746 



ELECTRICAL METHODS 



[Chap. 10 



By introducing the ratios x = r/h and c = h/h, we obtain the following 

 equations : 



2Trh\_{x - 



n=oo j.n 



L 2 y 



c) ^ ^1 ^y{x - cY + 4n2 



+ 2E 



kp- 



2Th l{x + c) "^ ^1 V(x + c)2 + 4n 

 k'' 



i 



"" 2Th Ix 



n=oo 



a: ^=l -y/x^ + 4n2 



1 



Therefore, the potential differences are : 



V -V - ^^^ / c 



2irn \x{x — c) 



+ 2 



n=oo r 



V(x - c)2 + 4n2 Va;2 



+ 4n2j 



= Z^i/ 



Vc-Vb- ^,. , ■ , 



+ 2 





+ 4n2 \/{x + c)2 + 4n2. 



If we let 



\/(x - c)2 + 4n2 = Va 

 Vx2"+4n2 = VB 

 V(x + c)2 + 4n2 = Vc, 

 the potential ratio is given by 



(10-426) 



> (10-42c) 



(10-42d) 



When A; = (homogeneous ground), the series in both numerator and 

 denominator vanish and the P.D.R. becomes 



Vb X — c 



(10-42e) 



The P.D.R.'s measured in the field must be referred to a "normal" 

 ratio, that is, the ratio for homogeneous ground. To this end, they are 



