510 M. E. Jochmann on the Electric Currents induced 

 i'tr cos e = \xu' -f bv 1 + tow', 

 •i <±t .x'—x , ,y'—y , ,z'—z 

 r r r 



. x- — x , c y'—y , c z'—z 



otcosS = u \-b- — - + fo , 



r r r 



and the above expression becomes, by substitution, 



2k r 

 2- dx 1 dy' dz' uu' + W + tow' 



3/ x'—x c y'—y , z l —z\( ,x'—x .y'—y ,z'—z\l 

 Z\ r r r J \ r r r/J 



This is the force with which, through the action of the current- 

 element u 1 , v', iv', the units of positive and of negative electricity 

 existing at x, y, z are separated in the direction of the connector 

 r. By resolving this electromotive force into its three rectan- 

 gular components, and taking the sum of the actions of all cur- 

 rent-elements, we obtain the following expressions for the com- 

 ponents of the electromotive action of the whole current-system 

 on the unit of electricity at oc, y, z : — 



v r. 7 Cdd dy' dz 1 x'—x . r . r , N 



X=— 2k\ % uw' + W + fow/) 



J r 2 r ' 



07 Cdx'dy'dz' o/—x/ x'—x r y'—y , c z'—z\ 

 J r* r \ r r r / 



(.x'—x , .*/ — y , ,z'—z\ 

 u' \-v' y - y - +w' ), 

 r r r / 



J r z r 



, Cdx' dy' dz f y' — y ( x'—x , ,y' — y , t z'—z\ 

 J r 2 r \ r r r J 



/ .x'—x i y'—y ,z—z\ 

 lu' v^- — ^ + w' ), 



\ r r r / 



«, Cdx' dy' dz' z' —z . . , t . , . , x 

 Z=-2A1 1 - — (ito' + W + fow') 



J r 2 r\r r r / 



(.x'—x iy'—y .z' — zX 

 r r r / 



These expressions admit of great simplification by introducing 



