Field produced by Electric Tramways. 429 



wires and rails reduces to the form 



luC %/i+? +i 2 Vh^ ! /V\ 2 



and when I=15(c.G.s.), w=0*4 and a=3"2x 10 5 cm., as at 



Stockton, this was equal to 7 x 10 ~ 5 , whence 



(/xa/2) = 0'61. 



If the calculations are confined to this approximation it is 

 best to use this value of fia/2, though it is probably too 

 small. 



Having thus shown how to find fia/2 from the vertical- 

 force disturbance, we may next use it to calculate the average 

 current in the rails and the total leakage. 



The average current between and a is 



^ C a i x dx 2Ie^-l 21, , / ,_. 

 «= ■ = — — =-== — tann. (ua/2) 



= 1 | 1- q(<t) ( approximately. 



The total leakage is the difference between the total cur- 

 rent I and the minimum current at the central point (i vl ). 

 Putting x = a/2 in the expression for i v we get 



T = t^Tl = sech W 2 ) = 1 ~ 2 ( ¥ ) a PP roximatel y- 



Using the more accurate (0*678) and the approximate 

 (0*61) values of jna/2 with the accurate and approximate 

 formulae respectively, we get the following results : — 







[ia/2=0-67S. 



pa/2=0-6L 



Equivalent current ... 

 Mean current 



83-9 p. 



cent. 



86 - 7 p. cent. 

 80-6 „ 



87 '4 p. cent. 

 81-4 „ 



Minimum current ... 



The leakages as deduced from the equivalent and minimum 

 currents are 



16*1 p. cent., 19*4 p. cent., and 18*6 p. cent, respectively. 



The general result of this discussion is that if accurate 



