220 On the Fundamental Law of Electrodynamics. 



facts established by experiment, in harmony with the prin- 

 ciple of the Conservation of Energy. 



I have already, m my previous communication, said that it 

 is theoretically most probable that the value of the constant n 

 is zero. Thereby the terms affected by the factor n fall away 

 of themselves ; and consequently the principle of the Conser- 

 vation of Energy is fulfilled not merely for closed currents, 

 but also for the single elements of them. 



Besides this simplification, however, a second can now be 

 introduced, which likewise refers only to a constituent of 

 the formulae not affecting the actions of a closed galvanic 

 current. 



I have, in deriving the above equations, already deviated in 

 some essential points from the views hitherto held. I have, 

 namely, taken into consideration not merely the relative 

 motion of the two particles of electricity, but also their abso- 

 lute motions ; and for the electrodynamic forces exerted by 

 the particles on one another I have neglected the assumption 

 that their direction must fall in the line joining the particles. 

 On the other hand, I have held fast to the hypothesis that the 

 two forces are equal and opposed to one another. Nevertheless 

 even this hypothesis is not necessary for forces such as the 

 electrodynamic ; if we drop it also, we can give to the funda- 

 mental equations the following form : — 



d 1 - 



x= ^£^ kvv,C0S€ ^ k iicr d i) ; 



A 



Y = -^(l^Wcose)-^(- 1 f); 



d- 

 Z^-^d-Wcos^^lgf). 



The force acting on the particle e, determined by these 

 equations, and the corresponding force acting on the particle 

 / satisfy by themselves alone the principle of the Conservation 

 of Energy ; for the work done by them during an element of 

 time is represented by the following complete differential, 



— d — ( 1 + k vv f cos e) . 

 r 



By employing a method introduced by Lagrange on another 

 occasion, the individual force-components can also be expressed 



