270 Prof, R. Clausius on the Determination of the 



tion of a closed current corresponding to the three fundamental 

 laws. 



According to my fundamental law the electrodynamic po- 

 tential of two quantities e and e' of electricity, supposed to be 

 concentrated in points, is represented by 



dx dx r 

 dt dt 



*^2 



If in employing this formula we put for e the unit of elec- 

 tricity, and for e' successively the two quantities AW and 

 — h'ds' of electricity contained in a current-element ds r , and 

 in regard to the velocity-components of the latter take into 

 account that they flow in the conductor in opposite directions 

 with the velocities c f and c\, while they have in common any 

 motion of the conductor, and if we then form the sum of these 

 two expressions, putting h'{c' ' + c\) = il ', and, lastly, integrate 

 this sum over the closed current, we get 



n^f^igW. .... (u) 



J r dt os 



If this expression of II be now inserted in equation (13), 

 we obtain from it in fact the value for X determined by equa- 

 tion (io). # dx d dz m m 



Since the velocity-components — , -^-, and -y, occurring m 



at at at 



the expression of II, are independent of the quantity s', with 



respect to which the integration is to be performed, we can 



put them outside of the integral-symbol and then give to the 



expression the following form: — 



n =* 2 Jjl^' < 15 > 



The sum here indicated contains three integrals, which 



. "da/ 

 differ from each other only by this — that in them either -^-7, 



"dv r ~bz' * s 



or ■—-, or -^j occurs. These three integrals, together with 



the factor k, we will, for brevity, represent by simple symbols, 

 putting 



^= h ftw ds '> ^ =k $;if ds '> H -^'l?*^ 16 > 



Then we get 



n = H *J +H t +H 4 • • • < 17 > 



