A new approach is devised for the study of thermodynamic systems composed of particles interacting with Coulomb forces, specifically applied to solutions of strong electrolytes (composed of ions of equal size). A method is constructed for the evaluation of the average number density as a function of position about an ion expressed as a series of terms dependent on the average potential about the ion. The problem is formulated in such a manner that averages of quantities are found by the method of steepest descents. The electrolyte equation is found in first approximation to be similar to the nonlinearized Debye‐Hu¨ckel equation, containing, however, terms referring to the ion size. When the ionic fractional volume is much less than one this equation becomes the nonlinearized Debye‐Hu¨ckel equation. In the limit of small concentrations it is also shown that the equation governing the electrolyte is precisely the nonlinearized Debye‐Hu¨ckel equation. The electrolyte equation is briefly discussed in higher‐order approximations.