- 

 stance, two electric particles are moving in parallel directions 

 with equal velocity, and consequently are, relatively to one 

 another, at rest, they may yet exert a reciprocal electrodynamic 

 action ; for to the medium existing between them they behave 

 differently from particles actually at rest. Further, with this 

 conception, we need not assume that the direction of the 

 electrodynamic force coincides with the line connecting the 

 two particles, but may also admit forces from other directions 

 as possible. 



Let, now, x, y, z and #/, y f , zf be the rectangular coordinates 

 of the two electric particles e and e r (concentrated in points) at 

 the time t ; and for the relative coordinates of the particle e to 

 the particle ef let us introduce the following symbols — 

 £=,£-./, v =y-y', $=zz-z f . 



* Translated from a separate impression communicated by the Author, 

 having been read before the Niederrheinische Gesellschaft fur Natur- und 

 Heilkunde, December 6th, 1875, 



