Manegold and Solf have reported systematic deviations of the electroosmotic properties of collodion membranes with narrow pores from predictions based on the Helmholtz-Smoluchowski model. To interpret the electroosmotic data quantitatively it is necessary to replace the assumption of the Helmholtz-Smoluchowski model that the thickness of the electric double layer is small compared with the pore radius by a new assumption. We have assumed that the counter ions are distributed homogeneously in the pore fluid. In Part I of this series of contributions, equations have been given describing the electroosmotic properties of a membrane with narrow pores based on the new assumption. These equations are derived here in detail and are applied to an analysis of the experimental data given by Manegold and Solf.