Ponder omotive and Electromotive Forces. 277 



exerted in the direction of the conductor-element by the cur- 

 rent or system of currents upon a unit of electricity (to which 

 we can ascribe any velocity of flow, c, we please) imagined in 

 the conductor-element. The force-components falling into the 

 directions of the coordinates are, acccording to our previous 

 notation, to be represented by dc, 3), and 3 ; and, in corre- 

 spondence with this, we will denote by © the force-component 

 falling into the direction of the element ds, therefore into the 

 s direction. We have then to put 



@= 3e |f-3>S + 3|=2 3 e|f. . . (34) 



In this we must now insert for the quantities 9£, 3), 3 their 

 values resulting from the three fundamental laws. 



According to my fundamental law ; in accordance with (13) 

 we can put 





~&x dt \^ dx 

 ~di 

 and consequently 



£T_ y BII B^ y~dx d ( BIT \ 



^~ Z ~dx a* ^-ds dt\^dxJ' 



If herein we use for II the expression given under (17), 

 namely 



we can put, if we wish to write all the terms singly, 



a# ~ds dt\~d% a^ ay b« b^ b«' 

 dy faHy a a? aiiy a^ , an y a^\ 

 dt \ ~d% ~&s a^ b$ a^ a«^ 



^/bh* b^ + bh* ay BH g B^\ 

 <& v a-^ B- s> By a« b^ a«/ 



Now, since the quantities H*, H y , and H* depend on s only 

 inasmuch as the coordinates occurring in them, x, y, z, of the 

 unit of electricity, are dependent on s, the three sums in 

 brackets represent the differential coefficients of the three 

 quantities with respect to s ; and hence we can write : — 



2 an af _ dx aHx + fy a h^ & bh 2 

 a^ a« ^ b# ^ b« dt ~ds ' 



