Absorbancy of a solution in the narrow lumen of a tubular membrane under dialysis is continuously measurable with a newly-developed apparatus using quartz optical fibers. The solute permeability of the membrane was determined by calculating time-dependent changes in the absorbancy measured with the apparatus by the mathematical solution derived for unsteady-state concentration profiles in an infinitely long composite cylinder. This method was independent of convective mass transport and osmotic flow through membranes, leading to superiority to ordinary techniques with respect to accuracy.