Theory of Magnetic Disturbance by Earth- Currents. 437 

 Hence 



F = 



4 y V^+a 2 



Now if the number of cars per mile is given V varies as a 2 ; 

 put Y=va 2 , v is the potential-difference between two points 

 1 mile apart. 



h va? 

 Hence total leak in length a= -— . 



J3ut total = ———-. 



o 



Therefore 1iv = \/ll' 2 , an obvious result when the meaning of the 

 quantities is considered, and 



-^ />va 4 „ rt -,/- - 



F„= 1 X-62X10- 1 , 



if the quantities be all in miles. 



A^rain we can eliminate a from these equations either by 

 the use of the equation I = \a, or by the use of the equation 

 V = va 2 . 



And we have the following four identical equations : — 



~ *62 . „ a 4 1 iri , 



Fv= — *n 2 ,. X 10-° 



.4 y vty + a 2 



•62 7 a 4 1 

 = — hv .- X 10~ J 



•62Av/V\ 2 1 



= - (-) j= =—r-XlO- 



4 y \ v J 



vV+S 



If we wish to find the connexion between the length of 

 the line and its distance from the observatory, so that when 

 its effect is a maximum it may be less than a given quantity, 

 8 say, then we must have the right-hand side of the above 

 equations less than 8. 



Now we have seen that X/l^/S is the maximum leak from 

 1 mile of the line. Let us call this L. Then 



V = 8L; 



