278 Prof. R. Clausius on the Determination of the 



or, now bringing in again the symbol of summation on the 

 right-hand side, 



g)a' ^s "~ ~ds dt 

 Accordingly the above equation for © passes into 



@=S ^7^^^-5T- " ' ' (85) 



As, then, the unit of electricity has a double motion, namely 

 the motion of the conductor-element and the flowing motion 

 which takes place in the conductor-element with the velocity c, 

 we will, in correspondence with the notation we have previ- 

 ously employed, put 



dx _ ~§x "ftx 

 ~dt^W d? 



dt ' "dt ~ds 



in which the differentiation indicated by ^ refers to the va- 



nations which are independent of the flowing motion of the 

 unit of electricity. We thus obtain 



Here the terms containing the factor c cancel one another, and 

 there remains 



=s -w^i-^-w^ (36) 



To this expression of © we can give a somewhat different 

 form by adding the quantity 



~d 2 x 



2H a 



"dfd t 



positive to the first term, and negative to the second term. 

 The two terms then become differential coefficients with respect 

 to s and t, and we get 



®=i SH -!f-j7 2H *if • • • ^ 



Finally, if in this we put for H* and the two other quanti- 



