General Formula for Apparent Resistivity
If there are two current electrodes and two potential electrodes on the surface of a half-space, the configuration can be represented as follows:
It is not necessary that the four electrodes be in a straight line.
If apparent resistivity is Ra and V is the difference in voltage between M and N then
Most modern earth resistivity instruments report V/I as resistivity, R. Therefore
For a clear derivation of the above equation, see:
Reynolds, J.M., 1997, An Introduction to Applied and Environmental Geophysics: New York, John Wiley & Sons, Inc. pp. 424-426