This theory, which is based upon McMillan and Mayer's cluster expansion of the grand partition function, is extended to include all of the components of the potentials of average force between sets of solute molecules or ions in the solvent at infinite dilution. The resulting cluster integral sum, which is a sum of integrals over an infinite number of infinite series of Mayer prototype graphs, is transformed into the sum of a single infinite series of integrals on graphs involving new types of bonds. These bonds are defined in a way first suggested by Meeron. There results a compact expression for the cluster integral sum.