This paper consists of an experimental chemical and another experimental physical part. The results are surveyed and the conclusions drawn in a third chapter. The chemical experiments were (aside from the preparation of the anodes for the physical tests) concerned with the question, whether or not the oxygen is deposited upon the anode during formation of the layer according to Faraday's law of equivalents, assuming in accordance with many of the former investigators, that the layer consists of an oxide and hydroxide of aluminum. The work covered a wide range of concentrations, temperatures and current densities. Not one of the observed phenomena was critically sensitive to variations of these conditions. While this is so, the results show, on the other hand, that the total amount of oxygen released at the anode is of an entirely different order of magnitude and much larger than the amount of oxygen included in the layer, as calculated on the basis of the general knowledge about the order of magnitude of the thickness of the layer. As a result of the physical investigation it is concluded that the behavior of the layer corresponds to that of a dielectric containing a large number of polar molecules. The electric field in the layer, and, therefore, the potential applied to it, determines its properties. The current, on the other hand, used in its initial, or in its recurring formation, is a secondary factor only, and does not involve any basically simple relations. Thus the law of chemical equivalents cannot be broadly applied in determining either the capacity or the resistance of the layer on the basis of its formation process. Although the present study deals with only a specific example of a broadly general type, the experimental methods developed and recorded and the hypotheses introduced should prove applicable to the investigation of other similar cases of conductivity; and applicable to a systematic presentation of the subjects of highly asymmetric conductivity, and the behavior of dielectrics containing polar molecules in extremely intense electric fields.