Field produced by Electric Tramways. 425 



into pairs of sources and sinks. Hence the statement is always 

 true, that if the earth may be regarded as a homogeneous 

 conductor, the vertical magnetic field produced by an electric 

 railway or tramway is due solely to the differential effect of 

 horizontal currents in the trolley-wire or other feeder and in 

 the rails, while the horizontal magnetic field is produced 

 solely by the stray earth-currents. 



This conclusion, though almost obvious, is important. 

 Experiment shows that the vertical-force instruments are 

 generally those which are most seriously affected by the es- 

 tablishment of an electric tramway in the neighbourhood of 

 an observatory. The question has been raised whether the 

 observatory might be protected by a river ; but the above 

 discussion shows that the direct effect of the current in the 

 trolley-wire could not be altered by any such natural feature 

 of the district. All that can be said is that a want of sym- 

 metry in the earth -currents might introduce a vertical 

 component opposed to that due to the current in the trolley- 

 wire. 



The simplest method of dealing with the rails is to regard 

 them as an insulated conductor by which a fraction of the 

 whole current returns to the generator. At a distance from 

 the line considerable with respect to the height of the trolley 

 above the road, the vertical force is practically produced by 

 the difference between the total current I and the hypo- 

 thetical uniform rail-current, the effect of which at the point 

 considered is equivalent to the actual rail-current, the strength 

 of which varies from point to point. 



The approximate theory based on these assumptions is thus 

 reduced to the determination of the vertical effects of a hori- 

 zontal current 1(1 — L) where L is < 1, and to the horizontal 

 disturbances produced by a source and sink of strength LI 

 placed in the positions of the generator and car respectively. 

 The effects of several cars can be obtained either by dealing 

 with each separately or by averaging. 



The calculations are quite simple and it is hardly necessary 

 to set them forth at length. 



Other things being equal, and the tramway being assumed 

 to be straight, the vertical force disturbance increases with 

 the length of the tramway, and for a tramway of given length 

 the disturbance is a maximum at points on a line perpen- 

 dicular to and bisecting it. 



Under similar circumstances the horizontal force dis- 

 turbance when the car is very distant is due only to the 

 inflow of the earth-currents to the generating station. As 

 the car approaches and passes the observatory the disturbance 



Phil Mag. S. 6. Vol. 1. No. 4. April 1901. 2 F 



