260 Prof. 11. Clausius on the Determination of the 



But the same increase can, on the other hand, be also denoted 

 by 



w ds dt; 



and we consequently obtain the equation 



a* §7~' < 3) 



Thereby the above equation is changed into 



or, after contracting the first and last terms on the right-hand 

 side, into 



£ft ~~ d* + &• W 



Returning now to the expression of the x component of the 

 force exerted by the quantity Ndsf of positive electricity upon 

 the unit of electricity, and applying the preceding method of 



transformation to the term h 1 -r( — j-\ in which =-Is the 



dt\r dt J 7 r dt 



quantity that was previously denoted generally by F, the ex- 

 pression changes into 



^4(- i+ <^-4(^)-4('?s)]- 



da/ . 

 The differential coefficient -j- in this may, lastly, pursuant 



to (1) be resolved into its two parts ; the expression then takes 

 the form 



(_ ox L dt\ot os VJ o£\?' Ot r os 



We can now express in a corresponding manner also the 

 x components of that force which the quantity —h'ds f of ne- 

 gative electricity (whose current-velocity is — c\) contained 

 in the element ds f exerts upon the unit of eleetricity. To this 

 end we have to substitute — h' for h' ', and —c\ for c' } in the 



