2$$ Prof. R. Clausius on the Determination of the 

 and negative current-electricites : — 



dr 

 dt ' 



3'- 

 ~~dt 





dr 

 dt ' 



9? 



"3* 



Cl 3? 



(2) 



In these the partial differential coefficient |— comprises the 



two changes undergone by r, on the one hand through the 



motion of the unit of electricity, and on the other through the 



motion of the element ds' of the conductor containing the 



"dr 

 particle of electricity; while ^-, refers to the change produced 



in r by the current-motion of the electricity-particle which 

 takes place in the conductor. 



Employing this method of notation, the x components of 

 the force which a current-element ds' exerts upon the moved 

 unit of electricity may now be determined, first, according to 

 the fundamental electrodynamic law advanced by me, because 

 it is the most convenient for the working and furnishes the 

 simplest expressions, to which, in order to obtain the expres- 

 sions corresponding to the two other fundamental laws, certain 

 terms must then be added. 



§3. 



According to my fundamental law the x component of the 

 force which one moved particle e of electricity undergoes from 

 another, e', is represented by the formula 



a! 



r$ _Z[~_1 _i_ Z. (dfsd^_ dydi/_ clz dz\l __ , d/ldx'\ ") 

 ee \'bxl + \dt dt + dt dt ^dtdtjj k dt\r~dt)f> 



which, if we signify a sum of three terms alike in form, which 

 refer to the three coordinate-directions, by writing only the 

 term referring to the x direction and prefixing to it the symbol 

 of summation, can be written somewhat shorter thus — 



,V r ( i ■ i^dx dx'\ , d (\ dx'\~\ 



e *WA~ 1+kl 'Ttirt)- k d-Arti)\- 



We now take, in the point x f , y' \ z f , a current-element ds' 

 in which the quantity of positive electricity h'ds' flows with 

 the velocity </, and the negative —h'ds' with the velocity 

 — d\ ; and we will first determine the x components of that 

 force which the positive electricity h'ds 1 exerts upon the above- 



