New detailed results for ionic distributions around charged spherical surfaces in electrolyte solutions,are presented using the formulation of dissociative electrical double layers (DEDL) with the Lubetkin, Middleton, and Ottewill dissociative law. Wide ranges of spherical radii and ionic strengths are considered, From these theoretical results the extent of ionic atmosphere and the number of ions contained therein are calculated to give an estimate of how many ions interact with a colloidal sphere. A new measure of the range of electrostatic repulsions is defined as the sum of the Debye length and the thickness of the co-ion exclusion shell. New results for extremely low charge densities indicate a possibility of significant electrostatic effects in such systems. These results, representing a synthesis of the classical theory of Debye-Huckel interionic interactions with the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, provide new insights into the co-ion exclusion phenomena in colloidal dispersions and related consequences, The DEDL theoretical approach, with emphasis on electrostatic consistency, has shown a greater explanatory power than the classical DLVO theory. The latter contradicts Maxwellian electrostatics unnecessarily.