Field produced by Electric Tramways. 431 



In the particular case under consideration, 



b = a/2, so that /3 = 0, and we get 



Also 



to 1 1 9 2>2 + 1„ 



*2n+ 2 =- X — ==— V? F 2B . 



» Vl + w 2 2n 



F = j 3 ^ _ 2 1 



= log— ==-2L — g 



e Vl + u 2 — 1 V1 + ** 



Hence approximating to the integral we get when 

 m=0*4 



4Tm fn^ 0-715//*aV 0-758/yaa\ 4 . \ 



a(^+^ { 11 ' 6+ -tr(7) + TrV2) + &c -r 



Or, if 1 = 150 amp., m=0*4, a — 2 miles = 3*2 x 10 5 cm., 



15x11-6 C 0-0616 ^Y 0-0653 /^a\ 4 

 -2(e^ /2 + 6-^2)1 + 2! V27 + 4! v 2/ 



Now the coefficients of this series are much smaller and 

 converge more rapidly than those in the expansion of 



h~=\{i-m+mj-m^-} 



Hence for a given value of fia/2 a nearer approach to the 

 true value of the expression is obtained if we take the accurate 

 value of the exponential term and evaluate the integral to a 

 given power of fiaj'2, than if we expand both expressions to 

 that power of /Jba/2. 



