Potentiometric measurements on cells with liquid junctions are sometimes used for calculations of single-ion activity coefficients in electrolyte solutions, the incidence of this being increased recently. As surmised by Guggenheim in the 1930s, such coefficients (of ions i), gamma(i) are actually complicated functions of mean ionic activity coefficients, gamma(+/-), and transport numbers of ions, t(i). In the present paper specific functions gamma(i)(gamma(i), t(i)) are derived for a number of cell types with an arbitrary mixture of strong electrolytes in a one-component solvent in the liquid-junction system. The cell types include cells with (i) identical electrodes, (ii) dissimilar electrodes reversible to the same ions, (iii) dissimilar electrodes reversible to ions of opposite charge signs, (iv) dissimilar electrodes reversible to different ions of the same charge sign, and (v) identical reference electrodes and an ion-selective membrane permeable to ions of only one type. Pairs of functions for oppositely charged ions are found to be consistent with the mean ionic activity coefficients as would be expected for pairs of the proper gamma(i) quantities by definition of gamma(+/-). The functions are tested numerically on some of the reported gamma(i) datasets that are the more tractable. A generally good agreement is found with data reported for cells with single electrolytes HCl and KCl in solutions, and with binary mixtures in the liquid-junction systems of KCl from the reference solutions and NaCl and HCl from the test solutions. It is found that values of gamma(i)(gamma(+/-), t(i)) functions, in general, do depend on the reference solution composition, which is at variance with the recent claim by Lladosa et al. [E. Lladosa, A. Arc e, G. Wilczek-Vera, J.H. Vera, J. Chem. Thermodyn. 42 (2010) 244-250] that "the ionic activity coefficients are independent of the nature and concentration of the reference solution". The results of the present study validate Guggenheim's interpretation and afford to amplify it by stating that such coefficients are misnomers in the sense that they do not represent thermodynamic properties of ions, and ought not to be called activity coefficients. (C) 2011 Elsevier Ltd. All rights reserved.