To answer the question as to whether Nernst's law holds and to what extent an electron transference occurs in a potentiometric cell, four criteria are discussed on the basis of practically relevant instances: (i) the total voltage, (ii) the chemical potential dependence of the voltage, (iii) the temperature dependence of the voltage and (iv) the chemical potential dependence of the temperature coefficient of the voltage. In view of recent findings on the peculiar property of the electron conduction parameters according to which these parameters may change with the chemical potential in the surrounding of the electrolyte, the agreement between the experimental and the Nernst value of the voltage may not longer be regarded a sufficient prerequisite for the validity of Nernst's law. Under such a circumstance useful information can particularly be derived from the criteria (ii)-(iv) which to date have received only limited attention. As a result, the present approach proves to be capable of quantitatively determining the deviation from the Nern.st voltage without knowing the extent of the electron transference and the Nernst voltage itself. Further evidence for the sodium potential dependence of the p-electron conduction parameter of Na-beta-alumina is given.