The authors inquiry into the quantitative aspects of the concepts of similarity as applied to a simple variety of library systems led to the consideration of a large family of association schemes. Each scheme was uniquely determined by a particular transformation function--a map from the set of similarity coefficients for terms or documents to the set of similarity coefficients for documents or terms. The transformations considered preserve the property of nonnegativity for sets of similarity coefficients, which allows one to show that there is a set of coefficients left fixed by any chosen transformation. This set of coefficients depends on the chosen transformation and represents exactly the degree of association demanded by consistency with the chosen transformation. Thus, for any transformation one arrives at a set of similarity coefficients which corresponds to it. An iterative method was advanced for the computation of our fixed set of similarity coefficients, and the particular analytic questions remaining center upon this method. It has not been shown that the iteration always converges, though experience indicates that convergence is the rule. If the iteration converges at all, it converges to a fixed point as desired. Experience further indicates that the fixed point obtained is independent of the starting set of coefficients, provided these coefficients are nonnegative, except possibly on a set of measure zero.