We reexamine similarity solutions for composition in a very long binary diffusion couple for the case in which the diffusivity and the density are functions of composition. For such solutions, the composition depends for sufficiently short times only on a similarity variable x/roott where x is distance and t is time. The classical Boltzmann-Matano treatment holds for the case in which the diffusivity is a function of composition but the density is independent of composition. It results in the selection of a unique (Matano) interface as the origin of coordinates for x and a formula for the diffusivity that depends on integrals of the concentration profile measured with respect to that interface. For density dependent on composition, Sauer and Freise generalized this solution by introduction of two Matano interfaces, one of which is at rest with respect to the left end of the diffusion couple and the other which is at rest with respect to its right end. Wagner reworked this generalization in terms of a unique (Wagner-Matano) interface and went on to derive a formula for the diffusivity that was indepenent of the location of that interface. We reconcile these treatments by examination of along but finite diffusion couple with careful identification of reference frames for the fundamental description of diffusion. (C) 2003 Elsevier Ltd. All rights reserved.