Field produced by Electric Tramways, 427 



uniform current, and must be distinguished from the mean 

 current in the rails. 



The latter may be determined in two ways : 



First, if i is the mean current in the rails, 



where K is the rail - resistance, and V the difference of 

 potential between their extremities. 



The measurements of these quantities at Stockton were 

 undertaken rather with the view of testing whether the Board 

 of Trade regulations w T ere fulfilled, than for determining the 

 mean current. The variations of the current and P.D. were 

 too rapid, and the values of i deduced from them are not 

 sufficiently in accord to command confidence. 



The mean of 9 observations gave i/l = 23 p. cent., but this 

 value is not only deduced from discordant numbers but leads 

 to too high a value of the disturbance at the observatory. 



In the second method of calculating the mean* we may 

 assume that the leakage at each point is proportional to the 

 difference of potential (u) between that point and the earth. 

 Thus if h and k be external and internal conductivities, and 

 i x be the current at the point #, 



7 dv , di x 7 



— i x =k-j- and — z=/w 



ax clx 



whence if /j? = h/k, 



dH x 



d^-^=°> 

 of which the solution is 



That is, as is shown, the problem is formally the same as 

 that of the Fourier-Bar. 



If the ends of the rails are at the points x = and x = a, 

 and if the whole current (1) passes through the rails at these 

 points 



k = l — — . 



Let now the point for which «r = be at a distance b from 

 the foot of the perpendicular drawn from the observatory to 

 a straight line, let y be the length of the perpendicular and 

 a the length of the line, then the vertical-force disturbance 



* See ' Electrician,' August 10, 1900, p. 595. 

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