The Debye-Huckel theory provides an adequate description of the be-havior of simple electrolytes at low concentrations. It contains, however, two inherent limitations: spherical symmetry, and the condition that the electrostatic potential energy of a test ion be small compared to kT. Several cases involving non-spherical geometry have been treated; Verwey and Overbeek' summarize the pertinent literature to 1948. In the case of polyelectrolytes2 (especially in the absence of added simple electrolyte), we find high concentrations of charge in small volumes; in the vicinity of such a multiple charge, the potential energy of a counter ion is necessarily many times kT. his results are not available in the literature at this time.