The Theory of Magnetic Disturbance by Earth- Currents. 433 



If we lake the case in which b=——, r 1 = r 2 = r, so that 



the arrangement (fig. 2) is as at Stockton, 



v+- 



(I.) 



From this equation the vertical force can be calculated. 

 It is, however, somewhat complex for use. I have, therefore, 

 examined the case in which it is supposed that the difference 

 between flow and return current is constant along the line, the 

 whole leak occurring at the sink. In Professor Pucker's 

 language, I have used the equivalent uniform current. 



In this case if k be the leakage coefficient, which is the 

 same as Prof. Pucker's 1 — L, 



1/ 



-p, _ Ik Ca4-b b 1 



v ~ y 1 r 2 



fiJ' 



using the same notation ; or taking the above symmetrical 

 case 



Ik a 



y r' 



F„= 



In this same case 



F,= 



L 



Now as to the value of k. 



We have from the theory developed by Mr. Parry and 

 Prof. Pucker, 





1 + €-^° 



and from the Stockton experiments fia/2 is about '64 and a is 

 '2 miles. 



