Ponder omotixse and Electromotive Forces. 261 



preceding expression, by which we get 



*3*\ r B* + r 557 3<V r B* ~7~Bs'/J 



The sum of these two expressions represents the x component 

 of the total force exerted by the current-element ds / upon the unit 

 of electricity. On forming that sum several terms cancel one 

 another, and others admit of simplification from the fact that 

 for the product h'(c f + c\) the symbol i f , which signifies the 

 intensity of the current in ds r , can be substituted, whence it at 

 the same time follows that the product h f (c' 2 — c f ^), which can 

 also be written in the form h r [d + c / i)(c r —c\), can be replaced 

 by i'ic'—c'^). Hence, if we denote by rds' the x component 

 of the force which the current-element ds r exerts upon the unit 

 of electricity, we get the equation 



H. 



Riemann's fundamental law may now be treated in the same 

 manner ; and this is very easy in connexion with the fore- 

 going. 



The x component of the force which a moved electricity- 

 particle e suffers from a moved electricity-particle ef is ex- 

 pressed, according to Riemann, by the formula 



*i 



,(°rf , k^/dx da/Y\ , , d rl (Ax dx'Yl 1 



ee \^r l -^{di-Tt)\ +k di[j\dj-iu))r 



This formula can also be written as follows — 



The first term of this expression agrees perfectly with the ex- 



