A simple resistor model consisting of three elements in parallel and representing (a) an element of solution and conducting solid particles in series, (b) an element of the solid particles only, and (c) an element of solution only, explains satisfactorily the experimental relationship between the conductivities of solutions used to saturate synthetic dirty sands and the conductivities of the saturated sands. The synthetic dirty sands consist of beds of ion-exchange particles.The same model is applied to give a theoretical explanation of the potential differences between two different solutions when these meet in the interstices of a synthetic dirty sand; excellent agreement is observed between theory and experiment. It is found that both potentials and resistivities depend on the same geometrical parameters. Hence they can be related to each other. The relationship is derived between the self-potential deflection and the resistivities of rock and invaded zone. It is compared to various formulae proposed by other investigators for interpreting logs in dirty sands.Conductivities and potential differences across plugs of 'synthetic dirty sands' containing oil have been measured. At high oil saturations the potential differences are almost as high as those across a solid membrane containing the same ion-exchange resin.