428 



Prof. A. W. Riicker on the Magnetic 



produced at the observatory by the opposing currents in the 

 trolley -wire and rails respectively is 



f 



(I-fr).V 



J(6+.*) f -+y}* 



= IT b + a 

 y \ 



dx 



} 



<s/(b + a) 2 +y 2 s/V + if 



ly r*_f* + 0&~*i_ 



1+V*J {(b + ^+y 2 ^ 



At Stockton the point of observation was opposite to the 

 middle of the line so that b= —a/2. 

 Therefore the disturbing force 



2a 



ly 



V Vd' + 4ty z e^-t-e" 



-/j.a/2 



r a 6f *.(x-a/2) _|_ € — /t(x-o/2) 



L \(x-al2)*+y*li dx - 



If now we write ^=(A + V)a/2 and y = na/2 this becomes 

 an v'T+^ ~~ «<> a/2 + e-^j J _, 



(\ 2 - r W 2 )t 



d\. 



The first term in this expression is the disturbance due to 

 the trolley-wire, which at Stockton was 43 y. The whole ex- 

 pression is the actual disturbance, viz., 7 y : hence, neglecting 

 signs and expanding the integral in terms of fia/2, we get 



4Iu 





It is easy to show that terms in higher powers of fi are 

 negligible, and that the expression thus obtained is more 

 accurate than if the denominator were also expanded. 



Now at Stockton a — 2 miles=3 2 X 10 5 cm., # = 0'4 mile, 

 and therefore w = 0*4. 



Substituting these values we get 



^{ll-6 + 0-715(^a/2) 2 }-36. 



Neglecting the second term this gives iia/2 = 0'636, 

 and substituting this value in the second term we get 

 /ia/2 = 0'678. 



If we adopt the rather less accurate but more convenient 

 plan adopted by Mr. Glazebrook, and expand throughout in 

 terms of fxa/2, the whole disturbance due both to trolley- 



