Ponder omotive and Electromotive Forces. 263 



for which, on account of the self-evident equation 



and because i' is indepndent of s' and hence in the last term 

 can be put with the rest under the differentiation -symbol, can 

 be also written 



*i 



zj/T ; rf^x'^x' .J-tfi\, 3 (V dx\] 



kM i- i TxV-ww + ^r-rw\rw 



This is the constituent resulting from the second term of the 

 above expression of the x component, of the force which the 

 current- element dsf exerts upon a moved unit of electricity 

 according to Biernann's fundamental law. The constituent 

 resulting from the first term agrees, as already stated, with 

 the value that holds good according to my fundamental law, 

 of the force-component which we have denoted by re// and 

 determined in the preceding section. Hence, if we denote the 

 total value of the force-component according to Riemann's 

 fundamental law by t\d£\ we get 



at 



ri==f + ^ W _^___ + __j + _^^j. (6) 



§5. 



Now, thirdly, Weber's fundamental law must be treated in 

 the same manner. 



According to this law, between two moved particles of elec- 

 tricity e and e! a repulsion takes place the intensity of which is 



k/dr\ 2 • 7 d 8 * 



ee' r\ fe /dr\* . 7 crr-i 



and from this, by multiplication with ' — ^-, we obtain the 



x component of the force which the particle e suffers, thus — 



,#— -Jr k /dr\ 2 , _ d 2 rl 



In applying this expression to the quantity of electricity 

 AW flowing in the current-element dsf with the velocity </, 

 and to the moved unit of electricity, we have again first to 

 replace e and e' by 1 and h'ds' . We will then, in accordance 



