text: This method was developed by German physicist Johann Wilhelm Hittorf in 1853., and is based on observations of the changes in concentration of an electrolyte solution in the vicinity of the electrodes. In the Hittorf method, electrolysis is carried out in a cell with three compartments: anode, central, and cathode. Measurement of the concentration changes in the anode and cathode compartments determines the transport numbers. The exact relationship depends on the nature of the reactions at the two electrodes. For the electrolysis of aqueous copper(II) sulfate () as an example, with  and  ions, the cathode reaction is the reduction  and the anode reaction is the corresponding oxidation of Cu to . At the cathode, the passage of  coulombs of electricity leads to the reduction of  moles of , where  is the Faraday constant. Since the  ions carry a fraction  of the current, the quantity of  flowing into the cathode compartment is  moles, so there is a net decrease of  in the cathode compartment equal to . This decrease may be measured by chemical analysis in order to evaluate the transport numbers. Analysis of the anode compartment gives a second pair of values as a check, while there should be no change of concentrations in the central compartment unless diffusion of solutes has led to significant mixing during the time of the experiment and invalidated the results.