Making use of the isotropic incident flux approximation, the disadvantage factor ζ for a two-region unit cell can be written as a linear combination of two so-called X functions, each of them depending on the properties of one region only. A general variational approach, based on Ritz-Galerkin's method, is used to find a closed expression for X in terms of the ‘weighted’ collision probabilities, From this expression the properties of X will be deduced once more, but then in a general way. An analytical calculation of X in slab geometry and a numerical one in cylindrical geometry are given. The results of the first have been used for a comparison with Theys' generalization of the Amouyal-Benoist-Horowitz theory; the results of the second example were compared with Leslie's calculation of the same X function by means of successive collision probabilities. It is furthermore shown that the same procedure that serves to calculate X functions gives, as an important by-product, the constant production and the isotropic abledo solutions of Peierl's integral transport theory. From these solutions the flux distribution in the unit cell (of arbitrary geometry) can be constructed. Sauer's simple recipe for calculating the X function is discussed and is shown to be inaccurate for weakly absorbing media.