8 L. J. PETERS AND J. BARDEEN 
the neighborhood of one electrode so that the potentials due to the distant 
electrode may be neglected. The potential difference is measured between two 
search electrodes at distances r and 27 from the current electrode. If the earth 
is homogeneous and of conductivity o, the potential difference between the 
search electrodes is: 

He eB 1 I 
v.= V0) — Ven = —[—-=]=—. (12) 
2ro Lr 2r door 
The resistivity p may, therefore, be determined as 
p = 1/e = AnrV,/T. (13) 
If the earth is not homogeneous, Eq. (13) may be used to define the apparent 
resistivity. Let Vi(r) be the potential of the current electrode. Then the ap- 
parent resistivity is 
4ur 
fo a [Vi(r) — Vi(2r)]. (14) 
This function is not independent of 7 except in the special case of a homo- 
geneous earth. The variation of the apparent resistivity with 7 is used to de- 
termine the changes of resistivity with depth. As may be expected from the 
potential variation, the apparent resistance is equal to the resistance of the 
upper layer when 7 is small. As r increases the apparent resistance approaches 
the resistivity of the second layer. Long before it reaches this value, a third 
layer may affect it, and then the apparent resistivity will have a tendency to 
approach the resistivity of this layer. When a great many layers are present 
the resultant curve may be rather complicated, and the interpretation diffh- 
cult. 
A more common method of prospecting which leads to the same value for 
the apparent resistivity was developed by Wenner and Gish and Rooney. 
The two current electrodes and the two search electrodes are placed in a line 
equidistant from one another. 
roar ere: 
The current enters the earth at A and leaves at B. The potential difference 
is measured between C and D. The common spacing is r. The apparent re- 
sistivity is again given by Eq. (14), where V; again represents the potential 
due to a single electrode. The advantages of the method are that the electrode 
spacing need not be excessively great, and that possible errors due to neglect- 
ing part of the field do not enter. However, to obtain values of the apparent 
resistivity for different values of 7, all four electrodes must be moved instead 
of only two as in the previous method. This method is often called the Gish- 
Rooney method of electrical prospecting. 
In order to illustrate the results that may be expected under favorable 
conditions, a typical Gish-Rooney survey which was taken along a line of 
core drill holes is shown in Figs. 5 and 6. Fig. 5 shows the curves of apparent 
152 
