Chap. 10] ELECTRICAL METHODS 



Hence, the difference of potential between the point A and B is 



715 



Vb = 



- H ^ - 1 



2t L Vx? + yl V{1 - x,f + y\ 



A;" 



-2Z 



+ 



^1 Va:? + ?/? + (2nA)' 



fc° 1 



^1 V(i - xi)' + ?/? + {2nhf VxfVy 

 1 . ^f ifc" 



-2Z 



Va - 2:2)' + yl n=i Vx^ + 2/2 + (2n/i)' 



+ 2Z 



2n/i)4 



(10-37a) 



^1 V{1 - x,y + 1/2 + (2n/i) 



From this general formula the potential difference between any two points 

 maj'^ be determined. 



For the electrode arrangement in the Wenner-Gish-Rooney method, 

 Xi = a, yi = 0, X2 = 2a, y2 = 0, I = 3a, so that 



Vb = 



27r La 2< 





-2I: 



A;° 



-i + ^ 



2E 



1 V'(2o)2 + (2nft)= 2o ^ a 



h.a n=« ' fcn 



+ 2E 



or 



7.4 - y« = 



27ra 



1 + 42: 



i V(2a)2 + {2nhy ^ ^i Va^ + (2n/i)2 



-4Z 



a 



L - 1/' + (¥)' "■ /' + (?)T 



27ra 



(10-376) 



The quantity pi(l + 4F) is an apparent resistivity. If A; = (homoge- 

 neous ground) the formula becomes Va — Vb = Ipi/2Ta. Hence the 



" See J. N. Hummel, A.LM.E. Tech. Publ. No. 418. 



