ELECTRICAL METHODS 517 



is obtained when the separation between the potential and the current 

 electrodes is from one-third to one-half the desired depth of investigation. 

 In areas where the lateral variations in resistivity are relatively small, 

 it is usually advantageous to employ the larger separations. In all cases, 

 however, the particular characteristics of the area under investigation 

 must be taken into account. 



One of the chief reasons for the indifferent results obtained in many 

 electrical resistivity investigations has been the blind application of a 

 fixed configuration to areas in which the relative conductivities of the 

 upper and deeper materials make that configuration unsuitable. 



The more widely employed electrode arrangements are illustrated 

 in the following sketches, t Whatever configuration is employed, the rela- 

 tion between the resistivity and the observed quantities {E/I and electrode 

 separation) may be obtained by using Equation 8 twice. 



The technique of applying Equation 8 will be illustrated for the Wen- 

 ner electrode configuration. The formulas for the other electrode arrange- 

 ments shown in Figure 313 may be derived in a similar manner. 



Wenner Configuration'^ (Figure 313a) 



The four electrodes are arranged in a straight line, the current 

 electrodes being separated by a fixed distance, 3a, while the potential 

 electrodes are situated at points distant a and 2a from the source respec- 

 tively. The potential at P due to the source and sink is obtained by sub- 

 stituting a for ri and 2a for ro in Equation 8. That is, 



27r\ a 2a / 



The potential at R due to the source and sink is obtained by substituting 

 2a for ri and a for r2. That is, 



27r \2a a J 

 Hence, the potential difference between the two points is 



27rL V fl 2a/ \2a a / J 27ra 

 and 



Pa — Z-n-a I J I 



It is of interest to point out that theoretically Wenner's formula holds 



t See also J. N. Hummel, "A Theoretical Study of Apparent Resistivity in Surface Potential 

 Methods," A.I.M.E. Geophysical Prospecting. 1932, p. 392. 



% Frank Wenner, "A Method of Measuring Earth Resistivity," Bull. U.S. Bureau of Standards, 

 Vol. 12, 1916. 



H. Gish and W. J. Rooney, "Measurements of the Resistivity of Large Volumes of Undis- 

 turbed Earth," Terr. Mag. 30, 1925, pp. 161-188. 



