The ion-optical properties of the accerlerating tube made of a series of coaxial cylinders in a DC accerlerator have been investigated. The potential distribution in such an accerlerating tube has been found both theoretically and experimentally by means of an electrolytic trough. The field in the accerlerating tube is found to be not exactly uniform as usually considered but it should also consist of a periodic part.The paraxial-ray equation for describing the ion trajectory in such a periodic field has been solved. The profile of the ion beam does show an undulatory shape, especially in the low energy region. The periodic field produces a significant focusing effect. A formula for describing the focal length of the ion-optical system was derived. The space charge effect has also been considered.