The paper has for its principal object the theoretical and experimental investigation of the electric field produced when a current flows in an electrolytic cell having plane parallel electrodes. On the theoretical side a general expression for the electrolytic conductance is derived in terms of the stream flux and the potential difference between the electrodes, and is applied to special problems of complex transformations. The distribution of the electric stress along the surface of parallel plane electrodes is also determined mathematically (see Section 1). The experimental work has been planned with two objects in view : (1) To verify the theoretical results by means of experiments in which the mathematical conditions are represented with sufficient and reasonable accuracy (see Sections 2 and 3) ; and (2) to apply the theoretical results for the solution of certain practical questions, and to investigate experimentally how far such applications agree with test results (see Section 4). Both objects have been in some measure satisfactorily attained. On the side of electro-physics the validity of Ohm's law is proved for any elemental current in the electrolyte by a direct experiment devised for this purpose (see Section. 3). The significance of this result lies first in its providing tangible evidence of the coincidence of stream lines with lines of force everywhere in the electrolytic medium, and secondly, in its proving that under certain conditions an electrolytic may be taken to represent a perfect homogeneous dielectric with something approaching mathematical precision. As an example of the practical application of this theorem, a method is derived for calculating the conductance of such apparatus as metal-refining and simple electro-deposition tanks, and certain types of liquid rheostats. A practical chart which is provided for this purpose may prove useful to the designers of such apparatus (see Section 4). Furthermore, the results obtained may find a field of application in the measurement of electrical and magnetic phenomena where the distribution of energy is analogous to that shown to exist in the electrolytic cell, as, for example, the capacity of an irregular system of conductors or the eluctance of a magnetic circuit.