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that when integrated in G along a small curved closed aS/;„_2 in a 

 Spn—\ perpendicular to G, it indicates the force in the direction of 

 G caused by the current element E, or also the vector potential 

 in the direction of E, caused bj an elementary magnet with 

 intensity unity in the direction of G. 



Let us now call the potential x {E, F) of two "-'-vectors unity 

 E, F the symmetric function F^{r)cos(p, where r represents the 

 distance of the points of application of both vectors and (p their angle 

 after parallel transference to one and the same point of their con- 

 necting line, then we know that this function x gives, when e. g. E is 

 integrated over a closed curved Spn—2 which we shall call e, not 

 only the negative energy of a magnetic "—'scale with intensity unity 

 bounded by e in the field of a vortex unity perpendicular to F but 

 also the component along F of the vector potential caused by a 

 system of vortices about e with intensity unity. , 



From this ensues again for the vector potential F of a vortex 

 element, that when the vortex element is integrated to a system of 

 vortices about a closed curved Spn-i it becomes the vector potential 

 determined according to § VII of that vortex Spn-2; so that the 



vector potential of an arbitrary 2A" is obtained as integral of the 

 vectors V of its vortex elements, in other words : 



2X=^2/j-^^FAr)dr, (//) 



where for each point the vector elements of the integral are first 

 brought over to that {)oint parallel to themselves and there are 

 summed up. 



X. So let us consider an arbitrary force field as if caused by its 

 two derivatives (the magnets and the vortex systems), we can then 

 imagine that both derivatives are propagated through the space 

 according to a function of the distance vanishing at infinity, causing 

 thereby the potential of the field. 



For, the field X is the total derivative of the potential: 



f^r^ ^1 (r) dx + f^^ F, (r) dr. 



The extinguishment of the scalar potential is the stronger, as it is 

 at great distances of order ^-t"-')'", the vector potential only of 

 order re-'-»-^^". 



