Ponder omotive and Electromotive Forces. 259 



mentioned moved unit of electricity in the point x, y, z. For 

 that purpose we have to substitute in the preceding expression 

 1 and h'ds for e and e f , by which we get 



The product 



d_ /l dx> 

 dt 



\r dt) 



we can bring into another form : and as the corresponding 

 transformation has frequently to be employed in other cases 

 also, we will presently work it out somewhat more generally. 

 Let F be any quantity which, in the way stated of those refer- 

 ring to the positive current-electricity in the preceding section, 

 depends on t and s' '; then, in accordance with (1) and (2), we 

 can write 



dt ~ ^t + c -ds> 

 or, after multiplication by li' , 



11 dt ' l ~dt +,lC -ds' 

 and this can be transformed into 



dt & Bs* a? 



Herein another differential coefficient can be substituted for 



— _ . - . The element ds f of the conductor is bounded bv two 



cross sections corresponding to the lengths of arc s' and / ds r . 

 The two quantities of electricity which Sow through these cross 

 sections during the time dt, and of which the first passes into 

 and the other passes out of the element ds f , are represented by 



WdtsaLd (h>c r +'^ c p-dAdt: 



and hence follows that the increase which takes place during 

 the time dt, of the quantity of positive electricity in ds' , is 

 represented bv 



as 



