Abstract The method of displacement electrophoresis is described and its analogy with displacement chromatography shown. The apparatus consists basically of a capillary tube, a few tenths of a millimetre bore and thin walled, uniting two vessels, each containing an electrode. For the analysis of anions the cathode vessel contains an anion less mobile than any in the sample mixture to be analysed. The capillary tube is filled with a solution of a salt of an anion more mobile than any in the sample and a buffering cation. The anode vessel contains the buffering cation. The electrodes must not produce interfering ions or gas. To reduce disturbance by electroendosmosis a long chain soluble polymer is used to increase the viscosity of the solution in the capillary tube, and the electrode vessel is closed at the end to which electroendosmosis would cause flow if it were open. The sample is introduced between the cathode and the capillary, and a constant current is passed between the elec­trodes. The anions in the sample move initially at different speeds until they are separated in order of their mobility. Then all the anions in the apparatus move down the capillary at the same speed, assuming the tube to be of constant bore, since the concentrations so adjust themselves that the potential gradient at any point is inversely proportional to the mobility of the anions at that point. The boundary between each successive pair of ions is more or less sharp, depending upon the diffusion constants, the potential gradient, the difference in mobility, and the disturbance caused by electroendosmosis, temperature difference across the capillary, and flow of liquid. Each zone has a characteristic pH. Once the train of anions has separated it proceeds down the capillary unchanged. Since each zone has a particular potential gradient, it has also a particular rate of heat generation per unit length and a particular temperature. It is thus possible to follow the separation by means of fixed thermocouples on the outside of the tube, which will record the fronts as they pass under the thermocouple. A thermocouple measuring the temperature of the capillary relative to its surroundings plots a series of steps on a recorder, the height of a step from the baseline being a measure of the mobility. The length of the step is preferably measured from the distance between the peaks of the record provided by a differential thermocouple measuring the difference in temperature along a short length of the tube, which gives a record which is the differential of the step curve. The length of step is proportional to the length of tube occupied by that species of ion and hence to the quantity. A qualitative and quantitative analysis is thus possible. A theory is given of the points mentioned above. An experimental paper will follow.