514 M. E. Jochmami on the Electric Currents induced 



conductor ; for, of course, any additional system of closed cur- 

 rents may always be replaced by a distribution of magnetism. 



According to Weber's law*, the electromotive force induced 

 by the magnetic element /t in the conductor-element at x, y, z, 

 moving with the velocity vr— \/u 2 + b 2 -f-fo 2 , is equal to 



r z 



in which expression r denotes the distance between the elements, 

 k the constant of magnetic induction, and <j> the angle enclosed 

 by the directions of r and ot. The constant k will be identical 

 with the one previously represented by this letter, provided the 

 intensities of all currents be measured by electro-magnetic units. 

 The direction in which this electromotive force strives to separate 

 the electricities in the element at x, y t z, is perpendicular to the 

 plane through r and the direction in which this element moves. 

 Consequently, if \, /jl, v be the direction-angles of the electro- 

 motive force, 



{(a/— x) cos X + (y'—y) cos fju + (z 1 — z) cos v=0, 

 UCOS\-f &COS//.+ focosj/ = 0, 



cos 2 X+ cos 2 yu,+ cos 9 v=l. 



The equations give at once the values 



«rcos\= v • , — &* 



r&mcp 



toftf 7 — x)— uCz'— z) 



fff COS Lb— — - -. — j 1 - — -* 



r sin 9 



u{y , —y)—b{x ! —x) 

 fs cos v= vy . — x * 



rsm<p 



Accordingly the rectangular components of the electromotive 

 force at x, y, z induced by the magnetic particle fju at x 1 , y 1 , z 1 

 are 





^ ^ 



Electrodynamische Maassbestimmungen, 1st memoir, p. 345. 



