text: This method was developed by British physicists Oliver Lodge in 1886 and William Cecil Dampier in 1893. It depends on the movement of the boundary between two adjacent electrolytes under the influence of an electric field. If a colored solution is used and the interface stays reasonably sharp, the speed of the moving boundary can be measured and used to determine the ion transference numbers.
  The cation of the indicator electrolyte should not move faster than the cation whose transport number is to be determined, and it should have same anion as the principle electrolyte. Besides the principal electrolyte (e.g., HCl) is kept light so that it floats on indicator electrolyte.  serves best because  is less mobile than  and  is common to both  and the principal electrolyte HCl.
  For example, the transport numbers of hydrochloric acid (HCl(aq)) may be determined by electrolysis between a cadmium anode and an Ag-AgCl cathode. The anode reaction is  so that a cadmium chloride () solution is formed near the anode and moves toward the cathode during the experiment. An acid-base indicator such as bromophenol blue is added to make visible the boundary between the acidic HCl solution and the near-neutral  solution. The boundary tends to remain sharp since the leading solution HCl has a higher conductivity that the indicator solution , and therefore a lower electric field to carry the same current. If a more mobile  ion diffuses into the  solution, it will rapidly be accelerated back to the boundary by the higher electric field; if a less mobile  ion diffuses into the HCl solution it will decelerate in the lower electric field and return to the  solution. Also the apparatus is constructed with the anode below the cathode, so that the denser  solution forms at the bottom.
  The cation transport number of the leading solution is then calculated as
  where  is the cation charge,  the concentration,  the distance moved by the boundary in time ,  the cross-sectional area,  the Faraday constant, and  the electric current.