Abstract True transference numbers may be determined by measuring the quantities of ions and solvent transported across a membrane on passing an electric current. In most previous work concentrations on one or both sides of the membrane have been allowed to change during the run. Ideally, the concentrations should be maintained invariant during the electrolysis to minimise transfer of solvent and solute by osmosis and diffusion, respectively. The maintenance of constant concentrations may also be important if the membrane characteristics show irreversibility on changing concentrations as is found with Cellophane in alkaline solutions. In the present paper a technique is described for holding solution compositions constant requiring only relatively simple equipment. Reversible electrodes are not essential and the method allows determination of both ionic and solvent transference numbers simultaneously. The cell described is rapid to assemble and an excellent membrane-cell seal is obtained eliminating solution leakage. Transference number data for Cellophane in potassium hydroxide solutions covering a wide concentration range, determined using the technique described, are presented.