An idealized model is postulated embodying the essential features of industrial caustic-chlorine cells with horizontal flowing-mercury cathodes. This model is examined in detail, and relations expressing the local anode potential, cathode potential, and ohmic potential drop in the electrolyte in terms of local current density and other parameters are established. These relations are combined to give a system of equations relating current density at any location along the cell to applied total potential and to operating conditions in the cell upstream of the point in question. Numerical solutions of these equations for several cases of cell operating conditions are carried out on a digital computing machine. The effects of changes in operating parameters upon average current density, individual electrode potentials, and current distribution are evaluated. (auth)