424 Prof. A. W. Riicker on the Magnetic 



conductors by which the current is conveyed to and from the 

 cars. If the return conductors are insulated and parallel to 

 the trolley-wires, the outgoing and returning horizontal 

 currents are equal (since there is no leak), and the effects are 

 zero at any point in the same horizontal plane as the rails, the 

 distance of which from the line is considerable with respect 

 to the height of the trolley-wires above the ground. 



The proof of these statements may be deduced directly 

 from first principles. 



It an electrical current flows from a source placed in 

 the surface of an infinite uniform conductor bounded by a 

 plane, the resulting magnetic field will have no component 

 perpendicular to the surface. For if a plane be drawn 

 through the source perpendicular to the surface it is evident, 

 from the symmetry of the system, that the components 

 parallel to this plane of the magnetic fields, produced by 

 the currents on opposite sides of the plane, will be equal 

 and opposite. 



Again, let the circuit be completed by an infinite linear 

 conductor passing through the source and perpendicular to 

 the surface, and let the total current flowing through this 

 conductor and diverging from the point where it meets the 

 surface be I. The force due to the whole system at a point 

 in the surface at a distance r from the foot of the per- 

 pendicular is 2I/r, and since half of this is due to the 

 current in the linear conductor, the other half is due to* 

 the currents diverging from its extremity. 



If we now place in the surface a sink equal to the source,, 

 the same statements hold good with regard to it ; and we thus 

 arrive at the conclusion that the current system flowing from 

 the source to the sink has no component perpendicular to 

 the surface, and that the component parallel to the surface 

 is the resultant of two forces 1/r and — I/r', where r and r r 

 are the distances from the source and sink. 



If we now regard the source and sink as the points at which 

 the current passing through an electric motor enters the earth 

 and returns to the generating station, it is evident that for 

 points at some distance from the railway or tramway the 

 trolley-wire may be represented by an insulated linear con- 

 ductor joining the source and sink. The magnetic field pro- 

 duced by this conductor will be everywhere perpendicular 

 to the plane surface which represents the earth, and of course 

 can be easily calculated. 



So far no attention has been paid to the rails. In reality 

 the current flows into the soil from the rails or vice versa, but 

 however complicated .the system may be it can be broken up 



