Theory of Magnetic Disturbance by Earth- Currents. 439 

 We thus obtain the following table of values of a and V. 



Table T. 



y- 



a. 



V. 





1 



105 



i 

 225 





2 



1-45 



4-25 





3 



1-78 



6-25 





4 



205 



8-5 





5 



2-30 



10-5 



Or, if we take /z' 2 /8 = '0225, so that the leak in 1 mile is 

 2 \ per cent., the current being 150 amperes for each mile of 

 track, and the resistance of a mile of track 0*0135 ohm as 

 before, we have : — 





Table IT. 







y- 



a. 



V. 





i 



1-15 



2-6 





2 



1-75 



6-25 





3 



214 



925 





4 



25 



125 





We may use the equation to find at what distance the 

 Board-of-Trade potential-difference is innocuous, and what is 

 the corresponding length of line. Substituting in the fourth 

 equation V= 7, v = 2, and hv = 6, I find 



y = 3'28 miles. 



And since Y = va 2 , the corresponding length of line will be 

 V3'5, or 1 # 87 miles. Thus in round numbers 2 miles of 

 track carrying a current of 300 amperes with a potential- 

 difference of 7 volts between the ends might produce a vertical 

 magnetic force of *5 x 10~ 5 units on an observatory at a 

 distance of 3 miles. 



If we remember that \ is the current required to drive the 

 cars in a mile of line, we can put the rule thus : — 



Multiply the current in amperes required to drive the cars 



