710 ELECTRICAL METHODS [Chap. 10 



1. In the Wenner-Gish-Rooney method the two potential electrodes are 

 placed on a line with the two current electrodes, so that all four electrodes 

 are situated at equal distances from one another. With a as the distance 

 between the electrodes, ri = R2 = a and n and Ri = 2a. Then the 

 expression for the resistivity, from eq. (10-316) is 



p = 2Ta J . (10-31c) 



2. In the Lee partitioning method an additional potential electrode is 

 provided halfway between P and R. Two potential measurements are 

 made, one for the left and another for the right interval. With ri = a, 

 7-2 = 2a, Ri = fa, and R2 = fa, the resistivity 



p = 47ra^, (10-31d) 



where Vpc = Vpr is the potential difference between the center stake 

 and the adjacent potential stake. 



3. The asymmetrical double probe method is an arrangement with the two 

 potential probes placed at equal intervals from one power electrode but 

 unsymmetrically placed in respect to the center. If I is the distance 

 between the current electrodes and a the potential-electrode interval, 

 n = a, r2 = I — a, Ri = 2a, and R2 = I — 2a, and the resistivity 



y 2aa-a)a-2a) . 



'-^""T {l-2ay + al • ^^^-^^'^ 



Eq. (10-31e) gives the Wenner formula when I = 3a. 



4. The asymmetrical single probe method results from the last by leaving 

 out one potential electrode and measuring the potential of the remaining 

 electrode against that of the next power electrode. Then ri = 0, r^ = I, 

 Ri = a, and R2 = / — a, so that with Ve as half the potential difference 

 between the power electrodes 



„ {Ve - V) a(l - a) f . 



p = 2. -^— . ^-^— ^^ . (10-31/) 



5. The double equidistant probe method is a modification of arrangement 3, 

 with the second power electrode far removed. With n = a, »'2 = «», 

 Ri = 2a, and R2 = <», 



p = iiraj . (10-31sr) 



6. The double probe method with unequal probe spacing differs from the 

 last by an unequal probe spacing and is generally used with a potential 



